Algebra 1 G9

English Spanish

Vertical-line test (p. 269)  The vertical-line test is a method Prueba de la recta vertical (p. 269)  La prueba de recta Visual Glossary
used to determine if a relation is a function or not. If a vertical es un método que se usa para determinar si una
vertical line passes through a graph more than once, the relación es una función o no. Si una recta vertical pasa por el
graph is not the graph of a function. medio de una gráfica más de una vez, la gráfica no es una
gráfica de una función.
Example
y

2 x
24
Ϫ2 O
Ϫ2


A line would pass through (3, 0)

and (3, 2), so the relation is not a
function.

W

Whole numbers (p. 18)  The nonnegative integers. Números enteros positivos (p. 18)  Todos los números
enteros que no son negativos.

Example 0, 1, 2, 3, . . .

X

x-axis (p. 60)  The horizontal axis of the coordinate plane. Eje x (p. 60)  El eje horizontal del plano de coordenadas.

Example y-axis

2 x-axis
2
Ϫ2 O
Ϫ2 origin

x-coordinate (p. 60)  The first number in an ordered pair, Coordenada x (p. 60)  El primer número de un par
specifying the distance left or right of the y-axis of a point in ordenado, que indica la distancia a la izquierda o a la derecha
the coordinate plane. del eje y de un punto en el plano coordenadas.

Example In the ordered pair (4, -1), 4 is the
x-coordinate.

x-intercept (p. 322) The x-coordinate of a point where a Intercepto en x (p. 322) Coordenada x por donde la
graph crosses the x-axis. gráfica cruza el eje de las x.

Example The x-intercept of 3x + 4y = 12
is 4.

Glossary i 861

English Spanish

Y Eje y (p. 60)  El eje vertical del plano de coordenadas.

y-axis (p. 60)  The vertical axis of the coordinate plane.

Visual Glossary Example y-axis

2 x-axis
2
Ϫ2 O
Ϫ2 origin

y-coordinate (p. 60)  The second number in an ordered Coordenada y (p. 60)  El segundo número de un par
pair, specifying the distance above or below the x-axis of a ordenado, que indica la distancia arriba o abajo del eje x de
point in the coordinate plane. un punto en el plano coordenadas.

Example In the ordered pair (4, -1), -1 is
the y-coordinate.

y-intercept (p. 308) The y-coordinate of a point where a Intercepto en y (p. 308) Coordenada y por donde la
graph crosses the y-axis. gráfica cruza el eje de las y.

Example The y-intercept of y = 5x + 2 is 2.

Z

Zero-product property (p. 568)  For all real numbers a and Propiedad del producto cero (p. 568)  Para todos los
b, if ab = 0, then a = 0 or b = 0. números reales a y b, si ab = 0, entonces a = 0 ó b = 0.

Example x(x + 3) = 0
x = 0 or x + 3 = 0
x = 0 or x = -3

Zero of a function (p. 561) An x-intercept of the graph of Cero de una función (p. 561) Intercepto x de la gráfica de
a function. una función.

Example Thee zzeerroossooff yy =ϭxx22-Ϫ44aarere{Ϯ22. .

2y

Ox
Ϫ2

x ‫ ؍‬؊2 x ‫ ؍‬2


862

Selected Answers

Chapter 1 3a. 3  b. 11  4. c + 1 c; $47.30, $86.90, $104.50,
$113.30  10
Selected Answers
Get Ready! p. 1 Lesson Check  1. 25  2. 8  3. 196  4. 23  5. 1728  6. 0 

1. 6  2. 5  3. 1  4. 20  5. 15  6. 44  7. 72  8. 150  9. 400 # #7. exponent 3; base 4  8. The student subtracted before
4 5 1 12
10. 8  11. $294  12. 5   13. 7   14. 7   15. 13   16. 0.7  multiplying; 23 - 8 2 + 32 = 23 - 8 2 + 9
= 23 - 16 + 9 = 7 + 9 = 16
17. 0.6  18. 0.65  19. 30.119123  2250..A0n.s4w6e  r2s1m. a1114y vary. 8
22. 7 1 24. Exercises  9. 243  11. 16  13. 27   15. 0.004096  17. 2 
10 15   23. 10  
19. 4.5  21. 53  23. 16  25. 1728  27. 4  29. 1024 
Sample: 20 + 15  26. Answers may vary. Sample: A
31. 496  33. 3458  35. mv; 15,000, 20,000, 25,000 
simplified expression is one that is briefer or easier to
37. 256  39. 5  41. 12
work with than the original expression.  27. Answers

may vary. Sample: To evaluate an expression means to find Lesson 1-3 pp. 16–22

its numeric value for given values of the variables. GnuomtbIet?rs ,1naa.tu8r abl n. u5m  cb.e61r s,dw. h191o le2.nuabmobuetrs6, 

Lesson 1-1 pp. 4–9 3a. rational
integers 
Got It?  1. + 2a. b. 18 c.
n 18  6n  n   No; 6 less a number b. rational numbers  c. rational numbers  d. irrational
1
y means 6 - y and 6 less than a number y means numbers  4a. 1129 6 11.52  b. Yes; 4 3 7 117 also
y - 6.  3a. 4x - 8  b. 2(x s+um8) ocf.t1e2n5+timx   e4saa. the sum of a compares the two numbers. 
number x and 8.1  b. the number x
5. Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4 num- b72,er-s2  2.1.,ra1ti5o,na1l 9, 3.5 
and 9  c. the quotient of a number n and 3  d. five times Lesson Check  1. irrational

a number x less 1  5. subtract 2 from the number n5u. mrabtieornsa, linntuemgebres rs3a. n-d5i,rr1at1io6n,a4l .n1u,m1407b e4rs. a6b.oAunt s4wienr.s 

of sides in the polygon; n - 2
Lesson Check  1a. numerical  b. algebraic  c. numerical 
t21h acn. 20n7  3. six times a may vary. Sample: 0.5  7. Rational; its value is 10, which
2a. 9t b. x- m + 7.1  d. 5. the quotient of number c1an0b.2e9wisriattennonarseaperaattiinogo,fntownoteirnmteingaetrisn, g110n.u  m8.bIerrra. tional;
c  4. one less a number x  a

number t and 2  6. 4 less than the product of 3 and a E2x1e. arcbiosuets1  69 .263  .1a1b.o4u t1138. 762 51.5a.b13o u1t71.31i.n4.  1297.. about 4 
rational
number t  7. Numerical expressions are mathematical

phrases involving only numbers and operations. Algebraic numbers  29. rational numbers, integers  31. irrational

expressions are mathematical phrases that include one or numbers  33. rational numbers  35. irrational numbers 
4534.3373...,T5-1r23u222e257;06A 14n-29s0w9.. e8-3r s4994,m.5-34a. y16-63v,2a1,-ry2-2; .a7414n,,1y21-.,in21-1t36e15 7g15,e621r..4c-aa b0n4o.76bu3.et -e1x259p9fr,te s-s6ed,
more variables. An algebraic expression includes at least

one variable. A numerical expression does not include any

variables.  8. 49 + 0.75n  q1  139. .8t2th  e15p.ro5dnu+ct
Exercises  9. p + n4u  m11b.er8n 6.7 
17. 5 more than a of 12 and x 

21. one more than the product of 9 and a number n  as a rational number.  55. False; Answers may vary; 2 is a

23. the difference of 15 and the quotient of 1.5 and d  positive number and an integer.  57. 4117   59. 201  
100
25. 5 more than the product of 9 and a number n; 61. 306   63. about 12 ft  65. 864 ; its value 3.14181 is
q9uno+tie5n t2o7f .58an-d9nr. “2  93.337a.y4-.540 n3  1b.. 100 275 c
It should be “the
$40.50  35. A  closer to the value of p than 110, which is 3.16227 c  
67. no; no the real number line extends indefinitely in
37. Answers may vary. Sample: An umpire picks up b
both the positive and negative direction.  69. It is true for
baseballs for a game in addition to the three he had. 
products involving two numbers greater than 0 and less
39. Answers may vary. Sample: Yes; sometimes you cannot
than 1.  71a. 4  b. 10  c. 7  d. 13  73. I  75. 16  76. 78 
be sure from a verbal description what order is intended for 3880 19
34   77. 512  78. 14 + x  79. 4(y + 1)  80. z   81. 3 t 
the operations.  41. 2x + 6 or 6 + 2x  43. G  45. 82. 18  83. 72  84. 442  85. 9
5 7 48. 1
46. 14   47. 10   6   49. 3  50. 3  51. 1  52. 4

Lesson 1-2 pp. 10–15 Lesson 1-4 pp. 23–28

GfraocttioItn? b1araa. c8t1s abs.a28g7r ocu.p0in.1g2s5y m2bao. l2s7in  cbe. 7  c. 17  d. A Got It?  1a. Identity Prop. of Mult.  b. Commutative
you simplify
Prop. of Add.  2. 720 tennis balls  3a. 9.45x  b. 9 + 4h 
c. 2   4a. True; Commutative Prop. of Mult. and Identity
numerator and denominator before you divide. 3n

Selected Answers i 863

Prop. of Add.  b. False; answers may vary. Sample: 0 1 - 3 0 = 0 - 2 0 = 2  b. No; check students’ work. Sample:
4(2 + 1) ≠ 4(2) + 1  c. No; it is true when a and b are 0 3 + (16) 0 = 0 -3 0 = 3 but 0 3 0 + 0 -6 0 = 3 + 6 = 9 
both either 0 or 2.
71. H  73. F  75. yes  76. no  77. yes 
Lesson Check  1. Comm. Prop. of Add.  2. Assoc. Prop. 78. rational numbers  79. rational numbers  80. rational

of Mult.  3. $4.45  4. 24d  5a. no  b. yes  6. Comm. Prop. numbers, whole numbers, natural numbers, and integers
81. rational numbers  82. irrational numbers  83. 18.75
Selected Answers of Mult.; Assoc. Prop. of Mult.; multiply; multiply 84. 17  85. 318

Exercises  7. Comm. Prop. of Add.  9. Ident. Prop. of

Add.  11. Comm. Prop. of Mult.  13. 36  15. 9.7  17. 80  Lesson 1-6 pp. 38–44

19. $110  21. 18x  23. 110p  25. 11 + 3x  27. 1.2 + 7d  dGc.ivoi-dt 1eId1t? b dy1. aa{.ne-16g 9a30t. ivb-e.$is27.n24e  g4caa.t.i-v-e52101a30 nd db.t.1hY6ee os2;paap.op8so itsbeit.iov{fea4
29. 1.5n  31. 11y  33. False; answers may vary. Sample:
8 , 4 ≠ 4 , 8  35. true; Mult. Prop. of - 1 
37a. 497 mi  b. 497 mi  c. The Commutative Property of

Addition applies to this situation.  39. no  41. yes  43. yes  positive divided by a positive is also negative. 

45. no  47. Hannah can only afford to give all her friends Lesson Check  1. 36  2. - 5   3. - 16  4p.o89si ti5ve. -5
6.   Ϫ5 Ϫ5 32 7a. 2; a number
the same gift.  49. 390  51. 0  53. no; (a - b) - Ϫ5
c ≠ a - (b - c)  55. no; (a , b) , c ≠ a , (b , c) 
57. (b + c)a = a(b + c) and ba + ca = ab + ac by the Ϫ15 Ϫ10 Ϫ5 has a positive and negative
0 square root.  b. 1; 10 5 0,
Comm. Prop. of Mult.  59. H  61. F  62. - 6,1.6, 16,
63  63. 851,.11 0628  6. 4118. - 4.5, 1.75, 14,141  so there is one square root.
65. 14  - 17, 1.4, Er3i4150mex1397c,pe....iprx1r3o--rco.8p=461ice25s4  ayr e43 l,5fs2o35tr9 ha1f..9.ce.---t.n-1io93521231xn856,  y3 3 w2-°4=153Fh7125. 0i.c..6..-h-T2121S0h 3i0.is.ne40.9F5nc-9 i re 2s.3m251t5x7.-3u c..≠h6.l9t--ai34-p0n.592l212,yg 5856teb200-h3 0u7 e1-1,s3.n5h23o29-e.r21yb.l1s11y1=4$t 212o1t5  046h11t2543he5b79. e y6..-415t{11ha8e.0.03.I5f
66. 1  67.

Lesson 1-5 pp. 30–36

Got It?  1. - 4 2a. - 24  b. - 2  c. - 2  d. - 8  3a. 13.5 #Zero Property of Multiplication. b. Suppose there is a
b. any value where a = b  4. - 2473 ft, or 2473 ft below
sea level  value of y such that x , 0 = y. Then x = 0 y, so x = 0.
Lesson Check  1. - 3  2. - 3  3. - 3  4. - 7  5. 2  6. - 7  But this is a contradiction, since x ≠ 0. So there is no
7. 0  8. Subtracting is the same as adding the opposite.  value of y such that x , 0 = y.  67. Always; the quotient is
9. The opposite of a number is the number that is added - 1. 69. - 8  71. I 73. 30 74. - 10 75. - 10  76. Ident.
Prop. of Add. 77. Comm. Prop. of Mult. 78. Assoc. Prop.
to it to equal 0. If a number is positive, its opposite is
of Mult.
negative. However, if a number is negative, its opposite is

positive.
Exercises
11. 5

Ϫ3Ϫ2Ϫ1 0 1 2 3 4 5 6 7 Lesson 1-7 pp. 46–52

13. - 5 Got It?  1a. 5x + 35  b. 36 - 2t  c. 1.2 + 3.3c

Ϫ7Ϫ6 Ϫ5Ϫ4 Ϫ3Ϫ2Ϫ1 0 1 2

15. 3 d. - -26ym412x++  39yan  . 24a-..a$43-2x95-  5b13a6.. x2by-. 13b611.+ -c211. x2- m4cn.x454+  +c1.2128xy3z
d.
Ϫ5Ϫ4Ϫ3Ϫ2Ϫ1 0 1 2 3 4 5 d. 1 -
2
17. - 12
-
6yz3  d. No; it is already simplified since there are no like
Ϫ14 Ϫ12 Ϫ10 Ϫ8
terms to combine.
19. - 11  21. 5  23. - 11  25. 4-.42 02.37 .3-9.3 12.69 .431163.
31. - 20  33. 48  35. - 2  37. 15 Lesson Check  1a. 7j + 14  b. - 8x + 24  c. - 4 + c 
43. d. - 11 - 2b  2. - 8x2 + 3xy + (- 9x) + (- 3)  3. 2ab +
$48.54  45. - 7.1  47. The sum of - 4 and 5 is 1+61, (- 5ab2) + (- 9a2b)  4. yes  5. no  6a. yes  b. no;
not -1; -4 - (- 5n)eg=a-tiv4e +557.=F1in d4t9h.e-a1b12s o5lu1te. 1 
53. positive  55. value of Commutative Prop. of Mult.  c. yes  d. no; Associative

each number. The sign of the number with the larger Prop. of Add.  7. 500 - 1; answers may vary. Sample:
These numbers are easily multiplied by 5, making it
absolute value will be the sign of the sum.  59. False; if
possible to use the Distr. Prop. to solve this using mental
both numbers are negative, the difference is larger than
math.  8a. yes; no like terms  b. This expression can be
the sum. If the absolute values are equal, the sum is 0. 
simplified by using the Distr. Prop.  c. No; 12xy and 3yx
6cmh1e.=c2k09s,.t6tuh2deeinrne.t ss6u’ l3wt.wo-rikll2.b Se6a5m-.pmSloe=:m0em3t-i m61e70s.=; 1Wo00n2 ly60 =9trau2.eaYwnedsh;en
are like terms. 

Exercises  9. 6a + 60  11. 25 + 5w  13. 90 - 10t
15. 112b + 96  17. 4.5 - 12c  19. f - 2  21. 12z + 15

864

23. 3 - 71nd7  3235..-522x0+-57 d  2  375. .38 --93+x 72c9  .357.--581t8a       y = x + 6 Megan’s and Will’s Laps
31. - 12 y
1111 + 17b
10
39. m - n - 1  41. 40.8  43. 897  45. 23.4 
47. 24.6  49. $49.50  51. $4725  53. 20x  55. - 2t  8
57. 17w2  59. 5y2  61. - 3x + y + 11  Will’s Laps Selected Answers
63. 3h2 - 11h - 3  65. the product of 3 and the

difference of t and 1; 3t - 3  67. one-third the difference 6x
1
of 6 times x and 1; 2x - 3   69. The sum, not the product, 0 2 4 6 8 10
#of the terms should be found; 4(x + 5) = 4x + 4 5 = Megan’s Laps
4x + 20.  71. 33x + 22  73. 35n - 63  75. 0
77. - 5m3n + 5mn  79. 23x2y - 8x2y2 - 4x3y2 - 9xy2 b. The graph would start at (0, 5) instead of (0, 2) and y

81. 1 (9 + 12n) = 9 + 12n = 3 + 4n  83. Answers would always be 5 greater than x.
3 3 3
may vary. Sample: 3(m - 2n - 5).  85. 45d + 26  3a. 54 tiles
Orange tiles 4 8 12 16
87. 24 + 2t  89. - m - 9n + 12
Total tiles 9 18 27 36

Lesson 1-8 pp. 53–58

Got It?  1a. open  b. true  c. false  2. yes  3. 49 = 14h  b. Blue tiles 12 34 48 yellow tiles

4. 9  5a. - 10  b. Answers may vary. Sample: - 5  6. The Yellow tiles 2 4 6 8
solution is between - 8 and - 9.
Lesson Check  1. no  2. 15  3. p = 1.5n  5. Answers
Emxaeyrvcairsye. sS a7m.pfalels:e3x  = 15.  6. 9 13. open  15. open  Lesson Check  1. no  2. yes
9. true  11. false  3. Drink Cost

17. no  19. yes  21. no  23. yes  25. 4x + (- 3) = 8 Drinks bought 1 2 3 4

27. 115d = 690  29. 13  31. 6  33. 12  35. 6  37. 2 Cost ($) 2.50 5 7.50 10
39. 4  41. 6  43. 4  45. 8  47. between - 5 and - 4
49. 2004  51. An expression describes the relationship Drink Cost
     y = 2.50x 10 y
between numbers and variables. An equation shows that

two expressions are equal. An expression can be simplified

but has no solution.  53. - 6  55. between 3 and 4  8
57. between - 3 and - 2  59. 0  61. Check students’
work.  63. 120 lb  65. Answers may vary. Sample: The Cost ($)
6

friend knows an odd number divided by an even number 4

cannot be an integer.

Review p. 60 2

1. Answers may vary. Sample: For the sum - 3 for the 00 2 4 x
x-coordinate, you could roll a 4 on the negative cube and a 6
1 on the positive cube. For the sum 4 for the y-coordinate,
Drinks Bought
you could roll a 1 on the negative cube and a 5 on the
positive cube.  3. Answers may vary. The number on the 4. 110 Calories  5. With inductive reasoning, conclusions

negative cube must be greater than the number on the are reached by observing patterns. With deductive

positive cube. reasoning, conclusions are reached by reasoning logically
from given facts.  6. Answers may vary. Sample: Both
Lesson 1-9 pp. 61–66
equations contain unknown values. An equation in
Got It?  1a. yes  b. yes  c. no  d. yes
one variable represents a situation with one unknown
2a. Megan’s and Will’s Laps
quantity. An equation in two variables represents a
Megan’s laps 1 2 3 4 5
11 situation where two variable quantities have a
relationship.  7. All; y is 2 more than x.
Exercises  9. no  11. no  13. yes  15. yes

Will’s laps 7 8 9 10

Selected Answers i 865

17. Bea’s and Ty’s Ages 9. 51t + 9  10. 63 - 14  11. b - k   12. the sum of 12 and
h 5
a number a  13. 31 less than a number r  14. the product
Bea’s age 4 5 6 7
of 19 and a number t  15. the quotient of b
Ty’s age 1 2 3 4
and 3  16. 3 less than the product of 7 and c  17. the sum

of 2 and the quotient of x and 8  18. 6 less than the
Selected Answers y = x - 3 Bea’s and Ty’s Ages
quotient of y and 11  19. 13 more than the product of 21
7y
ab2n5.d.Th4de8   2s2u0r6.f.a8c81e 312a  r21e7.a1.i2s450re  d22u28c..e73d169t  o22a39..fo91u.28r3t h 234o0f.ai1t.s0201  6
Ty’s Age 5

3 previous value.  31. 615 mi  32. irrational   33. rational

1 x 34. irrational  35. rational  36. 10  37. 7  38. 5 
00 1 7
35 39. rational numbers, integers  40. rational numbers
Bea’s Age
41. irrational numbers  42. rational numbers, whole

19. Sides and Triangles numbers, natural numbers, integers  43. rational numbers
r9awtio-na3l 1n u4m8b.er-s 9465  .49-.1054 , 5-01.234, 11.-6 44t6  .5-1.01.8, 97,
44. 13
47.
Number of sides 3 6 9 12

Number of triangles 1 2 3 4 52. yes  53. no  54. no  55. no  56. 5  57. - 5  58. - 9
59. 1.8  60. - 144  61. 40  62. - 3  63. - 19  64. 3 
1 65. - 8  66. 60  67. 16  68. 12  69. - 11  70. 19 
3
y = x   8y 71. 32--y11-04014+  7282a1. .7-675-.6- 67y123 j 8.+224.2 5y7 -87.43v.  28- 3713.09 -. 76315yy. -+1066x   - 15 
76.
Number of Triangles 6 80.

4 84. - 2ab2  85. $2850  86. Yes; the variable parts of the

2 terms are the same.  87. yes  88. no  89. no  90. yes

00 x 91. 10  92. between 12 and 13  93. between 2 and 3 
9 12
3 6 94. between 3 and 4  95. yes  96. no  97. no  98. no

Number of Sides 99. y is 5 more than the product of 10 and x;

21. 56 in.  23. y = x - 12; 52 in. y = 10x + 5.  80 y
55, 65, 75
25. Number of Houses
12 3 4 5 60
20
Number of Windows 4 8 12 16 40

20
a. 36 windows  b. k + 4  20 y
x
Number of Windows 16 00 2 4 6 8

12

8 Chapter 2

4 Get Ready! p. 77

00 1 2 3 4 x 1. Answers may vary. Sample: For each lawn mowed,
5

Number of Houses $7.50 is earned; y = 7.50x.  2. Answers may vary. Sample:

27. yes  29. no  31. 11 h  33. Check students’ work.  30 pages are read each hour; y = 30x.  3. 3 
35. y = - x - 3.5; the graph is of a line, which passes 4. - 10  5. 8  6. -8  7. 7.14  8. 195. .-12690k 21 01.6-. 11735x  y
through (0, - 3.5), (3.5, 0)  37. H  39. F  40. no  41. yes  11. 17  12. - 3  13. 576  14. - 16.4 
42. yes  43–48. Check students’ work.  47. 9  48. - 3  2.75 
49. - 14  50. - 27  51. 40  52. - 30  53. - 1  54. - 81
17. 2t + 2  18. 12x - 4  19. Answers may vary. Sample:
The shirts might look the same but be different sizes or

Chapter Review pp. 68–72 different colors; the triangles will be the same shape but

1. irrational  2. opposite  3. like terms  4. absolute value  different sizes.  20. Answers may vary. Sample: The model
5. inductive reasoning  6. 737w  7. q - 8  8. x + 84 
ship is the same shape but just a smaller size than the

actual ship.

866

Lesson 2-1 pp. 81–87 51. 4 should be added to each side; 2x - 4 + 4 = 8 + 4
so 2x = 12 and x = 6.  53a. 4  b. yes  c. Answers may
Got It?  1a. - 8  b. The Subtr. Prop. of Eq. states that vary. Sample: The method in part (a) is easier because it
subtracting the same number from each side of an equation doesn’t involve fractions.  55. 10.5  57. 4  59. about 2 km 
61. 2 in.  63. No; the left side of the equation is 0 and the
produces another equation that is equivalent.  2a. - 6  b. 2 right side of the equation is 4.  65. No; division by 0 is
3mau.lt32ip  lbyi.ng- 4.375  4a. 57  b. - 72  5a. 16  b. Yes; not allowed.  67. 46  69. 5  70. 3.8  71. 144  72. 6.5 
each side of the second equation by the Selected Answers
2 73. false; sample: 0 - 5 0 - 0 2 0 ≠ - 5 - 2  74. false;
reciprocal of 3 produces the first equation.  6. 6 months  sample: - 4 + 1 = - 3, 0 - 4 0 = 4 and 0 - 3 0 = 3 
54  1
Lesson Check  1. - 4  2. 13  3. 4 4. 3 b = 117; 351 75. 35 - 7t  76. 4x - 10  77. - 6 + 3b  78. 10 - 25n

pages  5. Subtr. Prop. of Eq.  6. Div. Prop. of Eq.  7. Add. Prop.

of Eq.  8. Mult. Prop. of Eq.  9. Check students’ work. Lesson 2-3 pp. 94–100

Exercises  11. 19  13. - 9  15. 26  17. 7.5  19. 132 
21. 13.5  23. 2  25. - 4  27. - 4  29. 0.16  31. 5 
33. - 2125  3  457. .18715   37. - 117  39. 81  41. - 34  43. 12  Got It?  1a. 6  b. 3  2. $14  3a. 6  b. Yes; divide both
45. - 49. 24  51. p = city's population at 6sLied. esAssnooswnf teChreshmeeqcaukya vt1aio.rny4. b11S51ya m32pf.ilre-s:t7.S  u43ba.tr.2a2 c4t2134.1 2.3b  5.fr.2o161m6  5eft.a c1h2.55

start of three-year period; p - 7525 = 581,600; 589,125
s65xh53=o..u$-2ld42135 2b064e07.m  .75u-35lt2..ip52-l 1ie261da19c b.e5ys-7 9.712, 75n7.13o1 2t.5491E95;a0.(c93hl)e1(ts-14tied3 re66s )1o7=.f731t(h.9  e621) 13es9xq.=2u0,a1.s8t2oi o n
side, and then divide each side by 0.5.  7. Answers may
79. A  81. B  82. 10,000 83. 52x  84. 6 - x  85. m + 4 
86. 2  87. 2365  88. 1 vary. Sample: Apply the Distr. Prop., and then add 28

to each side and divide each side by 21.  8. Answers

may vary. Sample: Multiply each side by the common

denominator 18 to clear the fractions. Add 72 to each

side and then divide by - 4.  9. Answers may vary.
Sample: Amelia’s method: it does not involve working
Lesson 2-2 pp. 88–93
with fractions until the end.
67p e1r 3h.  25374  .
Got It?  1. 16  2. 56 ads  3a. 26  b. 6 = x - 42 ; 26; Exercises  11. 2 6  15. 17. - 10  19. 3x +
4 6x + 20 = 92; $8 21. 6  3.75 or 3 3   25. 7 37 
4
answers may vary. Sample: The equation in part (a) is 253C719om... 2361b . i5n52 e394..t1h96.e.3257l i 5k54eo53rt..e9$4rm134.2 5s73 o 51n47. 5.t27h.5Ae 4n33lse3w73ft. e4s2ris7d31me.  33oa5y1f5.6tv h5a4e6ry9e.85.qS 1ua3.ma57tpi.ool51ren :.1 

easier because it uses fewer fractions.  1
x 2
4. 3 - 5+ 5 = 4 + 5 Add. Prop. of Eq.
= 9 Use addition to simplify.
x = 9 Mult. Prop. of Eq.
3 ~3
x ~ 59. 3 games  61. 25  63. 20  65. 4 weeks  67. 4 c
3 3

x = 27 Use multiplication to simplify. Lesson 2-4 pp. 102–108

Lesson Check  1. - 5  2. 63  3. - 7  4. - 13  5. $.62 
6. Subtr. Prop. of Eq. and Mult. Prop. of Eq.; subtr. 
Got It?  1a. - 4  b. The answer is the same, - 4. 
7. Add. Prop. of Eq. and Div. Prop. of Eq.; add.  8. Add. 2. about 27 months  3a. - 5  b. 4  4a. infinitely many

Prop. of Eq. and Mult. Prop. of Eq.; add.  9. Subtr. Prop. solutions  b. no solution

of Eq. and Div. Prop. of Eq.; subtr.  10. Answers may vary. Lesson Check  1. 7  2. - 3  3. infinitely many solutions 

Sample: No, you must either multiply both sides by 5 first or 4. no solution  5. 100 business cards  6. C  7. A  8. B 

write the left side as the difference of two fractions and then 9. If the numeric values are the same on both sides, it is
aEdxde35rctiosebos th11sid. e-s.12  13. - 1  15. - 2  17. - 27  19. 126 
an identity. If they are different, there is no solution.
3
21. - 3  23. 16 boxes  25. $1150  27. 29  29. - 2  31. - 8  Exercises  11. - 9  13. 6  15. - 4  17. - 1 4   19. 22 ft 

33. 8  35. 6  37. - 15  39. 2.7  41. 5  43. - 3.8  45. 0.449  21. 25  23. - 37  25. 18  27. no solution  29. no solution 
4311a. i.d6ed0n tbity. 4d303  c. .6236d0 
47. 15 - 9 = 9 - 3p - 9 Subt. Prop. of Eq. 35. - 19  37. no solution  39. -9 
+1 = 4d0; 120 mi; 48 mi/h 
6 = - 3p Use subtraction to simplify. 43. Subtraction should be used to isolate the variable,
- 3p
6 = -3 Div. Prop of Eq. not division by the variable. 2x = 6x, so 0 = 4x, and
-3

-2 = p Use division to simplify.   x = 0.  45. 2 months  47. about 857 bottles  49a. always
c
49. 9 + -5 -9 = - 5 - 9 Sub. Prop. of Eq. true  b. sometimes true  c. sometimes true  51. Check
= - 14 Use subtraction to simplify.
c students’ work.  53. Check students’ work.  55. Check
-5 = - 14 ~ - 5 Mult. Prop. of Eq.
c ~ = 70 Use multiplication to students’ work.  57. B  59. A  60. 5  61. - 6  62. 1 
-5 -5 63. 0.9 m  64. 22  65. 9  66. 11.2
c

simplify. 

Selected Answers i 867

Lesson 2-5 pp. 109–114 and q  7. n and p  8. mq and np  9. Yes; sample: One

Got It?  1a. 4 + 5n; -3; 2, 7  b. y = 10; y = 4 method creates an equation using the fact that the cross
2. x = - tp- r  2
3. 6 in.  4. about 55 days products are equal, and the other method creates an

+ equivalent equation using the Mult. Prop. of Eq. to clear
2
Lesson Check  1. y = 2x + 12   2. b = a 10   the denominators.
3. x = m 5 31Ex19e.. 1r-c06i s322e 1s3. 311.41- . 25-3 1.3952.56.  8321 d23o5.z4.e.n-2  131575 .2.a71b1.o24u..5t7 1514  72p.9e1.o61p123le   
Selected Answers p 2n   4. F = 9 C + 32  5. 40 yd  6. literal
+ 5
equation  7. literal equation  8. both  9. both 

10. Answers may vary. Sample: They are the same in each $.07 $143.32
1 kWh x kWh
case since you are isolating a variable by using inverse 39. = ; 2047. 4 kWh  41. at the same time as
  51. 3 was not
operations. They are different because, in an equation in you  43. 1.8  45. 2.7  47. 4.2  49. - 2
3
one variable, to isolate the variable, inverse operations are
fully distributed when multiplying 3 and x + 3; 16 =
used on numbers only. In a literal equation, inverse operations x = 73.  53. Check students’ work. 
59. 22 h  61. H  63. 1.5  64. 7  65.
are used on variables as well as numbers. 3x + 9, 7= 3x,
57. -75  
Exercises  11. y = - 2x + 5; 7; 5; - 1  13. y = 3x - 9; 55. -4   90 
5 3
12 9 - 56  15. 5x - 4; 1 - 32; 11 15   4
- 5 ; - 5 ; y= - 4 - 4 - 4   66. 190  67. no solution  68. 69. identity  70. 2 5 or 2.8 

17. y = x + 4; 21 ; 2; 5   19. x = m p n  21. x = r t s  71. 2 2 or 2.13  72. 6 2 or 6.6  73. 3 or 0.6
4 2 + + 15 3 5

23. x = S - C  25. x = A - C  27. x = 2y - 4  29. 4.5 in.  Lesson 2-8 pp. 130–136
31. 7 C Bt
39. h n ay + a 
cm  33. 0.4 h  35. h = 7/ ; 8 ft  37. x = b 3 was Got It?  1. 24  2. 30 ft  3a. about 66 mi  b. Write and
= - 108.4°F 
= 3V   41. a 2b - x  43. 45. solve the proportion 2 = 1 ; 1 in. represents 125 mi. 
pr2 250 x
added to the left side of the equation instead of
4. 300 ft
subtracted; 2m - 3 = - 6n, 2m - 3 = n.  47. 5 cm3 
49a. A = 2s2 + 4sh  b. h = A --62s2 ; 14 cm  Lesson Check  1a. 32.5 cm  b. 1 : 2.5  2. 225 km 
c. A = 6s2  51. 3. The order of the letters in each triangle tells which parts
4s are corresponding.  4a. yes  b. no  c. yes  5. Answers may
6  53. 92 chirps 54. 5  55. 3  56. - 4  
vary. Sample: No, it is greater than 100 times since 100 mi
57. 3  58. identity  59. no solution  60. 147  61. - 40 
8 7 is more than 100 times greater than 1 in.
62. 567  63. 100  64. 3  65. 5   66. 45 Exercises  7. ∠F ≅ ∠K, ∠G ≅ ∠L, ∠H ≅ ∠M,

Lesson 2-6 pp. 116–121 ∠I ≅ ∠N, FG = GH = HI = FI   9. 40  11. 100 
KL LM MN KN
13. 37.5 km  15. 225 km  17. 67.5 ft  19. 6 12AfJt. * 2 1 ft
Got It?  1. No; Store C is still the lowest.  2. 12.5 m  CJ instead of 2
21. no  23a. The student used
#3a. about 442 m  b. about 205 euros  4a. about 22 mi/h 
b. Yes; 60 s 60 min is the same as 3600 s. hba.vBAeCJ s=ideGFNsHt h2a5t.a3re9,i3n0p4rotipmoertsi o2n7(.thYeess;aamllesqleunagrtehs),wailnl d
1 min 1h 1h
Lesson Check  1. 8 bagels for $4.15  2. 116 oz  3. 12 m  the measures of corresponding ∠s are equal (90°). 
29. Answers may vary. Sample: No; the finished table
4. 80 2 ft/s  5. not a unit rate  6. unit rate  7. No; a
3 could have been a parallelogram with different angles
conversion factor is a ratio of two equivalent measures in
than the parallelogram in the sketch. The angle measures
different units and is always equal to 1.  8. Greater; to
were not given.
convert you multiply by 16.

Exercises  9. Olga  11. 189 ft  13. 40 oz  15. 240 s  Lesson 2-9 pp. 137–143

17. about 8.2 m  19. 7900 cents  21. about 35 in.  Got It?  1. 60%  2. 75%; the answers are the same. 
3. $3600  4. 41 32  5. 4 yr
23. 1.875 gal/h  25. 87  27. 150  29. 18  31. 0.5 mi  Lesson Check  1. 30%  2. 120%  3. 28  4. 48  5. $180 

33. 5 oz  35. recipe B  37. Miles; kilometers; kilometers

cancel out and miles are left.  39. 1580.82 INR; 19.98 GBP 

41. Answers may vary. Sample: Estimating the size to the 6. 100  7. $75  8. Answers may vary. Sample: 12 is what

nearest inch is appropriate because the carpenter is leaving percent of 10?

an estimated amount on either side of the television, not Exercises  9. 20%  11. 2623..54%00  1  235. .421232.%5  2175..232632  
17. 13  19. 16  21. $52 
an exact amount.  43. 2255.6 mm

Lesson 2-7 pp. 124–129 29. $108  31. part; 5.04  33. part; 142.5  35. percent;
1
Got It?  1. 5.6  2a. 1.8  3. - 5  4. 145.5 mg 1333 3   37. 66,000 mi2  39. 16  41. 75  43. B  45. 121%;
Lesson Check  1. 4.8  2. 27  3. 3  4. 5  5. 6.75 h  6. m
it costs more to make a penny than the penny is worth.

868

47. The values for a and b are reversed; 3 = p , 11%  59. decrease; 20%  60. decrease; 11%  61. increase;
1.5 100 32%  62. about 47%  63. about 39%  64. Yes; 50% of
1.5p = 300, p = 200%.  49. $181  51. 29 61%  38° is 19° and 38° + 19° = 57°.

( )53. 25 students  55. F  57. 14.4 cm  58. 18 cans 15
59. c = 1.75 + 2.4 m - 8 ; 2 8 mi  60. 1250%  Chapter 3 Selected Answers

61. 0.6  62. 175%

Lesson 2-10 pp. 144–150 Get Ready! p. 161

Got It?  1. about 32%  2. about 17%  3. about 16%  1. 7 2. = 3. 7 4. 6 5. 7 6. - 4 7. 1 8. 2 9. 3
10. - 12 11. 32.4 12. 23 13. 29.5 14. - 28 15. - 12
4. 65.5 in. and 66.5 in.  5. It would be smaller since the 16. 48 17. 5 18. - 24 19. - 10 20. 1.85 21. - 24

measurement of each dimension is closer to the actual 22. - 2 23. 3 24. 60 25. - 4m a2y6v.a3r y.2S7a.m12p l2e8: T.w2.o5
29. 4.1 30. 24 31. Answers
value of each dimension.

Lesson Check  1. about 2%  2. about 61%  3. 7.25 ft inequalities are joined together. 32. Answers may vary.

and 7.75 ft  4a. percent decrease  b. percent decrease  Sample: the part that the two groups of objects have

c. percent increase  5. 0.05 m  6. A percent increase in common

involves an increase of the original amount and a percent

decrease involves a decrease of the original amount. Lesson 3-1 pp. 164–170

Exercises  7. increase; 50%  9. decrease; 7%  Got It?  1a. p Ú 1.5  b. t + 7 6 - 3  2a. 1 and 3 
b. The solution of the equation is - 2. The solution of
11. decrease; 4%  13. increase; 54%  15. increase; 27%  the inequality is all real numbers greater than - 2.
3a. Ϫ4 Ϫ2 0 2 4
17. about 55%  19. about 13%  21. 1.05 kg; 1.15 kg 

23. about 28%  25. 175% increase  27. 42% decrease 

29. 39% increase  31. 48.75 m2; 63.75 m2 

33. 505.25 ft2; 551.25 ft2  37. The original amount is   b. Ϫ6 Ϫ4 Ϫ2
18 - 12 6
12, not 18; 12 = 12 = 0.5 = 50%.  39. 12.63  0

41a. 21%  b. 21%  c. 21%; sample: the new length is   c. 2 3 4 5 6 7 8 9 10

1.1 times as great as the original length. 1.12 = 1.21 or 4a. x 6 - 3  b. x Ú 0  5. No; the speed limit can only be
nonnegative real numbers.
121%, which shows a 21% increase over the original
2
amount of 100%.  43. I  45. 66 3 %  46. 64.75  47. 21 Lesson Check  1. y Ú 12  2a. no  b. no  c. yes  d. yes
48−51. 3. Ϫ6 Ϫ4 Ϫ2 0 2   4. x … - 3 
1
Ϫ3 Ϫ2.8 2 2

Ϫ3Ϫ2 Ϫ1 0 1 2 3 5. Substitute the number for the variable and simplify. If

- 3, - 2.8, 12, 2 the number makes the inequality true, then it is a solution

of the inequality.  6. Answers may vary. Sample: x Ú 0,
whole numbers, a baseball team’s score during an inning,
Chapter Review pp. 152–156
amount in cubic centimeters of liquid in a chemistry
1. inverse operations  2. identity  3. rate  4. scale
5. cross products  6. - 7  7. 7  8. 14  9. 65  10. 3.5  beaker; x 7 0, counting numbers, length of a poster,
11. - 4  12. - 5  13. - 8  14. $6.50  15. Add. Prop. of distance in blocks between your house and a park 

7. Check students’ work.

Eq.; Simplify.; Div. Prop. of Eq.; Simplify.  16. 11  17. 8  Exercises  9. b 6 4  11. k 7 31   13a. yes  b. no  c. yes
9
18. - 7.5  19. 38185  20. 28  21. 14.7  22. 4h + 8h + 15a. yes  b. no  c. no  17. D  19. A
50 = 164; $9.50  23. 37t + 8.50t + 14.99 = 242.49;
5 tickets  24. - 90  25. 7.2  26. identity  27. no solution  21.

02468

28. 8xx h== =app-1++qc6sbq  +33614h..;4x80=fct- m2t 9-3.5r6d .531=25.1mx3dm0= +m3365-;.3p1960inm. i  23. 0
30.
33. Ϫ7 Ϫ5 Ϫ3 Ϫ1

25.

Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4

37. 78 in.  38. 71 oz  39. 2.25 min  40. 3960 yd  27.

4 6 8 10

41. 240 loaves  42. about 6 lb  43. 5 s or about 0.45 s  29. x 7 - 4  31. x Ú 2 33. x Ú 5 35. Let p = the
11 number of people seated; p … 172. 37. Let w = number
44. 21  45. - 4  46. 1.6  47. 21  48. 39  49. - 1  of watts of the light bulb; w … 75. 39. Let m = amount
of money earned; m 7 20,000. 41. Check students’
50. 12 in.  51. 42 in.  52. 300%  53. 108  54. 170  work. 43. x … 186,000 45. b is greater than 0. 47. z is

55. 60 seeds  56. 30%  57. 72 students  58. increase;

Selected Answers i 869

greater than or equal to 25.6. 49. 21 is greater than or 23. r 6 0 

equal to m. 51. 2 less than g is less than 7. 53. r more than Ϫ4 Ϫ2 0 2 4 6

6 is greater than - 2. 55. 1.2 is greater than k. 57. Answers 25. s 6 4.7  4.7
may vary. Sample: No more than means “is less than or
23456
equal to,” since the amount cannot be greater than the
27. c 6 1 37 
Selected Answers given number. No less than means “is greater than or equal 1 3
7
to,” since the amount cannot be less than the given number. 

59. 998 7 978, so Option A 7 Option B. 61. Answers may Ϫ1 0123
vary. Sample: Use reasoning or guess and check to see that 357
29. 3  31. 4.2
the values of x that are less than 3 make the inequality 33. x … 5 

true. 63. line graph that shows an open circle at - 3 1
stretching to shaded circle at 3 65. C 67. A 69. increase;
35. c 7 - 7 
20% 70. decrease; 10%  71. decrease; 67% 72. 44 
1254 74. 3 Ϫ9 Ϫ7 Ϫ5 Ϫ3
73. - - 3 75. - 1 7   76. 11 77. - 2 78. - 11 
79. - 9 37. a Ú - 1 

Ϫ1 0 1 2

Lesson 3-2 pp. 171–177 39. n 7 - 2 2   2
3 3
Got It?  1. n 6 2 Ϫ2

Ϫ4 Ϫ3 Ϫ2 Ϫ1

Ϫ4 Ϫ2 0 2 4 41. d Ú - 1 

2. m Ú 9  Ϫ2 Ϫ1 0 1 2

4 5 6 7 8 9 10 11 12 13 43. 3 + 4 + g Ú 10; g Ú 3 45. Add 4 to each side. 
47. Add 1 to each side. 49. yes
3. y … - 13  2

Ϫ19 Ϫ17 Ϫ15 Ϫ13 Ϫ11 Ϫ9 51. 51

4a. p Ú 8  b. Yes. The Ú symbol can be 17 x
used to represent all 3 phrases.
Lesson Check 53.   Ϫ3 13
1. p 6 5  m

Ϫ2 0 2 4 6

2. d … 10  4
5
4 6 8 10 12

3. y 6 - 12  55. d … 2  57. - 4 7 p 59. - 1.2 7 z 61. p 7 12 

Ϫ16 Ϫ15 Ϫ14 Ϫ13 Ϫ12 Ϫ11 63. h Ú -78   65. 5 7 Ú m 67a. yes  b. No; in the first
16
4. c 7 3 
inequality, r is greater than or equal to the amount. In the
123456
second inequality, r is less than or equal to the amount. 
5. w … 524  6. Add or subtract the same number from
each side of the inequality.  7a. Subtract 4 from each side. c. In part (a), these are equations with only one solution.
b. Add 1 to each side.  c. Subtract 3 from each side.
d. Add 2 to each side.  8. They are similar in that 4 is In part (b), because the inequality relationship is different,

being added to or subtracted from each side of the there is no relationship between the two inequalities. 

inequalities. They are different in that one inequality adds 69. Answers may vary. Sample: 94, 95, or 96. 71. The

4 and the other subtracts 4. graph should be shaded to the right, not the left.
Exercises  9. 6 11. 3.3
13. y 7 13  Ϫ3 Ϫ2 Ϫ1 0 1

11 13 15 17 19 21 73a. No; the solution should be a Ú 8.6 - 3.2, or
a Ú 5.4.  b. Answers may vary. Sample: Other numbers
15. c 6 - 4  that are not substituted could also be solutions to the
inequality. 75. at least $88.74  77. True  79. Not true;
Ϫ8 Ϫ6 Ϫ4 Ϫ2 0 2 sample: x = 5, y = 3, w = 4 

17. t Ú - 3  Lesson 3-3 pp. 178–183

Ϫ3 Ϫ2 Ϫ1 0 1

19. p 7 12  Got It?  1. c 7 2 

10 12 14 16 18 Ϫ4 Ϫ2 0 2 4 6

21. f 7 1   0 1 2 3 2. n 7 3 
3
012345

870

wm3aaa.lkk1e32,$2o7,f23.a,Sdooor rg4o.ucIfansydeosuu pbrot.ou4n71.5d570.d=ow16n23t,ob1u6t,yyoouucwanilnl ootnly 57. - 7 (1) 7 - 7 1 - 5 s2 Mult. Prop. of Ineq.
4. x 6 2  5 5 7
- 7 7
012345 5 s Simplify.

59. If the most expensive sandwiches and drinks are

ordered, the cost is 3(7) + 3(2) = 27, leaving $3. If the Selected Answers
most expensive snack is bought, the least number of
Lesson Check  1. D  2. B  3. A  4. C  5a. Multiplication
snacks you can afford is 1. If the least expensive
by - 2; it is the inverse of division by - 2.  b. Addition of
4; it is the inverse of subtraction of 4.  c. Division by - 6; sandwiches and drinks are ordered, the cost is

it is the inverse of multiplication by - 6.  6. The inequality 3(4) + 3(1) = 15, leaving $15. If the least expensive snack
is bought, the greatest number of snacks you can afford is
symbol was not reversed when multiplying by a negative.
( )-5 15. 61. x 6 20, x 6 30, x 6 40, . . . ; any inequality
- n 6 - 5(2), n 6 - 10 following the one that a is a solution to. This is because
5
each following inequality has the same solutions as the
Exercises
previous inequalities, with more values as solutions. 
7. x Ú - 10 
63. 3.14d 7 29.5 and d 7 9.4, so the men’s basketballs
Ϫ12 Ϫ10 Ϫ8 Ϫ6 Ϫ4 Ϫ2 need a 10–in. box; 3.14d 7 27.75, d 7 8.8 so the youth

9. p 6 32  basketballs need a 9–in. box. 65. D 67. w = / - 3,
18 = 2/ + 2(/ - 3), 18 = 4/ - 6, 24 = 4/, so / = 6
28 30 32 34 36

11. v … - 3  (Length is 6 in.). 68. x … - 11 69. y Ú 13.6 70. q 6 5 
71. - 1 7 c 72. -1 6 b 73. y … 75 74. 2 75. -2 
Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 76. 1 4

13. x Ú - 3 

Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0

15. m … 0  Lesson 3-4 pp. 186–192

Ϫ2 Ϫ1 0 1 2 Got It?  1a. a Ú - 4  b. n 6 3  c. x 6 25  2. any width

17. m 6 2  greater than 0 ft and less than or equal to 6 ft  3. m … - 3
4a. b 7 3  b. Answers may vary. Sample: adding 1 to
012345

19. m Ú 2  each side. This would gather the constant terms onto one

012345 side of the inequality.  5a. no solution  b. all real numbers

21. c 7 6  Lesson Check  1. a 7 2  2. t … 5  3. z 6 13  4. no
solution  5. greater than 0 cm and less than or equal to
0 2 4 6 8 10

23. z 7 - 3  0 8 cm  6. The variable terms cancel each other out and a
0
Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 false inequality results.  7. Yes; each side can be divided by

25. b … - 1   5 2 1 1 1 2 first.  8. No; there is no solution, since - 6 is not greater
6 6 3 2 3 6

Ϫ Ϫ Ϫ Ϫ Ϫ than itself. If the inequality symbol were Ú, your friend

27. h 7 - 13  would be correct. 

Ϫ15 Ϫ14 Ϫ13 Ϫ12 Ϫ11 Ϫ10 Exercises  9. f … 3  11. y 7 - 2  13. r Ú 3.5 
15. 5s Ú 250; s Ú 50 mph 17. k Ú 1  19. j 6 - 1 
29. q … 9  21. z 6 9  23. x 6 3  25. f … 6  27. m Ú - 5  29. all

5 6 7 8 9 10 real numbers  31. all real numbers  33. all real numbers 

31. no more than 66 text messages  33–35. Answers 43c.35T..hkxeyÚ…a1-r63e4 e 4q35u7.iv.5at.l5eÚnht95.   4d37.9.C.Dhn e4Úck9-ast.2u  dv4eÚ1n.t4sa’  Ú 0.5 
b. 4 … v 
may vary. Samples are given. 33. - 5, - 4, - 3, - 2  work.  51.
35. - 6, - 5, - 4, - 3 37. Multiply each side by - 4 and
reverse the inequality symbol. 39. Divide each side by 5. at

41. - 2 43. 4 45. Sometimes true; sample: It is true least $3750  53. 3y was subtracted from instead of added
2
when x = 4 and y = 0.5 but false when x = 4 and to each side; 7y … 2, y … 7 .  55. - 5, - 4, - 3, -2, -1, 0,
1, 2, 3, 4, 5, and 6  57a. boxes  b. 4 trips
y = - 2. 47. Sometimes true; sample: It is true when 73

x = 4 and y = 2 but false when x = 0 and y = 2. Lesson 3-5 pp. 194–199
49. at least 0.08 mi per min
3t 13t 2 MSimulpt.lifPyr.op. Got It?  1. N = 52, 4, 6, 8, 10, 126; N = 5x ͉ x is
51. 3( - 1) Ú of Ineq. an even natural number, x … 12}  2. 5n ͉ n 6 - 36 
-3 Ú 3a. 56or O, 5a6, 5b6, 5a, b6; 56 or O, 5a6, 5b6, 5c6,
5a, b6, 5a, c6, 5b, c6, 5a, b, c6  b. Yes; every element
53. 2(0.5) … 2112 c2 Mult. Prop. of Ineq. of set A is part of set B, since - 3 6 0.  4. A′ = {February,
April, June, September, November}
1 … c Simplify.
n
55. 51 5 2 … 5(- 2) Mult. Prop. of Ineq.

n … - 10 Simplify.

Selected Answers i 871

Lesson Check  1. G = {1, 3, 5, 7, 9, 11, 13, 15, 17}; 5a. - 2 6 x … 7  8
G = 5x ͉ x is an odd natural number, x 6 18} 
2. 5d ͉ d … 36  3. { } or O, {4}, {8}, {12}, {4, 8}, {4, 12}, Ϫ2 0 2 4 6
{8, 12}, {4, 8, 12}  4. W ′ = {spring, summer, fall}  5. A; its
complement is the set of all elements in the universal set b. (7, ∞ ) 

5 6 7 8 9 10

Lesson Check  1. 0 … x 6 8

Selected Answers that are not in A ′.  6a. Yes; the empty set is a subset of 0 2 4 6 8 10
every set.  b. No; the number 5 in the first set is not an
2. 1 … r 6 4 
element of the second set.  c. Yes; the element in the first
012345
set is also an element of the second set.  7. sometimes 
3. 85 … x … 100  4. x … 6; (- ∞, 6)  5. A, C, and D 
8. The student forgot that 0 is also a whole number. 6. Answers may vary. Sample: The bracket indicates a
Exercises  9. 50, 1, 2, 36; 5m ͉ m is an integer, - 1 6 specific number is part of the solution. The symbol ∞
m 6 46  11. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; 5p ͉ p is a means that the numbers continue without end. So a
natural number, p 6 116  13. 5 y ͉ y Ú 46  15. 5m ͉ m 7 parenthesis should follow.  7. x … 7 or x 7 7; (- ∞, ∞) 
- 56  17. 5p ͉ p Ú 16  19. { } or O, {a}, {e}, {i}, {o}, {a, e}, 8. The graph of a compound inequality with the word and
{a, i}, {a, o}, {e, i}, {e, o}, {i, o}, {a, e, i}, {a, e, o}, {a, i, o}, {e, contains the overlap of the graphs that form the inequality.
The graph of a compound inequality with the word or
i, o}, {a, e, i, o}  21. { } or O, {dog}, {cat}, {fish}, {dog, cat}, contains both of the graphs that form the inequality.
Exercises  9. - 5 6 x 6 7
{dog, fish}, {cat, fish}, {dog, cat, fish}  23. { } or O, {1} 
Ϫ5 7
25. {1, 4, 5}  27. 5 c , - 4, - 2, 0, 2, 4, c 6 
29. A′ = {Tuesday, Thursday, Friday, Saturday}  31. False; Ϫ6 Ϫ3 0 3 6 9
some elements of U are not elements of B.  33. True; the
empty set is a subset of every set.  35. M = 5m ͉ m is odd
integer, 1 … m … 196  37. G = 5g ͉ g is an integer6 
39. {Mercury, Venus, Earth}  41. { } or O  43. 5x ͉ x … 06  11. - 7 6 k 6 5  Ϫ7 5

45. { } or O  47. T ′ = 5x | x is an integer, x … 06  49. 1 Ϫ9 Ϫ6 Ϫ3 0 3 6

51. 512  53. A  55. D  57. Mum’s Florist: +26.40 = +1.025 13. 2 6 p … 5 
24
cFolosrtispte: r+r76o5s0e=.  012345
each. First Flowers +1.25 each. Mum’s
Florist has a lower 58. b 7 8  59. t … 5  15. 3 3 6 x 6 8 1   3 3 8 1
4 2 4 2
60. z 6 13  61. 6  62. - 3  63. 3
64.
0 2 4 6 8 10
4 6 8 10 12

65. 17. b 6 - 1 or b 7 2

Ϫ8 Ϫ6 Ϫ4 Ϫ2 0 2 Ϫ2 Ϫ1 0 1 2 3

66. 19. d Ú 2 or d 6 2 

2 4 6 8 10 12 14 Ϫ4 Ϫ2 0 2 4 6

Lesson 3-6 pp. 200–206 21. y … - 2 or y Ú 5 

Ϫ4 Ϫ2 0 2 4 6

Got It?  1a. - 4 … x 6 6 Ϫ4 0 4 8 12 16 23. x … 2 

b. x … 2 1 or x 7 6  Ϫ4 Ϫ2 0 2 4 6
2
2 1 25. x … - 1 or x 7 3 
2
Ϫ4 Ϫ2 0 2 4 6

0 2 4 6 8 10 27. (- 2, ∞ ) 

c. x is between - 5 and 7 does not include - 5 or 7. Ϫ4 Ϫ2 0 2 4 6

Inclusive means that - 5 and 7 are included. 29. (- ∞ ,- 2) or [1, ∞)
2
2. 3 6 y 6 6  Ϫ4 Ϫ2 0 2 4 6

2 31. (1, 6]  33. (- ∞ , - 5) or [5, ∞ )  35. - 3 6 x 6 4 
3 164  3  495. .2a32n…y 1t1h2a…n 1
4
0 2 4 6 8 10 37. 3 … x 6 v … 6  41. - 4 w6 12
43. 4 6 x 6 length greater 6 ft
3. Answers may vary. Sample: No, to get a B, the average and

of the 4 tests must be at least 84. If x is the 4th test score, less than 36 ft  47. any length greater than 11 m and

78 + 78 + 79 + x less than 23 m  49. any real number except 4 
4
Ú 84, 235 + x Ú 336, and x Ú 101, 51a. 102.5 … R … 184.5  b. 22 years old  53. B 
55. 35 … 10.4 + 0.0059g … 50, 24.6 … 0.0059g … 39.6,
which is impossible.  4169.49 … g … 6711.86; minimum water consumption is

4. y 7 3 or y … - 2  4169 gal and maximum water consumption is about

Ϫ4 Ϫ2 0 2 4 6

6712 gal.  56. { } or O, {1}, {3}, {5}, {7}, {1, 3}, {1, 5}, {1, 7},

872

{3, 5}, {3, 7}, {5, 7}, {1, 3, 5}, {1, 3, 7}, {1, 5, 7}, {3, 5, 7}, 39. t 6 -3 or t 7 7   7
B′ = 51, 2, 1 3 Ϫ3 3
{1, 3, 5, 7}  57. 7 Ú r  62. 3, 5, 7, 156  58. no  59. 3 6 b 
60. n … 3  61. = 63. 7 64. 7
Ϫ4 Ϫ2 0 2 4 6
Lesson 3-7 pp. 207–213
41. t … - 2.4 or t Ú 4  Ϫ2.4

Got It?  1. n = 3 and n = - 3 Ϫ4 Ϫ2 0 2 4 6 Selected Answers

Ϫ4 Ϫ2 0 2 4 6 43. - 4 … v … 5 

2. The 80 represents your friend’s starting distance from Ϫ4 Ϫ2 0 2 4 6
you. The 5 represents your friend’s constant speed of
45. - 11 … f … 2  Ϫ11 2
5 ft /s. She is 60 ft away at 4 s and 28 s.  3. no solution 
4. x Ú 0.5 or x … - 4.5 Ϫ12 Ϫ8 Ϫ4 0 4 8

47. any length between 89.95 cm and 90.05 cm, inclusive

49. d = 9 or d = - 9  51. no solution  53. y = 3.4 or
1 1
Ϫ8 Ϫ6 Ϫ4 Ϫ2 0 2 y = - 0.6  55. c = 8.2 or c = - 0.2  57. - 6 4 6 n 6 6 4

5a. 0 w - 32 0 … 0.05; 31.95 … w … 32.05  b. No; 213 is 59. - 8 6 m 6 4  61. 49°F … T … 64°F  63. The 200
represents your friend’s starting distance from you. The 18
part of the absolute value expression. You cannot add 213
until after you write the absolute value inequality as a represents your friend’s constant speed of 18 ft/s.
compound inequality. 6t 7=.4A49nsswaenrds 1m7a79y
Lesson Check  1. x = 5 or x = - 5  s  65. - 1 … y + 7 … 1, - 8 … y … -6
vary. Sample: To be more than 1 unit
Ϫ5 0 5
away from - 5 on a number line means x + 5 7 1 or
2. n = 7 or n = - 7  x + 5 6 - 1.  69a. between 193.74 g and 209.26 g,
inclusive  b. Yes; answers may vary. Sample: Some nickels
Ϫ7 0 7

3. t = 3 or t = - 3  could weigh more and some could weigh less, and their

Ϫ3 0 3

4. - 2 6 h 6 8  average could be the official amount.  71. 0 x 0 6 4
73. 0 x - 6 0 7 2  75. between 89.992 mm and
Ϫ2 0 2 4 6 8

5. x … - 3 or x Ú - 1  90.008 mm, inclusive  77. 2  79. 3  81. always 

Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 83. 4.265 85. 5  87. 120  88. - 282 … e … 20,320 

6. 2; there are two values on a number line that are 89. 36.9 … T … 37.5  90. 2x + 10  91. - 3y + 21 
92. 4 / + 5  93. - m + 12  94. A = 5x ͉ x is a whole
the same distance from 0.  7. The absolute value cannot number, x 6 106  95. B = 5x ͉ x is an odd integer,

be equal to a negative number since distance from 0 on 1 … x … 76  96. C = 5- 14, - 12, - 10, - 8, - 66 

a number line must be nonnegative.  8. Answers may 97. D = 58, 9, 10, 12, 14, 15, 166

vary. Sample: The equation is set equal to 2 and - 2. The
first inequality is set to be … 2 and Ú - 2. The second
inequality is set to be Ú 2 or … - 2. Lesson 3-8 pp. 214–220

Exercises  9. b = - 1 or b = 1 Got It?  1a. P = 50, 1, 2, 3, 46; Q = 52, 46;
2 2 P ∪ Q = 50, 1, 2, 3, 46  b. Answers may vary. Sample: If
B ⊆ A, then A ∪ B will contain the same elements as
Ϫ1 Ϫ 1 0 1 1 A.  2a. A ¨ B = 52, 86  b. A ¨ C = O  c. C ¨ B =
2 2 55, 76  3. A and E  4. 10  5a. 5x ͉ x Ú 36 ¨ 5x ͉ x 6 66 
b. 5x ͉ x 6 - 26 ∪ 5x ͉ x 7 56
11. n = 4 or n = - 4  Lesson Check  1. X ∪ Y = 51, 2, 3, 4, 5, 6, 7, 8, 9, 106 
2. X ¨ Y = 52, 4, 6, 8, 106  3. X ¨ Z = O  4. Y ∪ Z =
Ϫ4 Ϫ2 0 2 4 51, 2, 3, 4, 5, 6, 7, 8, 9, 106  5. 31 people  6. A ∪ B
contains more elements because it contains all the
13. x = 8 or x = - 8  elements in both sets.  7. The union of sets is the set that

Ϫ8 Ϫ4 0 4 8 contains all elements of each set. The intersection of sets is
the set of elements that are common to each set.  8. true 
15. m = 3 or m = - 3  9. false
Exercises  11. A ∪ C = 51, 2, 3, 4, 5, 7, 106 
Ϫ4 Ϫ2 0 2 4 13. B ∪ C = 50, 2, 4, 5, 6, 7, 8, 106  15. C ∪ D = 51, 2,
3, 5, 7, 9, 106  17. A ¨ C = O  19. B ¨ C = 526 
17. r = 13 or r = 3  19. g = - 1 or g = - 5  21. no 21. C ¨ D = 55, 76
solution  23. v = 6 or v = 0  25. f = 1.5 or f = - 2 
27. y = 3 or y = 0  29. no solution  31. no solution 
33. - 5 6 x 6 5 

Ϫ10 Ϫ5 0 5 10

35. y … - 11 or y Ú - 5

Ϫ13 Ϫ11 Ϫ9 Ϫ7 Ϫ5 Ϫ3

37. 4 … p … 10 

2 4 6 8 10 12

Selected Answers i 873

23. E F 21. t 6 - 3 
91
46 5 Ϫ11 Ϫ9 Ϫ7 Ϫ5 Ϫ3
82
22. y … 6 

0 2 4 6 8 10

Selected Answers 23. h 7 - 24 

Ϫ26 Ϫ24 Ϫ22 Ϫ20 Ϫ18 Ϫ16 Ϫ14

10 24. g 7 4 

G 2468

25. 10 girls  27. 5x ͉ x 7 - 36 ¨ 5x ͉ x 6 1396  25. n … 15 
29. ͉w Ú
6 ∪5w 16  31. 5x ͉ x 6 11 12 13 14 15 16

5w ͉ w … - 3 - 76 26. d Ú 16 13   16 13
4 27 27

∪ 5x ͉ x 7 216  33. W ∪ Y ∪ Z = 50, 2, 3, 4, 5, 6, 7, 86  10 12 14 16 18 20
35. W ¨ X ¨ Z = 566  37. 62 patients  39. A ¨ B = A 
41. 5(p, 2), (p, 4), (2p, 2), (2p, 4), (3p, 2), (3p, 4), 27. m 7 - 1 67  
171 Ϫ116771
(4p, 2), (4p, 4)6 43. {(reduce, plastic), (reuse, plastic),

(recycle, plastic)}  45. Sometimes; when A = B = C , Ϫ2 Ϫ1 0 1 2

the statement is true. When A, B, and C are distinct sets 28. 7.25h Ú 200; at least 28 full hours  29. k Ú - 0.5 

the statement is false.  47. F 49. x = 4 or x = - 4  30. c 6 -2  31. t 6 - 6  32. y … - 56  33. x 6 2 2
50. n = 2 or n = - 2  51. f = 2 or f= 8  52. y= 4 or 3
y= 8 -4 or xÚ 10  3 34. x … - 13  35. a … 5.8  36. w 7 0.35  37. 200 +
- 3   53. -5 … d … 5  54. x…
55. w 7 9  56. x 0.04s Ú 450; s Ú 6250  38. 5 6 or O, 5s6, 5t6, 5s, t6 
w 6 - 15 or = 4 or x = - 4   57. yes  39. { } or O, {5}, {10}, {15}, {5, 10}, {5, 15}, {10, 15}, {5, 10, 15}
3 3
58. no  59. yes
40. A = 50, 2, 4, 6, 8, 10, 12, 14, 166; A = 5x ͉ x is an
Chapter Review pp. 222–226 even whole number less than 186  41. B′ = 51, 3, 5, 76 
1 d 6 4  43. - 1.5 … b 6 0  44. t … -2
1. roster form  2. union  3. empty set  4. solution of an 42. - 2 2 …
inequality  5. equivalent inequalities
6. or t Ú 7  45. m 6 - 2 or m 7 3  46. 2 … a … 5 
47. 6.5 7 p Ú - 4.5  48. 65 … t … 88  49. y = 3
45678 or y = - 3  50. n = 2 or n = - 6  51. r = 1 or
r = - 5  52. no solution  53. - 3 … x … 3  54. no
7. solution  55. x 6 3 or x 7 4  56. k 6 - 7 or k 7 - 3 
57. any length between 19.6 mm and 20.4 mm, inclusive 
Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 58. A ∪ B = A 
59. P 60. N ¨ P = 5x ͉ x is a
8. R multiple of 66  61. 5 cats
7 2
4 6 8 10 12 14 9 64
15 8
9.   3.2 13

Ϫ1 0 1 2 3 4 3

10. x 7 5  11. x … - 2  12. x 7 - 5.5  13. w 7 6 

024 6 8 10 Q
4 6 8 10 12
14. v 6 10  Ϫ18 Ϫ16 Ϫ14 Ϫ12 Ϫ10 Ϫ8 Chapter 4

15. - 12 6 t  5 Get Ready! p. 231
16. n Ú 54  4

0 12 3 1. - 7 2. - 18 3. 2 4. - 1
8.6
17. 8.6 … h  5.

7 8 9 10 Bob’s and His Dog’s Ages (years)
Dog’s Age 0 1 2 3 4 5 6 7 8 9
18. q 7 - 2.5  Ϫ1 Bob’s Age 9 10 11 12 13 14 15 16 17 18
3
Ϫ4 Ϫ3 Ϫ2

19. 4.25 + x … 15.00; x … 10.75
20. x 6 3 

Ϫ1 0 1 2

874

Bob ’s and H is Dog’s A ges B = 9 + d, where B isBob’s Age (years) 12. - 3 13. 66 14. 6 15. 4 16. 0, - 4 17. 3, 7
Bob's age and d is his 18. no solution 19. 121, 32 20. Its value is based on the
first value. 21. 4 22. There are no breaks in the graph.
18 dog's age.
Lesson 4-1 pp. 234–239
14

10 Got It?  1a. Time, length; the length of the board Selected Answers

6 remains constant for a time before another piece is cut
off.  b. Time, cost; the cost remains constant for a certain
2 6 10 14 18 number of minutes. 2. C
00 2 Dog’s Age (years) 3a. Answers may vary. Sample:


Distance From
6. the Ground

Sue’s Number of Laps per Minute

Number of Minutes 0 1 2 3 4 5 6 7 8 9

Number of Laps 0 1.5 3 4.5 6 7.5 9 10.5 12 13.5

Begin Swing Slow Stop
Swinging Higher Down
S ue’s Num ber of La ps / = 1.5m, where m is
Time

per Minute the number of minutes b. The end of the graph would decrease sharply.

18 and / is the number of Lesson Check 1. Car weight, fuel used; the heavier the
laps.
car, the more fuel is used. 2. The temperature rises
Number of Laps
14 slightly in the first 2 h and then falls over the next 4 h. 

10 3. rising slowly: B; constant: C; falling quickly: D 

4. Answers may vary. Sample: the depth of water in a

6 stream bed over time

2 Exercises 5. Number of pounds, total cost; as the
00 1 3 5 7 9
number of pounds increases, the total cost goes up, at
Number of Minutes
first quickly and then more slowly. 7. Area painted, paint
7.
in can; the more you paint, the less paint left in the can.
Total Cost for Cartons of Eggs
Number of Cartons 0 1 2 3 4 5 6 7 8 9 You are using the paint at a constant rate. 9. A

11. Answers may vary. Sample:

Total Cost (dollars) 0 3 6 9 12 15 18 21 24 27

Total Cost for Cartons of Eggs C = 3n, where C is Hours of
the cost and n is Daylight
the number of
27 cartons. Time

Total Cost (dollars) 21 13. Answers may vary. Sample:

15 Time

9 15. The graph shown represents the relationship between thePulse Rate
number of shirts and the cost per shirt, not the total cost.
3
00 1 3 5 7 9

Number of Cartons

8–11. 5y Total Cost
4
(؊2, 2) 3
(؊2, 0) 2
Ϫ5Ϫ4Ϫ3Ϫ2 1x
O 1234 5

Ϫ2
Ϫ3
Ϫ4 (3, ؊3)

Ϫ5 (0, ؊5)

Number of Shirts i 875

Selected Answers

17. No, they are not the same. Your speed on the ski lift b. Add 4.  c. The 4x part of the equation means that for

is constant. Your speed going downhill is not. each triangle the perimeter is increased by 4. If you know

a. b. the perimeter of n triangles, then the perimeter when 1

Selected Answers more triangle is added will increase by 4.
Speed
Speed 2a. Yes; the value of y is 8 more

Time Time than twice the value of x; 16 y
y = 2x + 8. 12

b. N o; the input value 1 has 8
19. The three runners start at the same time. At time A, more than one output value. 4
00 x
one runner has a fast start, and the other two are a little 1 2 3

slower. At B, the second–place runner catches up to the Lesson Check

first–place runner and passes the first–place runner in 1a. y y increases by 1 for each
increase of 1 for x.
order to win at time C. At C, the runner that was in third 4
3
place catches up to the original first–place runner to 2

finish second. At D, only the original first–place runner 1 x
9.35 - 8.50 00 4
remains in the race. 21. B 23. 8.50 = 0.10, 1 2 3

or a 10% increase. Another 10% increase would b. 108 y Fyodreecarecahsienscbreya2se. of 1 in x,

bring your hourly wage to 1.1(9.35) = 10.285, or 6
$10.29. One further 10% increase would bring

your rate to 1.1(10.29) = 11.3135, or $11.32.  4
24. 5- 3, - 1, 1, 3, 4, 5, 7, 96 25. {1}  2
26. 5- 1, 1, 3, 4, 5, 7, 9, 126 27. {1, 4} 00 1 2 3 4 x
5
28. Co nnie’s Donald’s 8d
7 c. y x is 3 for any value of y.
Age Age
04 6 4
15 3
26 5 2
37 4
3 1 x
2 00 1 2 3 4
1
00 1 2 3 4 c 2.
5
Number of
d=c+4 Squares 1 2 3 4 10 30 n
29.
Number c Perimeter 4 6 8 10 22 62 2n + 2
Time of Cards
(hours) 6 3. independent: number of times you brush your teeth;
0 dependent: amount of toothpaste 4. a and b are
0

13 3 functions because for each input there is a unique
26
output, but c is not a function because there is more than
39 h one output value for the input value 3. 5. No; the
3
00 1 2 graph is not a line. 
Exercises
c = 3h
7.
Lesson 4-2 pp. 240–245
Number of
Got It?  1a.   Pentagons 1 2 3

Number of Triangles 1 2 3 4 Perimeter 5 8 11

Perimeter 10 14 18 22

Multiply the number of pentagons 12 y
by 3 and add 2; y = 3x + 2. 10
Multiply the number of 18 y Perimeter 8

triangles by 4 and add 6; 12 6
y = 4x + 6. 4
2
6 00 1 2 x
3
x
00 1 2 3 4 Number of
Pentagons

876

9. S tart with - 3 and add 5 y 19. graph of a line that goes through (0, 0); (1, 6), (2, 12);
for each increase of 1 for x; 12 the horizontal axis is labeled Distance and the vertical axis
y = 5x - 3. is labeled Time.

8 Lesson 4-3 pp. 246–251

4 x Got It? Selected Answers
4
Ϫ4 O 1a.   A   nonlinear
Ϫ4
1
2

1
4
11. Y es; for each additional n
1400 y 00 1 2 3 4 5
hour of climbing, you 1300
1200 b. No; you can always multiply a number by 21. The
gain 92 ft of elevation; denominator of the fraction will get larger and larger, so
y = 92x + 1127.
the value of the fraction will approach 0 but never reach it.
1100 1 2 x 2. The number of branches is 3 raised to the xth power;
00 3 y = 3x; 81, 243.

13. Yes; for every 17 mi traveled, 12 y y
200
the amount of gas in your 11

tank goes down by 1 gallon; 10 100
9
y = - 1 x + 11.2. 8 x
17 00 x 00 1 2 3 4 5
51
17 34 3. y = x2

15. 4y

2 Lesson Check

Ϫ2 O x 1. 16 y linear
Ϫ2 24 15
14
13
12
00 x
4
No; all points are not on a straight line. 1 2 3

17. Gas Distance, 2. y = 3x - 2 3. C 4a. linear function  b. nonlinear
Used, x y function 5. Only the first two pairs fit this rule. The rule
that fits all the pairs is y = x2 + 1.
0 40
Exercises
1 90

2 140 7.    y  9. 6y
4
3 190 8 Ϫ2 2x
O 24
y = 50x + 40 7

y 00 3 6 x Ϫ4
150 9 12 15

Distance (mi) nonlinear nonlinear

100 11.     linear

50 10 y

x 8
3 6
00 1 2 4

Gas (gal) 2x

Either distance or gas could be the independent Ϫ2 O 1 2 3

variable, depending on what information is supplied Ϫ4

and what is to be calculated.

Selected Answers i 877

13. y = 4x2 15. y = 2x3 17. Independent: r, 4. y
dependent: V ; volume depends on the length of the
radius. 19. Let y = number of bags, and y = 6pr2; 2
3nhiseab1as29artlghymse$;o.l4ro0ew5bt9aehg3ras,nc;o+5t1s2h.t9b6ep9asegoqrszu.o aiu2srne1nc.eoeafy.rx[l=1y. ]$x2o2.30n+.5eB81m2 392;;in5ttohh.ree[22v]a9l+–u1.o8e59zocofazynis Ϫ2 O
Selected Answers x
2

Ϫ4

computational error 8y Lesson Check
26. T he value of y is 3 4
1. y 2. y
more than twice
x; y = 2x + 3. 1 x
Ϫ2 O 4
00 x 4 2
3 Ϫ2
1 2

27. - 24, - 3, 14.5 28. - 11, 1, 11 29. - 18, 0, - 12.5 Ϫ2 O x Ϫ4
Ϫ2 2

Lesson 4-4 pp. 253–259 Ϫ6

Got It? 3.      y 4. y
1. 2 y
8 2
x x
4 Ϫ2 O 2
Ϫ2 O 2 Ϫ2
Ϫ2

Ϫ4 O 4x
Ϫ4

2a.      Total Weight (lb), W b. 700 lb; when g = 0, the 5a.     n h b.
spa is empty, and
3000 W = 700. Height (in.), h 30

2000 1 19.5

1000 2 21 20

00 100 200 300 3 22.5 10
Gallons of Water, g 4 24
5 25.5 00 2 4 6 8 10 12
3a.    9 continuous because you can 6 27 Number of Cones, n
have any amount of water
6Water (gal), w 7 28.5
3
8 30

00 1 2 3 4 5 6. discrete 7. continuous 8. The graph should not be
Time (min), t discrete; connect the points with a line so the graph is
continuous.

b. 64 discrete because you can Exercises
only have a whole number
Cost, C 32 of tickets 9.        y 11. 6 y

00 1 2 3 4 5 2 4
Number of Tickets, n 2x
x Ϫ2 O 2

Ϫ2 O 2
Ϫ2

Ϫ6

878

13.       y 15. y 33. No; the graph is still continuous over the appropriate
values of d and t.
20
2 x 35. 12 Continuous; lengths and areas
Ϫ2 O 2 can be any number.
x Ϫ20
Ϫ2 O 2 Area, A 8 Selected Answers
Amount of Money, a
Ϫ2 4

17. y 19.    4y 00 2 4
12 Length, ഞ
8 2 x 3 45
4 2 37a. 45 30
Ϫ2 O
Ϫ2 b0 1 2
a 0 15 30

x 15

Ϫ2 O 24 00 1 2 3 4
Ϫ4 Number of Basketballs, b

21. 8 After you drink 20 oz ofHeight (in.), h Discrete; you can only have whole numbers of basketballs. 
juice, the height is 0, so the b. 8  39. between 2 and 3 s  41. Table for y = 2x has x
values - 1, 0, 1, 2, 3 and corresponding y-values - 2, 0, 2,
6 interval 0 … j … 20 makes 4, 6; graph of the line y = 2x; graph passes through
4 sense. The height goes from (0, 0) and (1, 2). Table for y = 2x2 has x values - 1, 0, 1,
0 … h … 6; continuous, 2, 3 and corresponding y-values - 2, 0, 2, 8, 18; graph of
y = 2x2 is U-shaped going through ( - 1, - 2), (0, 0),
2 because you can have juice (1, 2), (2, 8).

00 10 20 in any amount.

Amount of Juice (oz), j Lesson 4-5 pp. 262–267

23. 40 aTnhye number of pizzas can be Got It? 1. W = 50,000 + 420m
whole number, except
2a. C = 12 + 15n; $162  b. No; making the stay shorter
Cost, C 30 zero, so 0 6 p. 1 pizza costs only halves the daily charge, not the bath charge. 
20 $14, so 14 … C.
3a. A = b2 + 2b; 288 in.2
b. 20 The graph is not a line.
10

00 1 2 3 4 5 6 Area, A 16
Number of Pizzas, p 12
8
4
25. 27.
y y 00 1 2 3 4
6
Base, b

1 x 2O x Lesson Check 1. C = 3.57p 2. f = h  
2 Ϫ2 2 12
Ϫ2 O 3. y = x + 2 4. V = (d + 1)3 5. dependent, a;
Ϫ2 Ϫ6 independent, b 6. You can’t add holes and minutes.

The correct rule is t = 15n. 7. Continuous; side
length and area can be any positive real numbers.

29.   1 y 31. 8 y E1199x37e..crdpmc=2=is e6-2.s119 .059A-.+C=500.=39tw5;8t2-+  11-12652n0.w af1t;= 181.8f93ht.2-+ A6122b3=. 5.32A=hnw+sw 25ehr2s;may
O
x

Ϫ2 2 4

Ϫ4 Ϫ2 O x vary. Sample: The rule covers all values, whereas the
Ϫ6 Ϫ4 2
Ϫ8
table only represents some of the values. 

25. d = - 3.5 - 108m; - 435.5 m

Selected Answers i 879

27a. Lesson 4-6 pp. 268–­ 273

Cost of Meal $15 $21 $24 $30 Got It?  1a. domain: {4.2, 5, 7}; range: {0, 1.5, 2.2, 4.8}

Money Left $37.75 $30.85 $27.40 $20.50 0 not a function

Selected Answers b. m = 55 - 1.15c  4.2 1.5
Money Left, m 5 2.2
c. 60 7 4.8

50 b. domain: 5- 2, - 1, 4 76; range: 51, 2, - 4, - 76
40
30 Ϫ2 1 function
20 2
10 Ϫ1 Ϫ4
4 Ϫ7
00 10 20 30 40 7
Cost of Meal, c
50 2a. function  b. not a function 3. 1500 words 
4. 5- 8, 0, 8, 166 5a. domain: 0 … q … 7, range:
29a. d = 1.8w  b. No; the room is not wide enough. 0 … A(q) … 700  b. The least amount of paint you can
32anftd  use is 0 quarts. The greatest amount you can use is
c. 6 31. Table has x-values - 4, - 3, - 2, - 1, 0, 1, 2,
3, 4 corresponding y-values 7, 6, 5, 4, 3, 2, 1, 0, - 1; 3 quarts. 

the graph is a line that passes through (0, 3) and (3, 0); Lesson Check  1. domain: 5- 2, - 1, 0, 16, range: {3, 4,
5, 6}
the function rule is y = - x + 3  33. B  35. C

37.        y  38. 10 y Ϫ2 3 function
4
66 Ϫ1 5
0 6
1

2 x Ϫ3 O x 2. yes 3. 9 4. 5- 2, - 1, 0, 1, 26 5. f (x) = 2x + 7
Ϫ2 O 2 Ϫ4 3 6. Answers may vary. Sample: Both methods can be

Ϫ4 used to determine whether there is more than one

39.     3 y 40. y output for any given input. A mapping diagram does

Ϫ3 O 6 not represent a function if any domain value is mapped
Ϫ2
x 2x to more than one range value. A graph does not represent
3 a function if it fails the vertical line test. 7. No; there
Ϫ2 O 2
exists a vertical line that intersects the graph in more than
41.     y Ϫ8
one point, so the graph does not represent a function.
6 42. 18 y Exercises  9. domain {1, 5, 6, 7}, range 5- 8, - 7, 4, 56;
2x yes  11. domain {0, 1, 4}, range 5- 2, - 1, 0, 1, 26;
Ϫ2 O 2 no  13. not a function 15. function 17. $11 
19. 5- 39, - 7, 1, 5, 216 21. 5- 7, - 2, - 1, 36
Ϫ8 23. 0 … c … 16, 0 … D(c) … 1568

9 x 1400Vitamin D (IU), V(c)
3 1200
3 1000
Ϫ3 O 800
600
Ϫ6 400
200
43. 132 oz 44. 4.5 m 45. 51 ft 46. 1.5 min 47. 9 days
00 2 4 6 8 10 12 14 16
48. 9500 m 49. - 36 50. 21 51. 111.6 52. - 9 53. 14 Cups of Milk, c
53  56. 21
54. 1 55. 16 25. function; domain: 5- 4, - 1, 0, 36, range: 5- 46
27. 5; if f (a) = 26, then 6a - 4 = 26 and a = 5.
29a. c is the independent variable and p is the dependent
variable.  b. Yes; for each value of c, there is a unique
value of p. c. p = 5c - 34  d. 0 … c … 40, 0 … p … 166
31. function 33. not a function 35. A horizontal line is a
function because each value of x has a unique value of y; a

880

vertical line is not a function because the x-value has more 45. A(n) = A(n - 1) + 1, A(1) = 4 47. 2, 12, 47 
than one y-­value associated with it.  37. 23  39. 6  41. 5.25  49. 17, 33, 89 51. - 2, 8, 43 53. - 3.2, - 5.4, - 13.1
43. 11 stamps 45. E = 5h + 7  46. a = 4.5s + 10  55. Yes; the common difference is - 4; A(n) =
47a. time and distance A(n - 1) - 4, A(1) = - 3; A(n) = - 3 + (n - 1)(- 4). 
57. No; there is no common difference.  59. Yes; the
b. A Trip to the Mountains Selected Answers
common difference is - 0.8; A(n) = A(n - 1) - 0.8,
A(1) = 0.2; A(n) = 0.2 + (n - 1)(- 0.8). 61. 10, 11.2,
Distance From traveling D F 12.4; A(n) = 8.8 + (n - 1)(1.2)  63. - 2, - 4, - 6;
Home
BE A(n) = (n - 1)(- 2) 65. Answers may vary. Sample:

C rest stop A(n) = 15 + 2(n - 1) 67. 350, 325, 300, 275, 250,

A lunch 225; you owe $225 at the end of six weeks.

Time 69a. 1, 6, 15, 20, 15, 6, 1  b. 1, 2, 4, 8, 16; 64

48. 9, 12, 15, 18 49. 8, 15, 22, 29  71a. 11, 14  b. y c. The points all lie on a
50. 0.4, - 2.6, - 5.6, - 8.6 line.
15

10

Lesson 4-7 pp. 274–281 5

Got It?  1a. Add 6 to the previous term; 29, 35. 00 x
-212; ;2352, ,12-.654. .  4
b. Multiply each previous term by 1 2 3
c. Multiply each previous term by
73. x; 4x + 4  75a. The next figure is a drawing of a
d. Add 4 to the previous term; 1, 5.  2a. not an arithmetic blue pentagon.  b. Blue. The colors rotate red, blue, and

sequence b. arithmetic sequence; 2  c. arithmetic purple. Every third figure is purple, so the 21st figure is
purple. The figure just before that is blue.  c. 10 sides;
sequence; - 6 d. not an arithmetic sequence  3a. A(n) =
A(n - 1) + 6; A(9) = 51 b. A(n) = A(n - 1) + 12; figure 23 is in the 8th group of three figures; the number
A(9) = 119  c. A(n) = A(n - 1) + 0.5; A(9) = 11.3 of sides in each group of three figures is 3 + (n - 1);
d. A(n) = A(n - 1) - 9; A(9) = 25  e. Answers may substitute 8 for n.
vary. Sample answer: It depends on which term you are
Chapter Review pp. 283–286
trying to find. If you are trying to find the 2nd or 3rd

term, then yes, a recursive formula is useful. If you are 1. independent variable 2. linear 3. range
4. Answers may vary. Sample:
trying to find the 100th term, then no, a recursive

formula is not useful. 4a. A(n) = 100 - (n - 1)1.75;
$73.75  b. 57  5a. A(n) = 21 + (n - 1)(2) 
b. A(n) = 2 + (n - 1)(7)  6a. A(n) = A(n - 1) + 10  Speed (mi/h)
b. A(n) = A(n - 1) + 3
Lesson Check 1. Add 8 to the previous term; 35, 43. 

2. Multiply the previous term by - 2; 48, - 96. 3. not
an arithmetic sequence 4. arithmetic sequence; 9 
Time
5. A(n) = A(n - 1) - 2, A(1) = 9; A(n) = 9 - 2(n - 1)
6. - 6; the pattern is “add - 6 to the previous term.”  5. Answers may vary. Sample:

7. Evaluate A(n) = 4 + (n - 1)8 for n = 10; A(10) = Distance From
4 + (10 - 1)8 = 76. 8. Yes; A(n) = A(1) + Beach
(n - 1)d = A(1) + nd - d by the Distributive Property.
Exercises 9. Add 7 to the previous term; 34, 41. 

11. Add 4 to the previous term; 18, 22.  13. Add - 2 to
the previous term; 5, 3. 15. Add 1.1 to the previous
Time
term; 5.5, 6.6. 17. Multiply the previous term by 2; 72,
6. C hairs painted, paint left;
144. 19. not an arithmetic sequence  21. not an each time p increases by 1, 140
L decreases by 30;
arithmetic sequence 23. yes; 1.3 25. not an arithmetic L = 128 - 30p. Paint Left (oz), L 100

sequence 27. yes; - 0.5 29. not an arithmetic sequence  Selected Answers 60
31. A(n) = A(n - 1) - 11, A(1) = 99  33. A(n) =
A(n - 1) - 3; A(1) = 13  35. A(n) = A(n - 1) + 0.1; 20
A(1) = 4.6 37. A(n) = 50 - 3.25(n - 1); $11  00 1 2 3 4
39. A(n) = 7.3 + (n - 1)(3.4)  41. A(n) = 0.3 +
(n - 1)(- 0.3)  43. A(n) = A(n - 1) - 5, A(1) = 3  Number of
Chairs Painted, p

i 881

7. Snacks purchased, total cost; 14. Number of Chairs, n 2248 ndiusmcrebteer because the
of trips must
for each additional snack, Total Cost ($), C 30 be a
27
total cost goes up by 3; 24 20 whole number
C = 18 + 3s. 21 16
18 12
15 8
4
Selected Answers 00 2 4 6 8 10 12 14
00 1 2 3 4
Number of Trips, t
Number of
Snacks Purchased, s 15.   40 continuous because t
can take on any
8. I ndependent n, dependent E; Elevation (ft), E 360 35Water Level (in.), nonnegative value
340 30
the elevation is 311 320 25
20
more than 15 times the 15
10
number of flights climbed; 
E = 15n + 311. 5
00 3 6 9 12 15 18 21 24 27
300
00 1 2 3 4 Time (h), t
Number of
Flights Climbed, n 16. y

9. 21 y 10. 14 y 2
18 x
15 10 Ϫ3 O 1
12 Ϫ2
9 6
6
3 2 1 7. V = 243 - 0.2s 18. C = 200 + 45h 19. not a
00 1 2 3 x 00 1 2 3 x function 20. function 21. - 4; 6 22. 53; 33
4 4 23. 57.2, 1.12, - 4.2, - 34.66 24. A(n) = A(n - 1) + 5,
A(1) = 3; A(n) = 3 + (n - 1)(5) 
nonlinear linear 25. A(n) = A(n - 1) - 3, A(1) = - 2;
A(n) = - 2 + (n - 1)(- 3) 
11. y nonlinear 26. A(n) = A(n - 1) + 2.5, A(1) = 4;
A(n) = 4 + (n - 1)(2.5)  27. A(n) = A(n - 1) - 7,
80 A(1) = 18; A(n) = 18 + (n - 1)(- 7) 
28. A(n) = 4 + (n - 1)(3)  29. A(n) = 13 + (n - 1)(11) 
60 30. A(n) = 19 + (n - 1)(- 1) 
31. A(n) = 5 + (n - 1)(- 2)
40
Chapter 5
20

00 1 2 3 x
4

12. 5 y linear

Ϫ5 O x Get Ready! p. 291
Ϫ10 234
Ϫ15
Ϫ20 1. yes  2. no  3. yes  4. y = 1 x + 2  5. y = 3x - 2
Ϫ25 2
6. y = - x - 2  7. boat  8. bean plant 
9. f(x)
13.  5600    ccoannttinakueouosnbaencyause w x f(x)
40 nonnegative value 4
−2 1
30
20Cost ($), C 03 −2 O x
10 25 2
00 1 2 3 4 5 6 7 8
10. f(x)
Weight (lb), w
x f(x)
-1 2 -2 O x
2
00
1 -2 -2

882

11. 2 f(x) 35. 0; yes, because the 4y
slope is 0 and the line 2
x f(x) −2 O 2 x is horizontal. 
−2
0 −4 Ϫ4 Ϫ2 O 2 4 6 8x
2 −2 Ϫ2 Selected Answers

40

12. A(n) = 2 + (n - 1)3  13. A(n) = 13 + (n - 1)(- 3) Ϫ4
14. A(n) = - 3 + (n - 1)2.5  15. the steepness of the line
16. Two lines are parallel if they lie in the same plane and 37. - 0.048352; yes, 6y
do not intersect.  17. A y-intercept is the y-coordinate of because the slope
is approximately –0.05 4
the point where the line crosses the y-axis. and the line slopes
downward from left 2
Lesson 5-1 pp. 294–300 to right.  x
Ϫ40 Ϫ32 Ϫ24 Ϫ16 Ϫ8 O
Got It?  1. Yes; the rate of change is constant.  2a. 2 Ϫ2
Y-e31s,  cb.ecyaeus s3eath. e-s34lo  pe 5
b. 4y
b. is - 4 39. horse; mouse  41. $2050 per month  43. 6  45. 4  47. 3 
3
and the line slopes downward
49a. 5 b. y c. The slope is equal
from left to right. 2 40 to the common
difference.
x

Ϫ4 Ϫ2 O 2 30

Ϫ2

Ϫ4 20

4a. undefined  b. 0 10

Lesson Check  1. Yes; the rate of change between any x
t-o15h  o3r.iz-on35t a4l .chSlaonpgee;.s l5op. e0;is O 2468
two points is the same.  2.
the ratio of vertical change 51. Yes; the slopes from G to H, from H to I, and from G

the slope of a horizontal line is 0.  6. Answers may vary. to I all eaqreunalo12t   53. No; the slopes between all pairs of
points the same.  55. No; the slopes between all
Sample: Both methods give the same result. You need

the graph to count the units of change. You need the pairs of points are not the same.  57. -n
2m
coordinates of the points to use the slope formula. 

7. The student calculated the ratio of horizontal change Lesson 5-2 pp. 301–306

to vertical change, but slope is the ratio of vertical change
12th. ere
to horizontal change; is one bun per hot dog. Got It?  1. yes; - 4   2. y = - 5x ; 75 
Exercises  9. Yes; 1; 5

11. - 2  13. 4  15. 439  1279..1p o1s9it.iv-e;11  22 13.117.0i n2d3e.pe0ndent: 3a. y = 0.166x    0.4 y
25. 0  27. positive;
0.2
number of people; dependent: cost; $12/person 
x
33. 0; yes, because the 4y O 24
slope is 0 and the

line is horizontal.  2 b. 0.38; the slope is the coefficient of the x-term. 
4. yes; y = - 0.75x
Ϫ4 Ϫ2 O x
24 68 Lesson Check  1. yes; 3  2. y = 10x  3. 30 muffins 

Ϫ2 4. yes; y = - 1 x   5. always  6. never  7. sometimes
8. Yes; if q = 2 a direct variation
Ϫ4 kp, then p = 1 q, which is
k
with constant of variation 1k.
Exercises  9. no  11. yes; - 2  13. yes; 37   15. y = - 5x;
- 60  17. y 5 = 2.6x; 31.2
= 2 x ; 30  19. y

Selected Answers i 883

21.   2 y 23.   2y 5a.    y b. y
4
O x Ϫ2 O x x
Ϫ2 2 Ϫ2 2 2 Ϫ4 O 4

Ϫ2 O x Ϫ4
Selected Answers 3
Cost ($) Ϫ8

25. d = 10.56t  d

40 6. y = 35x + 65    Plumbing Repair Cost

20 250
200
O2 t 150
4 100
50
27. yes; y = - 1.5x; check students’ graphs  29. no;
check students’ graphs  00 1 2 3 4 5
31. y = - 20x  Hours

30 y Lesson Check  1. y = 6x - 4  2. y = - x + 1

x 3. y
2
Ϫ2 O 4
Ϫ20
x
Ϫ4 O 4

33. y = 6x  4. Yes; it is a horizontal line with a y-intercept of 5.

y x 5. Sometimes; answers may vary. Sample: y = 3x
6 represents direct variation, but y = 3x + 1 does not.
6 6. Answers may vary. Sample: You can plot points or you

O
Ϫ6

can use the slope-intercept form to plot the y-intercept

and then use the slope to find a second point.

35a. 48 volts  b. 0.75 ohm  37. No; as the rate increases, Exercises  7. 3, 1  9. 2, - 5  11. 5, - 3  13. 0, 4
the time decreases.  39. No; as the number of items you 1 1
15. 4 , - 3   17. y = 3x + 2  19. y = 0.7x - 2
purchase increases, the amount of money you have left
decreases.  41. y does not vary directly with x because 21. y = - 2x + 8   23. y = 2x - 3  25. y = - 2x + 4
5
5 1
y ≠ 0 when x = 0.  43a. 2   b. y = 2 x ; 52 lb  45. -6 27. y = 2 x - 2   29. y = -x + 2 
5 5
31.    33.
47a. c = 3.85g; yes; the constant of variation is 3.85  y y

b. c is about 0.12m  c. about $28.80  49. 165.6

51. 280.50  52. 1  53. 0  54. 6  55. - 35  56. 15  2 x Ϫ2 O x
57. - 11  58. 6  59. - 7 Ϫ2 O Ϫ2 2

Lesson 5-3 pp. 308–314

tGf-hrooe12mtxeqI-lteu?f73at .tt1 ioo2an.r.igoy-hf=12tt,h,32se23xo li-btnh.e1eT chsh3leoaapng.egrTaeohpsfehttoghmreayoplv=inhees-sldsa21honxowtus+nldd323ob-wuenn3it=s; 35. y = 5x + 65    3 7. - 3, 2 
12- 15 
Temperature 39. 9,
41. 9,
Temperature (˚F)
80 43. 2 - a, a 
negative. The slope is 21. b. y = - x + 2  c. No; the 60 45. 2030
40
slope is constant, so it is the same between any two 20
1 7
points on the line.  4. y = 2 x - 2 00 1 2 3 4 5

Hours

884

47a. y = 35x + 50 b. y 6. yes; 1 - 4 = 3(- 2 + 1)  7. Yes; answers may vary.
c. T he amount of time 80 Sample: y - a = m(x - b), y = mx - mb + a,
40 y = mx + (a - mb)
the repair takes and Exercises  9. y - 5
the cost must be O2 x 2 = - 3 (x - 4)
positive.  11. y = - 1(x - 4) 
Selected Answers
13.   y 15. y

24

49.   2 y 51. O y 53. y x x
Ϫ3 O 2 O 48
x Ϫ1 x 16
O1 Ϫ3 Ϫ4
Ϫ5 8
Ϫ2 x 3
4
O2 17. Answers may vary. Sample: y - 1 = - (x - 1)

19–21. Point-slope forms may vary. Samples are given.

55. a1 = - 1, an = an-1 + 4; y = 4x - 5; the common 19. y - 4 = 3 (x - 1); y = 3 x + 5   21. y - 6 =
difference of 4 is equal to the slope of the line in slope- 2 2 2
1 1
intercept form.  57. Answers may vary. Samples: graph - 3 (x + 6); y = - 3 x + 4  23. y = 8.5x; the slope 8.5

the line, determine whether the equation can be rewritten represents the hourly wage in dollars; the y-intercept 0

in the form y = mx + b.  59. -1   61. 3   63. B  65. D  represents the amount earned for working 0 h.
2 4
67. Sometimes true; if a 7 0 then ab 7 ac; otherwise 25. y
x
ab 6 ac.  68. y = 5x; 50  69. y = 2x; 20  70. y = 3x; 30 
O 48

71. t = - 9  72. q = 27  73. x = 7  74. - 3x + 15  Ϫ4

75. 5x + 10  76. - 4 x + 38   77. 1.5x + 18 Ϫ8
9

Lesson 5-4 pp. 315–320 27. Answers may vary. Sample: C - 10 = 5 (F - 50);
15°C  29. b = - 0.0018a + 212; 207.5°F  9
Got It?  1. y + 4 = 2 (x - 8)  2.   2y
3 O
Ϫ4 x
31a. j(x) = 2x - 2; check students’ drawings. 
Ϫ6 4 b. k(x) = 2x + 1; check students’ drawings.  c. Sample

answer: Adding a number to a function changes the

Ϫ8 y-intercept, and the slope remains the same. Adding a

number to the x-value of a function changes the y-intercept

7 and the slope remains the same.
3
3a. y + 3 = (x + 2)  b. They are both equal to Lesson 5-5 pp. 322–328

eyq=ua73txio+n 53o;f you can use any point on a line to write an Got It?  1a. 12; - 10  b. 4; 3   2. y
the line in point-slope form.  4a. Answers 2

may vary. Sample: y - 3320 = 1250(x - 2); the rate at 8

which water is being added to the tank, in gallons per

hour  b. y = 1250x + 820; the initial number of gallons x
of water in the tank O 48

Lesson Check  1. 94; (- 7, 12)  2. y + 8 = - 2(x - 3) 3a.    y b. 2 y
3. y
2
O x x
Ϫ2 2
2x 2 Ϫ2 O
O4
c.    2 y x d. 2 y x
4. Answers may vary. Sample: y + 2 = 2(x + 1) 2 2
5. the slope m of the line and a point (x1, y1) on the line Ϫ2 O Ϫ2 O
Ϫ2 Ϫ2

Selected Answers i 885

4. x + 3y = 0  5a. x + 15y = 60  b. domain: slope and a point, use the point-slope form. When you
nonnegative integers less than or equal to 60; range: have the standard form, it is easy to graph.

{0, 1, 2, 3, 4} 9 41. y
4
Lesson Check  1. 3, - 3x ؊ y ‫ ؍‬6

Selected Answers 2. y 3. horizontal line  x
4. x - 2y = - 6  4
4 5. 10x + 25y = 285; answers Ϫ4 O
؊3x ؉ y ‫ ؍‬6 Ϫ4 3x ؉ y ‫ ؍‬6
2 may vary. Sample: 1 $10 card and

x 11 $25 cards, 6 $10 cards and Two lines have the same slope but different y-intercepts.

O2 9 $25 cards, 11 $10 cards and Two lines have the same y-intercept but different slopes. 
43. The student did not subtract 1 from each side of the
7 $25 cards equation. The correct equation is 4x - y = - 1.

6a. point-slope form  b. slope-intercept form  c. point-slope

form  d. standard form  7. Answers may vary. Sample:

slope-intercept form; it is easy to find the y-intercept 45.   y 47. y

and calculate the slope from the graph. Ϫ8 4 8
4
Exercises  9. 2, - 1  11. - 230, 4  13. 1.5, - 2.5 Ϫ4 O x
Ϫ4 O4
15.   y 17. y x

Ox 2
O2
Ϫ2 2

x 49. y 51. Both functions have a

Ϫ4 Ϫ2 O x y-intercept at (0, 3). Both
Ϫ2 functions have a negative slope.
The first function has a slope of

19.   y 21. y - 3 and the second function has
4
x l6in, e6 th5a7ta.ps4al,ossp-ee58so t5hf r9-o.u12s.gqhua(0re, ;2t)haengdraph
4 x Ϫ6 O 6 53. 1+04, y-=1308  55.
Ϫ4 O of x is a
Ϫ6
(8, 0); the graph of 4x - y = - 1 is a line that passes
Ϫ12 through (0, 1) and (1, 5); the graph of x + 4y = - 12 is a

line that passes through (0, - 3) and ( - 4, - 2); the graph
of 4x - y = 20 is a line that passes through (5, 0) and
23. horizontal  25. horizontal (4, - 4).  61. 4x - y = - 2  63a. 200s + 150a = 1200 

27.   y 29. 2 y b. Answers may vary. Sample: student $1.50 and adult
8
x $6, student $2.25 and adult $5, student $3 and adult $4.
4 2
Ϫ2 O b. Check students’ work.  65. H  67. H

x 69–71. Point-slope forms may vary. Samples are given.
4 5 5 17
Ϫ4 O 69. y + 1 = - 8 (x - 5); y = - 8 x + 8  

70. y + 2 = 4 x; y = 4 x - 2 
3 3
31. 2x - y = - 5  33. 2x + y = 10  35. 2x + 3y = - 3 71. y + 1 = x + 2; y = x + 1 
37. 5j + 2s = 250
Answers may vary. Sample: 50 72. - 2 6 t … 3 
Points jewels and 0 stars, 48 jewels and 5
125 stars, 42 jewels and 20 stars Ϫ2 Ϫ1 0 1 2 3
100
Number of Stars 73. 1.7 … y 6 12.5  0246 8 10 12 14
74. x … - 1 or x 7 3  Ϫ2 Ϫ1 0 1 2 34
75
50
25
75. 2  76. 3  77. 0
00 25 50 75 100
Lesson 5-6 pp. 330–335
Number of Jewels

39. When you have a slope and the y-intercept, use the Got It?  1. y = 2x + 5  2a. Neither; the slopes are not
slope-intercept form. When you have two points or a equal or opposite reciprocals.  b. Parallel; the slopes are

886

ae3Lnqe. dusyasy=lo. =n-36.xCxy-h, e=y1c= -k4 -12a1x.16.+yxyea1s2=n 7b d64.xy.na=oyn =d6cx.y--n=32o2x 6 6+x2.-.1In0y2b;=oyt-h=4cx-as+61esx1,1you b. No correlation; the length of a city’s name and the

population are not related.  2a. Answers may vary. Sample:

compare the slopes of the lines. If the slopes are equal, then Body Length (in.) Body Length of a Panda y = 2.23x + 8.8; about Selected Answers
24.4 in.  b. No; an adult
the lines are parallel. If the slopes are opposite reciprocals, 30 panda does not grow at
25 the same rate as a young
the lines are perpendicular. 20 panda. 
15
Exercises  7. y = 3x  9. y = 4x - 7  11. y = 2 x   10
3 5
00 1 2 3 4 5 6 7 8 9
13. Perpendicular; the slopes are opposite reciprocals. 
Age (month)
15. Parallel; the slopes are equal.  17. Perpendicular; one

line is vertical and the other line is horizontal.  19. y = 1 x  3a. about $9964  b. The slope tells you that the cost
21. y 23. y= - 3 increases at a rate of about $409.43 per year.  4a. There
= - 1 x - 59   1 x + 5   25. y = - 1 x + 4 
5 2 2 2 may be a positive correlation, but it is not causal because
27. a and f; b and d, c and e  29. Sometimes; if the slopes
a more expensive vacation does not cause a family to own
are equal and the y-intercepts are not equal, then the lines a bigger house.  b. There is a positive correlation and a

are parallel.  31. 2; the common difference of an causal relationship. The more time you spend exercising,

arithmetic sequence represents the slope of the linear the more Calories you burn.

graph. Since the graphs of the sequences are parallel, Lesson Check 

their slopes must be equal. 

33. x = 3  35. y = - 100x + 600, y = - 100x + 1000; 1. Average Maximum Daily Temperature
parallel; the slopes are the same.  37. No; the slope of
in January for Northern Latitudes

segment PQ is 2, the slope of segment QR is - 1, and the 70 negative correlation 
1 60
slope of segment PR is 2 . No two slopes are opposite Temperature (؇F) 50
40
reciprocals, so no angle of the triangle is a right 30
20
angle.  39. G 10
0 25 30 35 40 45
41.   y 42. y
Latitude (؇N)
2

4 Ϫ2 O 2 x 2–3. Answers may vary. Samples are given. 

x 2. y = - 2x + 120  3. about 20°F  4. You use interpolation
O 48

to estimate a value between two known values. You use

43. 3y 44. y = 3x - 2  extrapolation to predict a value outside the range of the

45. y = 0-.252x5x+ +2591 .875  known values.  5. Both the trend line and the line of best
46. y =
fit show a correlation between two sets of data. The line

47. y = - 470x + 660 of best fit is the most accurate trend line.  6. If y decreases as x
7
Ϫ6 Ϫ4 Ϫ2 O x decreases, then there is a positive correlation because a
Ϫ2
trend line will have a positive slope.

Exercises  7. Jeans Sales

Lesson 5-7 pp. 336–343 120 Number Sold
100
Got It?  1a. Gasoline Purchases positive correlation 80
3 60
40
Gallons Bought 2 20

1 0 0 5 10 15 20 25 30 35 40
Average Price ($)

negative correlation 

0 0 2 4 6 8 10 12 14
Dollars Spent

Selected Answers i 887

9. Answers may vary. Sample: Exercises  7. It is a translation of y = 0 x 0 left 4 units.
9.   11. 5 y
Attendance at y = 5x - 9690; y
about 335 million
U.S. Theme Parks
Selected Answers Ϫ1O 1 x
Attendance (millions) 350
325 2
300
275 Ϫ4 Ϫ2 O x
250 2

0 1996 2002 2008 13. 10 y
1990 Year 4

11. y = 21.4x - 41557; 0.942; 1542.6 million tickets
13. no correlation likely  15. There is likely a correlation

and a possible causal relationship, because the higher the Ϫ4 O 4 x

price of hamburger, the less people are likely to buy.  15.   y 17.   3 y
17. Check students' answers.  19. about 7 cm 
21a. y = 10.5x + 88.2  b. 10.5; the sales increase by 2 x
about 10.5 million units each year.  c. 88.2; the estimated 3
number of units sold in the year 1990  23. A  25. D x
O 24
27. y = 5x - 13  28. y = -x + 5  29. y = - 2 x + 130   O1
30. 5  31. 0  32. 18  33. 12 3

Lesson 5-8 pp. 346–351 19. y 21. $0.78 y

Got It?  1a. The graph is the graph of y = 0 x 0 6
2 $0.61 Cost
translated 4 units up.  b. The domain of both graphs is all
O2 6 x $0.44
real numbers. The range of y = 0 x 0 is y Ú 0. The range of
y = 0 x 0 - 2 is y Ú - 2. x

2. 0 123

y Weight (oz)

Ϫ4 O 4 x 23.   y x 25. O y
2
Ϫ2 O Ϫ1 1 3x
Ϫ4
Ϫ2 Ϫ3

Ϫ8

3. y Buses4. 5 y 27. y = - 0 x + 2.25 0   29. y = - 0 x - 4 0  

4 4 31. (- 1, 3)
3
2 2 33. 4 y uItpis2autnraitnssalantdionrigohft y = 0x0
x 1
x 1 unit.
O 24 6
0 50 150 250 2

Students x
2
Lesson Check  1. y = 0 x 0 - 8 is y = 0 x 0 translated Ϫ2 O

8 units down; the graphs have the same shape.  35a. y b . (2, 3)  c. The x-coordinate is
the horizontal translation and
2. y = 0 x 0 + 9 4 the y-coordinate is the vertical

3. y 4. The graphs have the 2 translation; (h, k).
8
same shape; y = 0 x 0 - 4 x
is y = 0 x 0 translated 4 units
4 down and y = 0 x - 4 0 is O 24
Ϫ8 Ϫ4 O y = 0 x 0 translated 4 units right. 
x 37. Graph of y = - 0 x + 4 0 - 7 is a V-shaped graph

opening downward with the left side going through

( - 6, -9) and ( - 4, - 7) and the right side going through
( - 4, -7) and ( - 2, - -3
5. The student should translate the graph 10 units to 9).  39. 8   41. 1
the right. 2

888

42–43. Answers may vary. Samples are given. 35a. Heights and
Arm Spans
42. y = 0.25x + 5.05  43. y = 12.5x

44.   y 45. y 2.0

2 x 4 Arm Span (m) 1.8 Selected Answers
Ϫ2 O 2 2 1.6
Ϫ2 O
x 1.4
3 00 1.5 1.7 1.9 2.1
Height (m)

46.   3y 47. y b–d. Answers may vary. Samples are given.
b. y = 0.96x - 0.01  c. about 1.5 m  d. about 2.1 m
x
x Ϫ4 O 4 36.   y 37. y
2
Ϫ2 O Ϫ8 x
Ϫ12 Ϫ4 O 4
1 x
Ϫ2 O 2

Ϫ8

Chapter Review pp. 353–356 38.   y 39. y

1. interpolation  2. rate of change  3. point-slope form 1 4
Ϫ4 Ϫ2 O 2
4. opposite reciprocals  5. line of best fit  6. - 1  7. 0  8. 3 x
O 2 4x
9. undefined  10. 3  11. - 21  12. y = - 2x; - 14 
5 35 1 7
13. y = 2 x; 2   14. y = 3 x; 3   15. y = - x; - 7  16. no 

17. yes; y = - 2.5x  18. y = 4  19. y = x - 5  40. y
2
20. y = 3 x + 1  21. y = -x - 1 30

22.   y 23. 3 y 20

2 x 1x 10
x
Ϫ2 O 2 Ϫ2 O 2
0 2000 4000 6000 8000
Ϫ2

24.   y x 25. y Chapter 6
3
O1 2 Get Ready! p. 361
Ϫ2
O 2468 x 1. identity  2. 1  3. no solution  4. 3  5. 1.5  6. no solution
Ϫ4
7. x 6 3  8. r … 35  9. t 7 - 13  10. f Ú - 2  11. s 7 5
12. x Ú - 18  13a. 2x 23
c. 248 cm2  - 1  b. A = 1 x (2x - 1) 
2
26. y = 5x - 11  27. y = 9x - 5  28. Parallel;
the slopes are equal.  29. Neither; the slopes are not
-op18pxo+sit22e1 re3c2ip. rnoecgaalst.i v3e0c.oryre=la13tixon+ 4  14. 3 y
equal or
31. y = 1 x
O1 3
33. no correlation  34. positive correlation 

Ϫ3
Ϫ5

Selected Answers i 889

15. 4y 16. 1 y x 39. b = 25.t5 t + 40  ; 16 weeks
2 3 b =
Ϫ2 1
41a. Sometimes; if g 7 h, the lines intersect at one point,
x Ϫ3 but if g = h, the lines never intersect.  b. Never; if g 6 h,
Ϫ3 O 1 3 the lines intersect at one point, but if g = h, the lines
Selected Answers Ϫ2 never intersect.  43. A  45a. C = 20, C = 2.5h + 5 

17. inconsistent  18. deletes b. 6 h c. Garage A; it costs less for the time given.

46.   3y 47. y

Lesson 6-1 pp. 364–370 1x
Ϫ3 1 3
Got It?  1. (- 2, 0)  2. 5 months  3a. no solution 1x
b. infinitely many solutions  c. Systems with one solution Ϫ3 O 1 3 Ϫ2

have lines with different slopes. Systems with no solutions

have the same slope but different y-intercepts. Systems 48. y 49. 3y

with infinitely many solutions have the same slope and Ϫ5 Ϫ3 1x Ϫ5 Ϫ3 1x
O1 O1
the same y-intercept.

Lesson Check  1. (6, 13)  2. (16, 14)  3. (- 1, 0) 
4. (- 1, - 3)  5a. c = 10t + 8;  c = 12t  b. (4, 48); the
cost is the same whether you buy 4 tickets for a cost of

$48 online or at the door.  6. A, III; B, II; C, I  7. No; a 50. 1  51. - 1   52. - 2   53. 35   54. y = - 2x + 19
2 3
solution to the system must be on both lines.  8. No; two 3 8 1 14
55. y = - 2 x + 15  56. y = 15 x   57. y = 3 x - 3
lines intersect in no points, one point, or an infinite

number of points.  9. The graphs of the equations both Lesson 6-2 pp. 371–377

contain the point (- 2, 3). Got It?  1. ( - 8, - 9)  2a. 17 13, - 4 7 2  b. x; x + 3y = -7
Exercises  11. (4, 9)  13. (2, - 2)  15. (- 3, - 11)  9
17. (- 1, 3)  19. 27 students; 3 students  21. 10 classes  3. 5 new games  4. infinitely many

23. no solution 25. no solution Lesson Check  1. 125 151, 6 4 2   2. (3, 5)  3. no solution
11
y 2y 4. no solution  5. 7 singing, 5 comedy  6. Answers may

4 vary. Sample: Graphing a system can be inexact, and it is
1
very difficult to read the intersection, especially when
2
there are noninteger solutions. The substitution method is
x Ϫ2 Ϫ1 O 12 3 x
4 Ϫ1 better, as it can always give an exact answer. 
Ϫ4 Ϫ2 O
7. - 2x + y = - 1 because it is easily solved for y. 
Ϫ2 Ϫ2 8. 6x - y = 1 because it is easily solved for y.  9. False; it

has infinitely many solutions.  10. False; you can use it,

Ϫ4 but the arithmetic may be harder.

11. 13. 75, 2 15. (3, 0)
( )Exercises  (2, 6)  1- 2 7 2 

27. infinitely many solutions 29. infinitely many solutions 17. (- 11, - 19)  19. (- 12, - 5)  21. 0, - 1
2
y
y 23. 2 children, 9 adults  25. 18°, 72°  27. infinitely many

2 solutions  29. infinitely many solutions  31. one solution 

2 2x 33. Solve 1.2x + y = 2 for y because then you can solve
Ϫ2 O the system using substitution.  35. The student solved an
Ϫ4 Ϫ2 O x Ϫ2
Ϫ2 24 equation for x but then substituted it into the same

equation, not the other equation.

x + 8y = 21, so x = 21 - 8y
7(21 - 8y ) + 5y = 14
Ϫ4

147 - 56y + 5y = 14
  -51y = -133 
31. 13 h  - 133 31
33. You should substitute the values of x and y into both = - 51 = 51
( )y 2
equations to make sure that true statements result. 
35. No solution; the lines have the same slope and So, x = 21 - 8 2 31 = 21 - 1064 = 7
51 51 51
different y-intercepts so they are parallel.  ( )The solution is
37. Infinitely many solutions; the lines are the same. 571, 2 31 .
51

37. 20 more girls  39. 2.75 s  41. Answers may vary.

890

Sample: Solve the first equation, y + x = x, for y, so 33. (2, 0); answers may vary. Sample: Substitution; the Selected Answers
y = x - x = 0. But the second equation is not defined for first equation is easily solved for y.  35. (6, 5); answers
y = 0; therefore, there is no solution.  43a. 25 s after Pam
starts, 26 s after Michelle starts  b. Yes; 26 s after Michelle may vary. Sample: Substitution; the first equation is
starts, both runners will be at 195 m. Pam, who is running already solved for y.  37. (6, - 4); answers may vary.
at a faster rate, will go on to win. Sample: Elimination; you can multiply each equation by the

LCD of the denominators to eliminate the fractions. Then you

Lesson 6-3 pp. 378–386 can use elimination.  39. parasailing: $51; horseback riding:
( )$30  41.
Got It?  1a. (2, 7)  b. (- 1, - 2)  2. car: 20 min; truck: 2, 1   43. (5, 3, - 1)  45. 7  47. 5.46 
30 min  3a. Sample answer: You can multiply the first 2
49. 390  50. (7, 3.5)  51. (34, 27)  52. (5, - 3)  53. a 7 1 
54. x Ú 7  55. b 7 0.2  56. 2.75 h
equation by 3 to eliminate the y.

b. Sample answer: - 15x - 6y = 18; ( - 2, 2) Lesson 6-4 pp. 387–392
3x + 6y = 6
c. - 5(- 2) - 2(2) = 6; 3(- 2) + 6(2) = 6 Got It?  1. 720 books  2. The tanks will never have the

10 - 4 = 6 - 6 + 12 = 6 same amount of water because the solution to the system

4a. Sample answer: You can multiply the first equation by is ( - 2, 14), which is not a viable solution because it is not
possible to have time be - 2 hours.  3a. 3.5 mi/h; 1.5
3 and multiply the second equation by - 4 to eliminate x. mi/h  b. You will be pushed backward.
12x + 9y = - 57 ; 
b. Sample answer: - 12x + 8y = 40 (- 4, - 1) Lesson Check  1. 300 copies  2. 1 kg of 30% gold,

4(-4) + 3(- 1) = --1199 and 3(- 4) - 2(- 1) = - 10 3 kg of 10% gold  3. 2.25 mi/h; 0.75 mi/h  4. Before the
-16 - 3 = - 12 + 2 = - 10
c. break-even point, expenses exceed income. After the

5. no solution break-even point, income exceeds expenses.  5. Answers

( )L4e. sEslimoninaCthioenc;kth  e1.o(b2j,e3ct)i v2e.o(f1,th4e) e3li.mi2n75a,t-ion225m ethod may vary. Sample: elimination; neither equation is easily

solved for a variable.  6. You would need more of the

is to add (or subtract) two equations to eliminate a 15% brand, since 25% is closer to 15% than 40%.
variable.  5. The Addition Property of Equality says that
Exercises  7. 40 bicycles  9. $950 at 5% and $550 at 4%;

adding equals to equals gives you equals. This is what you Let x represent the amount of money invested at 5% and
are doing in the elimination method.  6. Answers may
vary. Sample: Decide which variable to eliminate, and then let y represent the amount of money invested at 4%. The
multiply, if necessary, one or both equations so that the
coefficients of the variable are the same (or opposites). solution to the system is (950, 550). 
Then subtract (or add) the two equations. This will result
in one equation with a single variable that you can solve. 11. 4 ft/s; 2 ft/s 
Then substitute to find the value of the other variable.
13a. Let x = the number of pennies and let y = the
number of quarters.

x + y = 15
0.01x + 0.25y = 4.35
The solution is 17.5 quarters and - 2.5 pennies.
Exercises  7. (4, 5)  9. (1, 5)  11. (3, 15)  b. No; you cannot have a negative number of coins.

13a. 12x + 2y = 90 b. solo act: 5 min; 15. (- 3, - 2); substitution because the second equation

       6x + 2y = 60 ensemble act: 15 min is already solved for y  17. A = - 3 and B = - 2.

15. (3, 1)  17. (5, 3)  19. (2, - 1)  21. no solution  19–21. Answers may vary. Samples are given.
23. one solution  25. infinitely many solutions  27. $12; $7
19. Substitution; both equations are already solved for y,
29. The student forgot to multiply the constant in the
so you can set them equal.  21. Substitution; the second
second equation by 4. emsoqilxuvteaudtrioeb;ny1its3h3ael31reemlaimdLyinosafottlivhoeend6mf.o5er%thyo. md2ixb3te.uc6rae6u  23s2e5mt.hLIetocvfaatnrhiaeabl5sloe%sbe

15x + 12y = 6
12x + 12y = - 12
so, 3x = 18  are lined up and the coefficients of the y-terms are the
x=6
31. Answers may vary. Sample: same. So one would simply have to subtract the second

3x - 2y = 7 equation.  27. 37  29. C  31. The slope of the line is
-
5x + 2y = 33 3 - 1 = 2. So y - 1 = 2(x - 3), or y - 1 = 2x - 6. The
4 3
equation of the line passing through the points (3, 1) and
Because the coefficients of the y-terms are already
(4, 3) is y = 2x - 5.  32. (- 7, 6)  33. (- 2, - 2) 
opposites, simply add the two equations to get 8x = 40, 34. (4, 2.5)  35. a 7 5  36. d … - 2.5  37. q … - 4
or x = 5. Substitute x = 5 into either equation to get
y = 4. The solution is (5, 4).
Lesson 6-5 pp. 394–399

Got It?  1a. yes  b. No; it could be on the line y = x + 10.

Selected Answers i 891

2. y 23. 3y 25.   1y x
O1 3
2 x Ϫ3 1 x Ϫ3
Ϫ4 Ϫ2 O 24 O1 3
Ϫ3
Selected Answers Ϫ2 Ϫ3 Ϫ5
Ϫ7
3a. 3 y b. 3y

1x 1x 27. y 29. 1 y x
Ϫ7 Ϫ3 O 1 Ϫ3 O 1 3
O1 3 5
Ϫ2 Ϫ3
3
4. Answers may vary. Sample: C Ϫ3
0 lb of peanuts and 3 lb of 3 1x Ϫ5
cashews; 6 lb of peanuts and 0 Ϫ3 O 1 3 Ϫ7
lb of cashews; 1 lb of peanuts 1P
and 1 lb of cashews O1 3 5 7 31. 9x + 12y Ú 120 Answers may vary. Sample:
y 4 lb of cod and 12 lb of
5Le. sys7on31 flounder; 10 lb of cod and
x-2 1. no 12 10 lb of flounder; 12 lb of
Check 
8 cod and 4 lb of flounder 
2. 5 y 3. y
3 4
Ϫ5 Ϫ3
3 1 00 4 x
O1 8 12 16
1x x
Ϫ3 O 1 3 3 r3e3p.reyse7n32tsxt-he3n  u3m5.be2r5o0fx + 475y … 6400, where x
refrigerators and y represents
Ϫ2
the number of pianos

4a.linye6ar21exqu-at1io  n5.aAndnsawleinresawr iilnl evaqruya. lSitaymaprelec:oTohredisnoalutetsioonfstohfe y

points that make the equation or inequality true. The graph of 15

a linear equation is a line, but the graph of a linear inequality 10
is a region of the coordinate plane.  6. Since the inequality is
already solved for y, the 6 symbol means you should shade 5
below the boundary line. All of these shaded points will make
the inequality true.  7. y Ú 5x + 1 00 x
5 10 15 20 25 30

Exercises  9. solution  11. solution  13. solution Yes; the point (12, 8) is not in the shaded region.
37. The student graphed y … 2x + 3 instead of
15.   3y 17. 1y y Ú 2x + 3. The other side of the line should be shaded.
O1
Ϫ3 1 Ϫ3 x 5y
O1 3
Ϫ2 x
3 Ϫ3 3
Ϫ5
1x
Ϫ3 O 1 3

19. 3 y 3 21.   3y x 39. - 5x + 1.5y Ú - 10, where x is the number of CDs
3 bought and y is the number sold; actual solutions include
1 7 x Ϫ3 1 only points representing whole numbers of CDs bought
O1 O1 and sold. The graph is a line in the first quadrant; passing
Ϫ2 through (2, 0) and (5, 10) and is shaded to the left. 
Ϫ3 41. The slope must be negative; in order for the point
(3, 2) to be above the line and the point (1, 2) to be
below the line, the boundary line must be sloping

892

downward. If the line had a positive slope, sloping Exercises  7. yes  9. no
upward, then the point (1, 2) would be above the line
and would satisfy y 7 mx + b, which is not what is 11. 6y 13. y
given.  43. G  45. 96 days 
4 3
46. 2 6 x … 7 
2 x 1 x Selected Answers
Ϫ3 Ϫ1 0 1 3 5 7 4 O1
Ϫ3 O 3
47. one solution: (- 6, - 9)  48. one solution: (2, 0) Ϫ2
49. no solution

Lesson 6-6 pp. 400–405

Got It? 2a. y 6 - 1 x + 1  15. y 17. y
1. y 2
1
y … 2 x + 1  5 3
3
3 b. No; the red line is dashed 1x
Ϫ3 O O 357
1 so points on that line are Ϫ2
Ϫ2 O
x not included in the
Ϫ2 35
solution. x
3

19. y 21. 5 y

3. y 2x + 2y … 126, 1 x3
x … 50, y Ú 10  Ϫ2 O 1
70
y
50 51 x

30 Ϫ3 O1 3 5 7

10 30 50 x 23. y… x + h2o,uyrs6d-riv31exn  25. y Ú 2, y 7 x + 1
00 10 70 27. Let x = by slower driver, let y

Lesson Check  1. = hours

driven by faster driver.

10 y

1x 8
Ϫ3 O 1 3
6
Ϫ2

4

2

2. y Ú 3x + 3  3. y 00 2 4 6 x
y 6 -x - 2 8 10
6

4 29a. y b . No; they have the same
slope and different
2 3 y-intercepts, so they will

00 2 4 x Ϫ3 O x never intersect.  c. no 
6 3 d. No; there are no points

4. You can substitute the ordered pair into each inequality that satisfy both
to make sure that it makes each true.  5. Not necessarily;
Ϫ3 inequalities.
as long as there is some overlap of the half-planes, then
the system will have a solution.  6. You need to find the Ϫ5

intersection of each of the two systems, but the intersections 31. You can buy 5 T-shirts and 1 dress shirt or 2 T-shirts
and 3 dress shirts.  33. C  35. Check students’ work. 
of lines will be a point or line and the intersections of 37. The graph shows two lines, one passing through (1, 1)

inequalities will be a line or a planar section.

Selected Answers i 893

and ( - 1, - 1) and the other passing through ( - 1, 1) and 32. y
(1, - 1). Four triangles are formed by these lines; upper,
left, and lower ones are shaded. Right triangle is not 16
shaded.
12

Selected Answers Chapter Review pp. 408–410 8

1. inconsistent  2. elimination  3. system of linear 4

equations  4. (- 8, - 11)  5. (- 2, 6)  6. (- 3, - 3)  7. no 00 4 x
134, 35 8 12 16 20
solution  8. 1- - 3 2   9. infinitely many solutions

10. 4 yr  11. The lines will be parallel.  12. (4, 7)

13. (3, - 10)  14. no solution  15. (- 1, - 2)  16. infinitely Chapter 7
1171, 188
many solutions  17. 1- - 17 2   18. $55  19. no Get Ready! p. 415

solution 20. (- 1, 13)  21. (- 11, - 7)  22. (5, 12) 
23. (4.5, 3)  24. infinitely many solutions  25. small 1. 0.7 2. 6.4 3. 0.008 4. 3.5 5. 0.27 6. 49 7. 5.09 
8. 0.75 9. 4 10. 16 11. 4 12. 2000 13. - 147 
centerpiece: 25 min, large centerpiece: 40 min 14. 100 15. 49 16. 117 17. - 31 18. 33% increase 
19. 25% decrease 20. 17% decrease 21. 5%
26. y 27. 2 y increase 22. { - 8, 0, - 24.5} 23. {18, 10, - 32.875} 
24. { - 11, - 1, 16.5} 25. yes; how quickly the plant
13 x grows 26. The quantity would increase rapidly. 
O 24 27. decreasing
11

9 Ϫ2

7 Ϫ4

5 Lesson 7-1 pp. 418–423

Got It?  1a. 614   b. 1  c. 91   d. 1   e. 116   2a. 1   b. n3 
6 x9

1x c.  4 b   d. 2a3  e. 1   3a. 1   b. - 1   c. 1   d. - 5  
O1 3 5 7 c m2n5 16 50 15,625 2
3

e. It is easier to simplify first. That gives you,1 * 1 = 1.
4. 600 represents the number of insects 2 weeks before
28. y 29. y
the population was measured; 5400 represents the

1 x population when it was measured; 16,200 represents
1 3
Ϫ5 Ϫ3 5 the number of insects 1 week after the population

3 was measured. 2

Ϫ3 5Le. s-s2o n6.C81h e7c.kd i1vi.si3o12n  28.. 1, m ≠ 0 3. 5s   4. 4 x3
b0 is t
1x equal to 1, not 0;
Ϫ5 O1 3 5 7
xn = a nx n = a nxn
Ϫ7 a-nb0 1 19  11. 215  13. 116  15.
Exercises 9. - 1 17. 1 19. 0.4

or 4  21. 4a, b ≠ 0 23. 5  25. 91n  27. 3   29. 1
9 x4 x 2y c 5d 7

30. y 31. y 31. 4s3 33. 6 , d ≠ 0  35. t7  37. - 217 39. - 225
3 ac 3 u11
1x Ϫ3 4 2815 45.
O1 3 5 7 1 41. 5  43. 100; there were 100 visitors 4 months
1
Ϫ3 before the number of visitors was measured. 
47. negative 49. negative 51. 10-1 53. 10-3 
Ϫ5 x 55a. 5-2, 5-1, 50, 51, 52  b. 54  c. an 57. 4gh-3 
3

Ϫ3 59. 8c 5d-4e 2  61.
11
n 3 1 7 5 2
6 8

n؊1 1 6 1 8 0.5
3 7 5

63. Answers may vary. Sample: Let a = 23, then
a-1 3 a2 49 , a-2 49 . 65.
= 2 , = and = No; answers may

894

vary. Sample: 3x-2 = 3 which is not the reciprocal of 3x 2. 3cL.ea5s.4s30ao430nb33mC  52h7.e acbbko. u116t1.z14n. 11c82. 5921g*.8b 112401 a130. .8jo81u1ylea2s20  o4bf..e88n1e1xrcg210y6
x2 5. 1.6 * 1011 6. 3.2 * 10-14  7. Answers may vary.

67. 21 69. 8 - 48m2 71. - 1 and 1 73. 1 75. 4.5 77. 4

78. y 79. 3 y

5 Sample: When you raise a power to a power you multiply Selected Answers

Ϫ2 O x the exponents. When you multiply powers with the same
2
base, you add the exponents.  8. The second student;
x
Ϫ3 O 2 Ϫ3 when you add like terms you add the coefficients and
Ϫ2
keep the same variable part.  9. Answers may vary.
( )Sample: x2, (x3)32, x52 5, (x5)52
1
80. 3y 81. y = - x + 4  Exercises 11. n32  13. x 4 15. x3  17. z 1  19. c 1
82. y = 5x - 2  2 3
10

x 83. y = 5952-xx13+1-x133-  21. x1  23. 1   25. 61g2 27. 1  29. y 19   31. 32j 35k11
2 84. y = 12 49a2 8y73 3
= 1
Ϫ4 O 85. y 17  m3 z 2
Ϫ2
33. j32  35. 1.024 * 1013  37. 8 * 10-9 
86. y = 1.25x - 3.79  32k26

87. 60,000  39. 2.56 * 1022 41. 1.3312053 * 1025

88. 0.07  89. 820,000 90. 0.003 91. 340,000 43. 4 45. 6   47. - 1  49. - 2 51. - 3 53. 243x3
7 8

Lesson 7-2 pp. 425–431 55. b23 57. - 8a5b4 59. 0 61. 9 63a. The student did
not simplify the expression inside the parentheses first. 
Got It?  1a. 89  b. (0.5)-11  c. 95  2a. 15x14 
12j 3 b. 25  65. yes; (7xyz)2  67. 3  69. 1  71. 4  73. 10; (2x)4,
b. - 56cd 2  c. k2   d. Since they have like bases,
( ) ( )(4x2)2, (16x4)1, (-2x)4, (-4x2)2,
# #you keep the same base and add the exponents; ( ) ( ) ( )116x4 1, 1 -2 21x -4, 14x2 -2,
- 4x 2
x a x b x c = x (a+b+c)  3. 6.7 * 1030 molecules of 1 -4,
- 2x

water 4a. 2 b. 3 c. 8  5a. 125 b. 9  c. 8 6a. 4c 4   Lesson 7-4 pp. 439–445
5

b. n 5   c. b c10 13   d. 441j 5 m 7
3 10 6 4
9
k5 mba85i lee .3ya4.z17x66  
Lesson Check 1. 812 2. 6n1127 3. 2.4 * 1010 4. 39,900 Got It?  1a. y 1   b. d 1   c. j3   d.
km  5. No; x and y are not like bases and they do not 2. about 169 4 2
share a common factor. 6. Sometimes; if the product ab
people per square b. Answers

is greater than 10, then the number will not be in may vary. Sample: You can simplify within the parentheses

scientific notation. 7. No; 4 * 3 = 12 and 1 + 1 = 7 so first to give you 1 2a-147 4 = a-17 or you can raise the
the correct result is 12a170. 2 5 10 ( )quotient to a power first,
a3 = a-17.  4. 25b2
a20 a2
Exercises 9. ( - 6)19 11. 29 13. ( - 8)0
y3 - 240m3 Lesson Check 1. 1  2. x12  3. n3  4. 625y16  
15. 5c10 17. x 19. r   21. 8.84 * 107 mi  y7 27 m3 81x 8

23. 5  25. 83 .4227.*1160,33484m  o2l9e.cu1l9es6 d373g937. 23.17.*9 1303-8.  21  5. 27 cubes 6. In raising a quotient to a power, the
35. 1
6  37. exponent goes to all the factors of both the numerator and

( )41. 8 * 10-8 43. 1a 45. - 12x 6 + 40x 4 47. 34  the denominator and in raising a product to a power, the

49. (2x+y) 345  51. (t + 3)65 53. 22.5 times 55. H  exponent goes to all the factors.
#7a. Answers may vary. Sample: g3 can be rewritten as
57. H 59. (3, 2)  60. (- 4, - 5)  61. (4, 7)  62. 18, 34, 46  1 , so g3 = 1 1 .
1 g-3 g7 g7 g-3
63. - 1, 7, 13 64. - 6.8, - 22.8, - 34.8  65. 16  66. 5x  2m4
67. 4n2 - 3x 3z 6 Exercises 9. 13 11. 0 13. 3 15. n3 17. y 2 19. n4
m  68. y2 t11 3b7
27m2 a6c 8
Lesson 7-3 pp. 432–438 21.  23.  25. 4 * 10-5 27. 4.2 * 103

Got It?  1a. p20   b. p20  c. p18  d. p18  e. yes; 29. 7 * 10-3 31. about 4.4 * 10-2 deer per acre 25y 8
9 81x 4 216 262,144 5 49x3
33. 64  35. y4  37. 15,625  39. n30  41. 2  43.
1
(am)n = amn = (an)(m)  2a. x22   b. w3  c. s4

Selected Answers i 895

s4h5o.u2lxd5 b4e7r.abis3e1d 4to9t.h5e3fsohuortuhldpboew1e2r 5a.n d51sim. Epalcifhiefda.ctor 104. (- 4, - 7)  y

53. The base d should only appear once. Ϫ4 Ϫ2 O x
Ϫ2 4
55a. about 1636 h  b. about 31 h  57. dividing powers

Selected Answers with the same base, definition of negative exponent

59. raising a power to a power, dividing powers with the
da1e9 fi6n7iti.o2yn1x05o f6n9e.gAatnivswe eerxspmonaeynvta r6y1. S. a1m61mp8le  s
same base, Ϫ6

63. a4 65. 105. (3, 5)  y
are given. 4

( ) ( ) I. 3 -3 = x2 3 Rewrite using the reciprocal.
x2 3

= (x 2)3 Raise the numerator and 2 x
33 denominator to the third 24
Ϫ2 O
power. Ϫ2

= x6 Simplify.
27
( ) y
II. 3 -3 = 3-3 Raise a quotient to a power 106. no solution  
x2 rule
1 x 2 2 -3

= 3-3 Power to a power rule 6
x-6
x6 4
= 33 Definition of negative
exponent 2
x
= x6 Simplify. Ϫ2 O 2 y
27 4
( ) ( ) III. 107.  4 y 108. 
3 -3 = x2 3
x2 3 Rewrite using the reciprocal. 2
# # x
= x2 x2 x2 Definition of an exponent 2
3 3 3 Ϫ2 O 2
x6 x
= 27 Simplify. Ϫ2 O 2

71. x6  73. 2  75. c6  77. y6 2  79. about 3 1 m Ϫ4
9y 8 27 a18b6 256x 3 Ϫ5

81. x = 7 and y = 4; use the two given expressions to
find the system of equations, x - y = 3 and
x - 3y = - 5. Solve the system to find the values
( ) ( )of x and y.  83. 109.  3 y 110.  y
m 7 85. 3x 3  87a. a-n  b. 1 2
n 2y an
a0
c. Since an equals both a-n and 1 , a-n must equal 1 , Ϫ2 O x Ϫ2 O x
an an Ϫ2 2 Ϫ2 2
which is the definition of a negative exponent.

89. n4x  91. 1   93. About 1.6 * 106 g/m3  95. H 
m3
97. The domain is 0 … b … 8 because you can use
between 0 and 8 bags. The range is 0 … A(b) … 9600
because A(0) = 0 and A(8) = 9600. Lesson 7-5 pp. 448–452

98. 8m2 99. 2s6   100. 2c 1   101. 9r 1   102. n15 Got It?  1a. 3  b. 2 c. 4  d. 6  2a. 26 a5  b. 5 23 x
27 3 2
23 2y2 
103. (0, 0)  3y c.  9 3a. s 23   b. 12x 4   c. 32y 5   d. 256a2 4. about
3 2

1868.1 Calories per day

x Lesson Check 1. 2  2. 3  3. 625  4. x12  5. 25 c 6. 4 23 d2 
Ϫ2 2
7. 2y 3   8. Sbaomthpl2e7aannswd eyr.:TThheereefxopreonthenetra23dniceaeldsshotoulbdebe
4 to

applied
Ϫ3 written as 23 (27y)2and then simplified to 9 23 y2. 

896

9. Sample answer: To multiply two radicals with the same be negative. 7. The student did not use the order of

radicand, first rewrite the expression in exponential form. # #operations correctly. You must evaluate the exponent1 3
(- 1) = 3 4-1 = 4 4
Then add the exponents.  10. Sample answer: No; before you multiply: f the x-values have 3 = .
Exercises 9. Linear; a
243 - 24 = 6 common

Exercises 11. 7  13. 5  15. 6  17. 23 a2  19. 25 2x  difference of 1 and the y-values have a common difference Selected Answers

21. 5 2x  23. 7 22d  25. 4 23 (3c)2  27. 4c2  29. 4x23  of 3.  11. Linear; the independent variable x is not an

31. 5y34  33. x34  35. $6062.20  37. 24 x5  39. 2c 26 d5  exponent.  13. Linear; the independent variable x is not an
exponent. 15. 12.5 17. - 3.44 * 1010 
19. 4800 foxes
41. 42x  43. b23 - b13  45. 2b35 - 4a43  47. y  49. about
21. y 23. 2 y
1.17 in.  51. 3 2x3 = 3x23; yes; 4x23 + 3x23 = 7x32 ; yes, x
2 x
7x23 = 7 2x3  53. $7.15  55. C 57. 7s23  58. 5t6  Ϫ2 O Ϫ2 O 2
59. - 32x20  60. - 6  61. 27d32  62. - 12c2  Ϫ2

63. 100a6  64. - 4y8  65. 9t23  66. 4x - y = - 7 
67. 2x - y = 13  68. 7x + 6y = 12 
69. 6x - 3y = - 17  70. x - 6y = 3  25. y 27. y
71. 9x - 36y = - 108  72. Add 3; 12, 15, 18. 
73. Subtract 6; - 8, - 14, - 20.  74. Increase the 2 x 2
1 1 1 4 x
denominator by one; 5 , 6 , 7 .  75. Add 5; 17, 22, 27.  O2
O 24

76. Subtract 4; - 9, - 13, - 17.  77. Take next perfect 29. 1600 y
square; 16, 25, 36.

Lesson 7-6 pp. 453–459 1400

Got It?  1a. Linear; the x-values have a common 1200 x
Ϫ2 O
difference of 1 and the y-values have a common difference 2
of 2.  b. Yes; the independent variable x is an exponent.
2. 14,580 rabbits 31. about 1.34 and about - 2.96
33. {0.16, 0.4, 1, 2.5, 6.25, 15.625}; increase
3a.  y b. 1 y
x 35. {0.3125, 1.25, 5, 20, 80, 320}; increase
2
x 2 37. {0.015625, 0.125, 1, 8, 64, 512}; increase

O2 Ϫ2 39. {1111.11, 333.33, 100, 30, 9, 2.7}; decrease

41a. y = 15 * 23n  b. y = 15 * 3n4

4a.  1600 y b. 300% 43a. y b. (0, 1)  c. No; the values of
y ‫ ؍‬4x
y are always positive. 

1200 4 y ‫ ؍‬2x d. When 0 6 b 6 1, the
graph decreases to the right,

800 y ‫ ؍‬0.25x but when b 7 1, the graph
x rises to the right. The larger
400 the value of b, the faster it
Ϫ2 O 2
x rises.
O2
45. f(x) = 200x 2  47. f(x) = 100x 2

5a. about –1.34  b. about – 0.45  c. about – 0.45 49a.
Lesson Check 1. 48 2. 5

3.  4 y 4.  y

2 x 2 b. Answers may vary. Sample: the values are close
Ϫ2 O 2
x though the exponential function is greater from 1 to 2,
O 24 the two functions are equal at x = 2, and then the
quadratic function is greater from 2 to 3.
5. Answers may vary. Linear functions have a constant

rate of change, while an exponential function has a
constant finite ratio. 6. No; the value of the base cannot

Selected Answers i 897

c. Answers may vary. Sample: The function values increase # #6. an = 162 2 2n - 1; = 2 =
1 3 an an - 1 1 3 2, a1 162 
#more rapidly.  51. 6  53. 3  55a. 4  b. 3  c. y = 4 3x # #7. an = 3 (2)n-1; an = an-1 (2), a1 = 3  8. Answers
d. 4 ; 324
9 #will vary. Sample answer: This is the explicit formula. The

Lesson 7-7 pp. 460–466 recursive formula is a1 = 1, an = an-1 ( - 1).  9. Both

Selected Answers Got It? 1. about 43,872 subscribers; 1.05m  arithmetic and geometric sequences can increase or

2. $4489.01  3a. about 55 kilopascals  b. The decimal decrease. Geometric sequences increase or decrease by a

equivalent of 100% is 1. constant ratio. Arithmetic sequences increase or decrease

Lesson Check 1. 4 2. 15 3. 0.2 4. 0.94  by a constant difference.

5. $32,577.89  6. If b 7 1, then it is exponential growth. Exercises 11. not geometric; no constant ratio 
If 0 6 b 6 1, then it is exponential decay.  7. The value of
n = 1 so the formula becomes A = P(1 + r)t.  13. geometric; constant ratio of 43  15. geometric;
17. 1 19. 4  21. -3 
( ) #8. The student did not convert 3.5% to a decimal; constant ratio of 2  3  
(4 2) = 500(1.00875)8 ≈ 536.09. # #23. an = 3 (2)n-1  25. an = 3 (- 4)n-1
A= 500 1 + 0.035 # #27. an = 686 1172n-1 29. a1 = 1, an = an-1
4

Exercises 9. 14, 2 11. 25,600, 1.01  13a. 15,000  #31. a1 = 2, an = an-1 (- 4)  5 

b. 0.04, 1.04  c. 1.04  d. 15,000, 1.04, x  e. about #33.
# #35.
39,988  15. $5352.90 17. $634.87 19. $5229.70  a1 = 192, an = -a1n;-a1n 1 23 2  
an = 48
2331,.2$3162 7279..0e7x p2o3n.e5n,ti0awl d.5e c2ay5 .3110.0e,x23p o2n7e.natibaol ut 134 2n = an-1 34, a1 = 48 
#37. f(x) = 8 2x-1; The graph of the function passes
#decay  33. No; the value of the car is about $5243.  through the points (1, 8), (2, 16), (3, 32), (4, 64).  39. not
# ( )geometric   n-1;
35. Answers may vary. Sample: y = - 4 1.05x; this is an #a1 = 98, an
exponential function, but it models neither exponential 71; 1
41. geometric; an = 98 7
growth nor decay because a 6 0. 37. neither 
= an-1 1  
39a. P = 400(1.05)n, where n is the number of years #43. geometric; - 12; an = 200 7
and P is the profit.  b. $5031.16  41a. $220  b. $3.96  1 2n - 1;
1 - 2 a1 = 200,
#an = an-1
c. $223.96  d. $193.96  e. 9 months  f. $18.07 1 - 1 2   45. arithmetic 
2

Lesson 7-8 pp. 467–472 47. arithmetic  49. geometric  51. Check students’
answers.  53. Both sequences triple for each following
Got It? 1a. geometric  b. arithmetic  c. geometric 
term. However, the first sequence starts at 5, while the
d. neither geometric nor arithmetic  2a. an = an-1 + 2,
a1 = 2; an = 2 + (n - 1)(2) second starts at 10.  55. G  57. I 
# ( ) # ( )b. an = an-1
1 , a1 = 40; an = 40 1 n-1 59. an = 0+ 9n; a1 = ==0,0-a,n7a,=na=ann=a-n1a-n+1-+91  +( -42 ) 
#3a. an = an-1 6, a1 = 14; an =2 2 60. an = 5+ - 2n; a1
61. an = -7 + 4n; a1
# #14 12, a1 =
# ( )648;
6n-1; a8 = 3,919,104  b. an = an - 1 62. x = - 8  63. y = - 2  64. a  =63845.  65. 75%
an = 648 n-1; a8 ≈ 5.06 increase  66. 37.5  67. 2x + 5y 4a + 2b 
#4. f(x) = 2 3x-1; 1 69. - 4c + 5d
2

200 y Chapter Review pp. 474–478

160 (5, 162) 1. geometric sequence 2. growth factor 3. decay factor

120 4. exponential growth 5. exponential decay 6. 1

80 (4, 54) x #17po.5w.419e- r829i0n. s4tx1ye268a .d9No.ofpq;m24- u13l0tisp.hl9yo iun1lgd1i.bt e1b96yr a41is.2e .d117t o.13t3h2.e4f35o8 u1r=t4h3. 12905 
(3, 18) # #18. a6 a2 = a8  19. x2y5 x3y6 = x5y11 
40 468 # # #20. a21
(2, 6) a21 = a  21. x32 x34 = x11   22. m43n12 m21n21 =
12
0
02

## # #54Le.. asansno==n54Ch4(e-nc-2k1) n; 1-a1.n;y=eansa;n=3- a12n.-41ye, sa;1(14-= 235).,  no  m54n  23. 2d5  24. x7  25. - x4y12  26. s19   27. p34q23  
a1 = 15

4  28. 6mn3  29. 7.8 * 103 pores 30. 3 31. - 5 32. 2 
1 x23 22
33. = x2 34. 1 2a1 1 = a41   35. 1 2x2y14 22 = 4x4y12
22

898

36. q12r 4 37. 1.7956 38. 243x 3y 11   39. - 4  40. x4  24, 36, 72 6. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50,
16 3r10z 60, 75, 100, 150, 300 7. 1, 2, 5, 10, 25, 50, 125, 250
8 8. 1, 3, 9, 23, 69, 207 9. x2 - 9x  10. 3d + 15
11. 24r2 - 15r  12. 34m - 29  13. - 36a2 - 6a
41. a3b27   42. 1  43. 7x 4  44. n35  45. e20  
w3 v 21 81c12 14. - s 2 - 7s - 2  15. 25x2  16. 9v25  17. 64c6 
18. 56m258  19. 81b6  20. 36p2q2  21. 7n  22. - 125t12
46. 2 * 10-3 47. 2.5 * 102  48. 5 * 10-5  Selected Answers
49. 3 * 103  50. Answers may vary. Sample: p2q3  1 3y2 
  1)  Simplify the expression within the parentheses. 8n5

  2)  Take the reciprocal of the rational expression raised to 23. 24. 5x  25.  -   26. 27. 3 

the third power. 28. A binomial is an expression with two terms.

  3)  Use the quotient raised to a power rule by applying the 29. b; (x + 4)(x + 4) = (x + 4)2, which is a square, and

exponent to both the numerator and denominator. (x + 4)(x + 4) = x2 + 8x + 16, which is a trinomial.

  4)  Simplify the numerator.

  5)  Simplify the denominator using the power rule. Lesson 8-1 pp. 486–491
51. 2m  52. 23 p2 25 r4  53. 6x2  54. 5 23 x 
Got It?  1a. 2  b. 5  c. 0 2.  5x 4, - 5x 2y 4 
55. 8 24 x3  56. x 23 25 2y  57. (xy)21  58. a41  59. b23  3a. 8x2 + 2x - 3, quadratic trinomial  b. Answers may
vary. Sample: Writing a polynomial in standard form
60. x2y3  61. 3x12  62. x52y53  63. 4, 16, 64 
allows you to see which monomial term has the greatest
64. 0.01, 0.0001, 0.000001 65. 20, 10, 5
66. 6, 12, 24 degree and how many terms the polynomial has.
4. - 12x3 + 120 x2 - 255x + 6022
67. 6y 68. y 5. - 4m3 - 4m2 - 2m + 21
Lesson Check 1. 4 2. 5  3. 11r 3 + 11 
4 2 x 4. x 2 - 3x - 7 5. quadratic trinomial  6. linear
2 binomial 7. The coefficient of the sum of like monomials
2 Ϫ2 O
Ϫ2 O is the sum of the coefficients. To add polynomials, you
x
2 group like terms and add their coefficients. A monomial

69. 70. y has only one term and a polynomial can have more than
one term. 

y Exercises 9. 3  11. 10  13. 0  15. no degree 
17. 11m3n3  19. 14t 4  21. 18v 4w 3
6 8 23. - 8bc4  25. - 2q + 7; linear binomial 
4 6 27. - 7x2 - 4x + 4; quadratic trinomial 
2 29. 3z 4 - 2z 2 - 5z; fourth degree trinomial
x 31. 9x2 + 8  33. 20x2 + 5  35. - 18x2 + 228x + 2300
Ϫ2 O 2 37. 2x3 + 8  39. 5h4 + h3  41. 9x - 1 
43. The student forgot to distribute the negative sign to
Ϫ2 O x all the terms in the second set of parentheses.
2
14x2 - x + 32 - 13x2 - 5x - 62 =
71a. 800 bacteria  b. about 1.4 * 1016 bacteria
72. exponential growth; 3 73. exponential decay; 0.32 4x2 - x + 3 - 3x2 - (- 5x) - (- 6) =
3 1 4x2 - 3x2 - x + 5x + 3 + 6 =
74. exponential growth; 2  75. exponential decay; 4 x2 + 4x + 9  45. - 5y3 + 2y2 - 6 
47. 3z3 + 15z2 - 10z - 5  49. No. Answers may
$2697.20 77. 463 people  78. 79. 1
76. 3  2  10  80. 5   vary. Sample: 1x2 - x + 32 + 1x - x2 + 12 = 4,

#81. 1 82. a1 = = which is a monomial.  51. 14pq6 - 11p4q - p4q4 
3   20, an an - 1
# #83. a1 = 5, an = an-1
#85. a1 = 10, an = an-1
21 184. a1 = 3, an = an-1 4 

10 Lesson 8-2 pp. 492–496

Chapter 8 Got It? 1. 15n4 - 5n3 + 40n 2. 3x 

3a. 3x213x4 + 5x2 + 42 b. - 6x21x2 + 3x + 22

4. 9x2(4 - p)

Get Ready! p. 483 Lesson Check 1. 12x4 + 42x2 2. 2a2 3. 3m(2m - 5) 

1. 1, 2, 3, 4, 6, 12 2. 1, 2, 3, 6, 9, 18 3. 1, 2, 4, 5, 10, 20, 4. 4x1x2 + 2x + 32 5. B 6. C 7. A 8. Answers may vary.
25, 50, 100 4. 1, 3, 9, 27, 81 5. 1, 2, 3, 4, 6, 8, 9, 12, 18,
Sample: 18x3 + 27x2

Selected Answers i 899

Selected Answers Exercises 9. 7x2 + 28x  11. 30m2 + 3m3  13. 8x 4 - 17. 2h2 + 11h - 63  19. 6p2 + 23p + 20 
28x3 + 4x2  15. 4  17. 9  19. 4  21. 3(3x - 2)  21. 4x2 + 11x - 20  23. b2 - 12b + 27 
25. 45z2 - 7z - 12  27. 4w2 + 21w + 26 
23. 712n3 - 5n2 + 42  25. 2x17x2 - x + 42  29. 4px2 + 22px + 28p  31. x3 + 2x2 - 14 x + 5 
33. 10a3 + 12a2 + 9a - 20  35. x2 + 200x + 9375 
27. 25x2(9 - p)  29. - 10x3 + 8x2 - 26x  37. - n3 - 3n2 - n - 3  39. 2m3 + 10m2 + m + 5 
31. - 60a3 + 20a2 - 70a  33. - t3 + t2 + t  41. 12z 4 + 4z3 + 3z2 + z  43. Yes, when you multiply
two polynomials you get a sum of monomials. A sum of
35. 20x2 + 5x; 5x(4x + 1)  37. 17xy31y + 3x2  monomials is always a polynomial.  45a. i. x2 + 2x + 1,
39. a5131ab3 + 632  41. 49; p = 7a and q = 7b, where 121  ii. x2 + 3x + 2, 132  iii. x2 + 4x + 3, 143 
a and b have no common factors other than 1, so b. The digits in the product of the two integers are the
p2 = 49a2 and q2 = 49b2. Since a2 and b2 have no coefficients of the terms in the product of the two
common factors other than 1, the GCF of p2 and q2 is binomials.  47. 6x2 + 24x + 24  49. 24c4 + 72c2 + 54

49.  43a. V = 64s3  b. V = 48(p)s2  
c. V = 64s3 - 48(p)s2  d. V = 16s2(4s - 3p)  e. about
182,088 in.3  24-5.131  5417.. 16x5; 8x2
50. 7x 4 + 3x - 5x3 5 49. + 4x + 5 
- 6x  
52. 7x4 + 2 x3 - 8x 2 + 4  Lesson 8-4 pp. 504–509

53. y … 54x - 2 54. y Ú 72x - 4 Got It?  1a. n2 - 14n + 49  b. 4x2 + 36x + 81
2. (16x + 64) ft2  3a. 7225  b. Answers may vary.
4y 4y Sample: You could write 85 as (80 + 5) or as (100 - 15).
3 4a. x2 - 81  b. 36 - m4  c. 9c2 - 16  5. 2496
3 2 Lesson Check  1. c2 + 6c + 9 2. g2 - 8g + 16
2 1x 3. 4r2 - 9 4. 4x2 + 12x + 9 in.2 5. The Square
1x Ϫ5Ϫ4Ϫ3Ϫ2 O 2 3 of a Binomial 6. The Product of a Sum and Difference 
O 1234567 7. The Square of a Binomial 8. Answers may vary.

Ϫ2 Sample: You can use the rule for the product of a sum
Ϫ3 Ϫ3
Ϫ4 Ϫ4 and difference to multiply two numbers when one
number can be written as a + b and the other number
55. y 6 - 1 x - 3 can be written as a - b.
3

y x Exercises  9. w2 + 10w + 25 11. 9s2 + 54s + 81 
4 13. a2 - 16a + 64 15. 25m2 - 20m + 4 
Ϫ4 Ϫ2 O 2 17. (10x + 15) units2 19. 36 - x2 in.2  21. 6241 
23. 162,409  25. v2 - 36  27. z2 - 25  29. 100 - y2 
Ϫ4 31. 1596  33. 3591  35. 89,991  37. 4a2 + 4ab + b2 
Ϫ6 39. g2 - 14gh + 49h2  41. 64r2 - 80rs + 25s2 
43. p8 - 18p4q2 + 81q4  45. a2 - 36b2  47. r 4 - 9s2 
56. 8x - 40  57. - 3w - 12  58. 1.5c + 4 49. 9w 6 - z 4  51. 8x2 + 32x + 32 
53. Answers may vary. Sample:
Lesson 8-3 pp. 498–503 a2 = b(a - b) + b2 + (a - b)2 + b(a - b) Area of
big square = sum of areas of the 4 interior rectangles
Got It? 1. 4x2 - 21x - 18 2. 3x2 + 13x + 4  = 2b(a - b) + b2 + (a - b)2 Combine like terms.
3a. 3x2 + 2x - 8  b. 4n2 - 31n + 42  = 2ab - 2b2 + b2 + (a - b)2 Distributive Property
c. 4p3 - 10p2 + 6p - 15 4. 4px2 + 20px + 24p  = 2ab - b2 + (a - b)2 Combine like terms.
5a. 2x3 - 9x2 + 10x - 3  b. Answers may vary. So, (a - b)2 = a2 - 2ab + b2 by the Add. and
Sample: Distribute the trinomial to each term of the Subtr. Prop. of = .
binomial. Then continue distributing and combining 22
like terms as needed. 55. No; 13 1 = 13 + 1 22 = 13 + 12 2 13 + 1 2 = 32 +
2 2 2
Lesson Check 1. x2 + 9x + 18  2. 2x2 + x - 15  1 1 21 22 1 1241 1
3. x3 + 5x2 + 2x - 8 4. x2 + 2x - 15 5. Find the sum 2(3) 1 2 2 + = 9 + 3 + 4 = ≠ 9 4
of the products of the FIRST terms, OUTER terms, INNER
terms, and LAST terms. 6. 3x2 + 11x + 8 7. The degree 57a. (3m + 1)2 = 9m2 + 6m + 1 = 3(3m2 + 2m) + 1
of the product is the sum of the degrees of the two Since 3(3m2 + 2m) is a multiple of 3, the expression
polynomials. on the right is 1 more than a multiple of 3. b. no;
(3m + 2)2 = 3(3m2 + 4m) + 4  59. C  61. The graph
shows a line passing through (4, 0) and (0, 5). Both
Exercises 9. y2 + 5y - 24  11. c2 - 15c + 50 
13. 6x2 + 13x - 28  15. a2 - 12a + 11  sides of the graph are shaded, but there is no overlap.

900

The solutions are the coordinates of the points on the (5v - 3)(3v + 8)  31. 20, (3g + 2)(3g + 2); 15, Selected Answers
line with equation 5x + 4y = 20. (3g + 1)(3g + 4)  33. 41, (8r - 7)(r + 6); - 5,
62. 6x2 - 11x - 10  63. 24m2 - 34m + 7  (8r - 21)(r + 2)  35. 6x + 4  37a. (2x + 2)(x + 2);
64. 5x2 + 53x + 72  65. decrease of 25%  66. increase (x + 1)(2x + 4)  b. yes  c. Answers may vary. Sample:
of 25%  67. increase of 25%  68. decrease of 12.5% Neither factoring is complete. Each one has a common
factor, 2.  39. 3(11k + 4)(2k + 1) 41. 28(h - 1)(h + 2) 
69. 6x12x3 + 5x2 + 72  70. 918x3 + 6x2 + 32 43. (11n - 6)(5n - 2) 45. (9g - 5)(7g - 6)  47. 2;
71. 7x15x2 + x + 92 explanations may vary. Sample: ax 2 + bx + c factors to
(ax + 1)( x + c) or (ax + c)( x + 1) so b = ac + 1 or
Lesson 8-5 pp. 512–517 b = a + c.  49.(7p - 3q)(7p + 12q)  51a. - 2, - 3 
b. (x + 2)(x + 3)  c. Answers may vary. Sample: if you
Got It?  1. (r + 8)(r + 3)  2a. ( y - 4)( y - 2)  set each factor equal to 0 and solve the resulting

b. No. There are no factors of 2 with sum - 1.  equations, you get the x–intercepts.
3a. (n + 12)(n - 3)  b. (c - 7)(c + 3)  4. x + 8
and x - 9 5. (m + 9n)(m - 3n) Lesson 8-7 pp. 523–528

Lesson Check  1. (x + 4)(x + 3) 2. (r - 7)(r - 6)  Got It?  1a. (x + 3)2  b. (x - 7)2  2. 4m - 9
3. ( p + 8)( p - 5) 4. (a + 4b)(a + 8b)  5. n - 7 and 3a. (v - 10)(v + 10)  b. (s - 4)(s + 4)
n + 4 6. positive 7. positive 8. negative  9. when the 4a. (5d + 8)(5d - 8)  b. No; 25d2 + 64 is not a
constant term is positive and the coefficient of the difference of two squares.  5a. 12(t + 2)(t - 2)
second term is negative b. 3(2x + 1)2
Lesson Check 1. ( y - 8)2 2. (3q + 2)2 
Exercises  11. 2 13. 2 15. (t + 2)(t + 8)  3. ( p + 6)( p - 6) 4. 6w + 5 5. perfect-square trinomial
17. (n - 7)(n - 8) 19. (q - 6)(q - 2) 21. 6 23. 1  6. perfect-square trinomial 7. difference of two squares
25. (w + 1)(w - 8)  27. (x + 6)(x - 1) 
29. (n + 2)(n - 5) 31. r - 4 and r + 1 33. A  8. In a difference of two squares, both terms are perfect
35. (r + 9s)(r + 10s) 37. (m - 7n)(m + 4n)  squares separated by a subtraction symbol.
39. (w - 10z)(w - 4z)  41a. p and q must have the Exercises  9. (h + 4)2 11. (d - 10)2 13. (q + 1)2
same sign.  b. p and q must have opposite signs.  15. (8x + 7)2  17. (3n - 7)2 19. (5z + 4)2
43. x - 12 45. 4x2 + 12x + 5; (2x + 5)(2x + 1)  21. 10r - 11 23. 5r + 3  25. (a + 7)(a - 7)
47a. They are opposites.  b. Since the coefficient of the 27. (t + 5)(t - 5) 29. (m + 15)(m - 15)
31. (9r + 1)(9r - 1) 33. (8q + 9)(8q - 9)
middle term is negative, the number with the greater 35. (3n + 20)(3n - 20)  37. 3(3w + 2)(3w - 2)
39. (x2)2 - (y2)2; (x - y)(x + y)(x2 + y2)  41. Answers
absolute value must be negative. So, p must be a negative may vary. Sample: Rewrite the absolute value of both
terms as squares. The factorization is the product of two
integer.  49. (x + 25)(x + 2) 51. (k - 21)(k + 3)  binomials. The first is the sum of square roots of the
53. (s + 5t)(s - 15t)  55. (x6 + 7)(x6 + 5)  squares. The second is the difference of the square roots
57. (r3 - 16)(r3 - 5)  59. (x6 - 24)(x6 + 5)  61. C of the squares. Example 1: x2 - 4 = (x + 2)(x - 2);
63. A 65. c2 + 8c + 16  66. 4v2 - 36v + 81  Example 2: 4y2 - 25 = (2y + 5)(2y - 5)
67. 9w2 - 49 68. ad  69. 8d   70. mn - c  71. 7x  43. [1]  Subtract by combining like terms.
72. 6 73. 3 b 7
149x2 - 56x + 162 - 116x2 + 24x + 92 =
Lesson 8-6 pp. 518–522 149x2 - 16x22 + (- 56x - 24x) + (16 - 9) =

Got It?  1a. (3x + 5)(2x + 1)  b. The factors are both 33x2 - 80x + 7
negative.  2. (2x + 7)(5x - 2) 3. 2x + 3 and 4x + 5 [2]  Factor each expression, then use the rule for factoring
4. 4(2x + 1)(x - 5)
Lesson Check 1. (3x + 1)(x + 5)  2. (5q + 2)(2q + 1)  the difference of two squares. 149x2 - 56x + 162 -
3. (2w - 1)(2w + 3)  4. 3x + 8 and 2x - 9 5. There are 116x2 + 24x + 92 = (7x - 4)2 - (4x + 3)2 =
no factors of 20 with sum 7. 6. 24  7. Answers may vary.
Sample: If a = 1, you look for factors of c whose sum is [(7x - 4) - (4x + 3)] - [(7x - 4) + (4x + 3)] =
b. If a ≠ 1, you look for factors of ac whose sum is b. (3x - 7)(11x - 1) = 33x 2 - 80x + 7
45. 11, 9 47. 14, 6  49a. Answers may vary. Sample:
Exercises  9. (3d + 2)(d + 7)  11. (4p + 3)(p + 1)  x2 + 6x + 9  b. because the first term x2 is a square, the
13. (2g - 3)(4 g - 1) 15. (2k + 3)(k - 8)  last term 32 is a square, and the middle term is
17. (3x - 4)(x + 9) 19. (2d + 5)(2d - 7)  21. 5x + 2 2(x)(3)  51. (8r3 - 9)2  53. (6m2 + 7)2  55. (x10 - 2y5)2
and 3x - 4 23. 2(4v - 3)(v + 5)  25. 5(w - 2)(4w - 1) 
27. 3(3r - 5)(r + 2)  29–33. Answers may vary. Samples
are given.  29. - 31, (5v + 3)(3v - 8); 31,

Selected Answers i 901

57a. (4 + 9n2)(2 + 3n)(2 - 3n)  b. They are squares of 60. y 61. y
square terms. c. Answers may vary. Sample:
Selected Answers 2 x 2 1 x
16x4 - 1  59. H  61a. c = 190 - 2p  b. graph of a line 24 6 1 34
through (0, 200), (1, 198), (2, 196), (3, 194), (4, 192), Ϫ2 O Ϫ4Ϫ3Ϫ2 O
Ϫ2 Ϫ2
(5, 190) Ϫ3
62. (6x + 7)(3x - 2) 63. (2x + 3)(4x + 3) Ϫ4
64. (4x - 7)(3x - 5) 65. 2 66. 3m 67. 4h2

Lesson 8-8 pp. 529–533

Got It?  1a. 12t2 + 52(4t + 7)  b. Answers may vary. Chapter Review pp. 535–538

Sample: In Lesson 8-6, you rewrote the middle term as the 1. binomial 2. polynomial 3. monomial 4. perfect-
square trinomial 5. degree of the monomial 
sum of two terms and then factored by grouping. In this 6. - 9r2 + 11r + 3; quadratic trinomial 7. b3 + b2 + 3;
cubic trinomial 8. 8t2 + 3; quadratic binomial
problem, there were already two middle terms. 9. 4n5 + n; fifth degree binomial 10. 6x + 8; linear
binomial 11. p3q3; sixth degree monomial 12. v3 + 5
2. 3h1h2 + 22(2h + 3)  3. Answers may vary. Sample: 13. 14s4 - 4s2 + 9s + 7 14. 9h3 - 3h + 3
15. 7z3 - 2z2 - 16 16. - 20k2 + 15k
2x, 5x + 2, and 6x + 1 17. 36m3 + 8m2 - 24m 18. 6g3 - 48g2
19. 3d3 + 18d2 20. - 8n4 - 10n3 + 18n2
Lesson Check 1. 14r2 + 32(5r + 2) 
2. 13d 2 - 52 (2d + 1) 3. 612x2 + 32(2x + 5)  21. - 2q3 + 8q2 + 11q 22. 4p13p3 + 4p2 + 22
23. 3b1b3 - 3b + 22 24. 9c15c4 - 7c2 + 32
4. Answers may vary. Sample: 4x, 3x + 1, and 3x + 2  25. 4g(g + 2) 26. 31t 4 - 2t 3 - 3t + 42
5. No; the polynomial is a perfect square.  6. Yes; when 27. 3h3110h2 - 2h - 52 28. 30; if the GCF of p and q
you write 23w as 20w + 3w the resulting two groups of
terms have the same factor, w + 5.  7. Yes; two groups of is 5, then the GCF of 6p and 6q is 6(5) = 30.
terms have the same factor, 4t - 7.  8. No; when you 29. w2 + 13w + 12 30. 10s2 - 7s - 12
factor out the GCF from each pair of terms, there is no 31. 9r 2 - 12r + 4 32. 6g2 - 41g - 56
33. 21q2 + 62q + 16 34. 12n4 + 20n3 + 15n + 25
common factor.  35. t2 + 6t - 27 36. 36c2 + 60c + 25
37. 49h2 - 9 38. 3y2 - 11y - 42
Exercises  9. 2z2, 3  11. 2r2, - 5 13. 15q2 + 12(3q + 8) 39. 32a2 - 44a - 21 40. 16b2 - 9
15. 17z2 + 82(2z - 5)  17. (2m + 1)(2m - 1)(2m + 3) 41. (3x + 5)(x + 7); 3x2 + 26x + 35
19. 14v2 - 52(5v + 6)  21. 14y2 - 32(3y + 1)  42. ( g - 7)( g + 2) 43. (2n - 1)(n + 2)
23. w1w2 + 62(3w - 2)  25. 3q(q + 2)(q - 2)(2q + 1) 44. 2(3k - 2/ )(k - / ) 45. ( p + 6)( p + 2)
27. 21d2 + 42(2d - 3)  29. Answers may vary. Sample: 46. (r + 10)(r - 4) 47. (2m + n)(3m + 11n)
48. (t + 2)(t - 15) 49. (2g - 1)(g - 17)
4c, c + 8, and c + 5  31. 9t(t - 8)(t - 2)  50. 3(x + 2)(x - 1) 51. (d - 3)(d - 15)
52. (w + 3)(w - 18) 53. 7(3z - 7)(z - 1)
33. 81m2 + 52(m + 4)  35. The factorization is correct, 54. - 2(h - 7)(h + 5) 55. (x + 2)(x + 19)
56. (5v + 8)(2v - 1) 57. 5(g + 2)(g + 1)  58. Answers
but it is not complete. The GCF of all the terms is 4x, not 4. may vary. Sample: If the expression is factorable then there
must be factors of 18 whose sum is b = 15. The factors of 18
4x 4 + 12x3 + 8x2 + 24x = 4x1x3 + 3x2 + 2x + 62 = are 1 and 18, 2 and 9, 3 and 6. None of these have a sum
4x 3x2(x + 3) + 2(x + 3)4 = 4x 1x2 + 22(x + 3)
equal to 15, so the expression is not factorable.  59. (s - 10)2
37. Answers may vary. Sample: Split the expression into 60. (4q + 7)2  61. (r + 8)(r - 8) 62. (3z + 4)(3z - 4) 
63. (5m + 8)2 64. (7n + 2)(7n - 2) 
three binomials. Find the GCF of each binomial, then 65. ( g + 15)( g - 15) 66. (3p - 7)2 67. (6h - 1)2 
factor again.  39. Answers may vary. Sample: 68. (w + 12)2 69. 8(2v + 1)(2v - 1) 

30x3 + 36x 2 + 40x + 48 = 213x2 + 42(5x + 6) 

41. (y + 2)(y - 2)(y + 11)  43. (6g3 - 7h2)(5g2 + 4h) 
45. (23 + 20)(22 + 21 + 20); 9(7)  47. D  49. B 
51. 5r(2r2 + 1)(r + 3)  52. (m + 6)2 53. (8x - 9)2 
54. (7p + 2)(7p - 2)  55. not a function 
56. function 57. function

58. 7y 59. y
6
5 x
4
3 Ϫ2 O 2 4 6
2
1x Ϫ2
O 1234 567
Ϫ4

Ϫ6

902

70. (5x - 6)(5x + 6) 71. 3n + 9 72. It is a perfect- 2. y domain: all real numbers,
square trinomial. 73. 3y2; 1 74. 8m2; 3  O x range: y … 0
Ϫ4 Ϫ2 24
75. 2d(d + 1)(d - 1)(3d + 2) 76. 1b2 + 12(11b - 6) 
77. 15z2 + 12(9z + 4) 78. 31a2 + 22(3a - 4) Ϫ6

Ϫ12 Selected Answers

Chapter 9 Ϫ18

Get Ready! p. 543 3. f ( x) = - 1 x2, f ( x) = - x2, f ( x) = 3x2
3
1. - 13 2. - 3.5 3. - 9 4. - 0.5 5. - 23 6. - 3 4. 65 y TAhnesywhearsvewtihll evasraym. Seasmhpaplee:,
7. y 8. y
O x
2 Ϫ4 Ϫ2 2 4 4 but the second parabola is
Ϫ4 Ϫ2 O 2 x 3
4 Ϫ2 2 shifted down 3 units.

Ϫ2 Ϫ4 1x

Ϫ4Ϫ3Ϫ2 O 1 2 3 4

Ϫ6 Ϫ2
Ϫ3
9. y 10. y
O 2 x 5a. 80 h about 2 s
4 Ϫ4 Ϫ2 4

2 Ϫ2

x Ϫ4 60
4
Ϫ4 Ϫ2 O 2 40
Ϫ2

20

11. 6y 12. y 00 2 4 t
6

4 2 x b. domain: 0 … t … 1.2; range: 0 … h … 20
2 24 Lesson Check
Ϫ4 Ϫ2 O Ϫ2 O
x Ϫ2 1. y 2. 18 y
24
O 12
Ϫ2 2 x 6

13. - 108 14. 0 15. 49 16. 25 17. 24 18. 144 Ϫ6 x
19. (2x + 1)2 20. (5x - 3)(x + 7)  4
21. (4x - 3)(2x - 1) Ϫ12
22. (x - 9)2 23. (6y - 5)(2y + 3) 
24. (m - 9)(m + 2) Ϫ4 Ϫ2 O 2
25. A quadratic function is of the form
f(x) = ax2 + bx + c, where a ≠ 0.  26. Answers will vary. (0, 0) (0, 0)
Sample: You can fold the graph along the axis of symmetry   
and the two halves of the graph will match. 27. Answers
3. 10 y 4. y
will vary. Sample: the product of two factors can only be Ox
6
zero if at least one of the factors is zero. Ϫ3 Ϫ1 1 3

2 x Ϫ6
Ϫ4 Ϫ2 O 24 Ϫ10

Lesson 9-1 pp. 546–552 (0, 2) (0, - 1)
     
Got It? 1. ( - 2, - 3); minimum
5. If a 7 0, the vertex is a minimum. If a 6 0, the vertex
is a maximum.  6. Answers will vary. Sample: They have

the same shape, but the second graph is shifted up 1 unit.

Selected Answers i 903

Exercises 7. (2, 3); maximum  9. (2, 0); minimum b. h(x) = 9x2 + 2; the graph of h(x) is narrower than the
graph of f(x).  c. Multiplying a quadratic function by a
11. f( x) domain: all real numbers; number shifts the graph up or down and changes the
10 range: f(x) Ú 0 width of the parabola. Multiplying the x value of a
quadratic function by a number only changes the width of
Selected Answers 6 the parabola.

2 x 39. 41.
Ϫ4 Ϫ2 O 24

13. 1125 f (x) draonmgea:inf:(xa)llÚre0al numbers;     v ertex: (0, 3) vertex: (0, - 6)

9 axis of symmetry: x = 0 axis of symmetry: x = 0
6 43. M 45. M  47a. a 7 0  b. 0 a 0 7 1  49a. graph of a
3x
Ϫ4 Ϫ2 O 2 4

parabola in the first quadrant, pointing down, with

15. O y x rdaonmgea:iny: all real numbers; intercepts (0, 135) and (11.6, 0) and passing through
… 0
(6, 99).  b. 0 6 x 6 9; the side length of the square
window must be less than the width of the wall. 
Ϫ4 Ϫ2 24

Ϫ2 c. 54 6 y 6 135; as the side length of the window
increases from 0 to 9, the area of the wall without the
Ϫ4
window decreases from 135 to 54.  51. I  53. F 

Ϫ6 55. 3r(5r + 1)(2r + 3) 56. 13q2 - 22(5q - 6) 

17. f (x) = x2, f (x) = - 3x2, f (x) = 5x2 57. 17b3 + 12(b + 2) 58. 0.75  59. - 0.4 60. - 3  
61. 8
7  62. 1  63. -2
19. f (x) = - 2 x2, f (x) = - 2x2, f (x) = - 4x2 20 8
3

21. 6y x 23. f(x) x Lesson 9-2 pp. 553–558
4 4 O 4
Ϫ4 2O Ϫ4 Ϫ2 2 Got It? b . Answers may vary.
Ϫ2 Ϫ2 1a. 3 y Sample: It is easy to
2 Ϫ2 evaluate a quadratic
2 function in the form
Ϫ4 1x y = ax2 + bx + c when
Ϫ2 O 1 2 3 4 5 6 x = 0. 
Ϫ8 Ϫ6
Ϫ2
25. 10 f(x) 27. 80 h Ϫ3
8 Ϫ4
Ϫ4 6 60 Ϫ5
4 Ϫ6
2O
Ϫ2 Ϫ2 2 x 40 2. 2 s; 69 ft; 5 … h … 69
Ϫ4 4 Lesson Check
Ϫ6 20 1. 4 y

00 1 2 3 4 5 6 t 2. 5 y
7
4
    about 2.2 s 2 x 3
29. domain: all real numbers; range: f(x) Ú 6 1 12345 2
31. domain: all real numbers; range: y … - 9 Ϫ4Ϫ3Ϫ2 O 1O x
33. Answers will vary. Sample: If a 7 0, the parabola Ϫ2 Ϫ5Ϫ4Ϫ3Ϫ2Ϫ1 1 2
opens upward. If a 6 0, the parabola opens downward. Ϫ3 Ϫ2
The vertex of the parabola is (0, c). 35. A  Ϫ3
37a. g(x) = 3x2 + 6; the graph of g(x) is shifted up
4 units and is narrower than the graph of f(x).

904

3. y 4. y it is almost always easier to use square roots to find its
4
Ϫ4 3 x solutions. 7. a and c have opposite signs; c = 0; a and c
2 Ϫ4Ϫ3Ϫ2 O 1 2 3 4 5 6 have the same sign.

Ϫ2 O Ϫ2 Exercises 9. no solution 11. { 2 13. { 3 15. 0
Ϫ2 x Ϫ3 5
234 Ϫ4 17. no solution 19. { 3 21. { 18 23. 0 25. { 2 Selected Answers
Ϫ5
27. { 2 29. { 4 31. { 3 33. Let x = length of side
Ϫ7 of a square, then x2 = 75; 8.7 ft 35. 7.1 ft 37. 0 39. 1
Ϫ8 01;4n4 6510. 4W3h.ennoysooulustuiobntr a4c5t .10{061from
41. n 7 0; n =
5. If a 7 0, the graph opens upward and the vertex is a 47. { 0.4 49.
each side, you get x2 = - 100, which has no
minimum. If a 6 0, the graph opens downward and the solution. 53. 6.3 ft 55a. = 6(A2)^2 - 24
vertex is a maximum. The greater the value of 0 a 0 , the
b. { 2; the solution(s) of the quadratic equation is (are)
narrower the parabola is. The axis of symmetry is the line the x-value(s) in column A that make(s) the value in
yx-i=nt-er2cbae.pTthoef gisra-p2hbat.hTehevertex
x-coordinate of the vertex column B equal 0.  c. Answers may vary. Sample: Find
the parabola is c. 6. First
each instance of a sign change in column B. The
and then graph the y-intercept. Reflect the y-intercept
solution(s) lie(s) between the corresponding x-values
over the axis of symmetry to get a third point. Then sketch
in column A.  57. 28 cm
the parabola through these three points.

Exercises 7. x = 0; (0, 3)  9. x = - 1; (- 1, - 3)  Lesson 9-4 pp. 568–572
11. x = 1.5; (1.5, - 4.75)  13. x = 0.3; (0.3, 2.45) 
15. x = - 0.5; (- 0.5, - 6.5)  17. B 19. A Got It? 1a. - 1, 5  b. - 32, 4  c. - 21, - 14  d. 72, 4
5
21. 1
y x ‫؍‬ 3 3 2a. - 2, 7  b. - 5, 4  c. 32, 6 3a. - 7  b. The quadratic

polynomials are perfect squares. 4. 17 in. by 23 in.
1 2 3 4 5 6 7 8x 9fi,rs6t  f3ac. t38o,r 3th 4e .q2u.a5dfrtabtiyc
Ϫ2 O Lesson Check 1. 4, 7 2. - 4 ft
Ϫ20 6. To solve the equation, you
Ϫ30
Ϫ40 ( )31 , 1 expression, then set each factor equal to 0, and solve.
3 ؊33 3
7. No, if ab = 8, then there are infinitely many possible
values of a and b, such as a = 2 and b = 4 or a = - 1
and b = - 8.
23. x ‫ ؍‬2 8 y (2, 7) 25. 2 xy‫ ؍‬1.5 Exercises 9. - 54, 74, 8
17. - 1.5, 12 19. - 7 11. 0, 2.5  13. - 3  15. - 8, 4 
4 x - 54, 8 21. { 34 
2 34 Ox - 3, 7  23. 1.5, 4 25. +

Ϫ3Ϫ2 O 1 Ϫ1 1 2 3 4 27. 4 ft by 6 ft 29. { - 4, - 2}  31. { - 5, - 2} 33. q2
Ϫ2
Ϫ3 7q - 18 = 0; - 9, 2  35. x = 2 and x = 1; the
Ϫ4
Ϫ5 (1.5, ؊3.5) x-intercepts of the parabola are the same as the zeros of

27. 25 ft; 625 ft2; 0 6 A … 625 the function.  37. 2; { k 39. 0, 4, 6 41. 0, 3  43. - 5,
- 1, 1  45. - 3, - 2, 3 

29a. (- 1, 19)  b. (- 2, - 5) 31. $50  Lesson 9-5 pp. 576–581

( ) ( )33. The value of b is -6, so Got It? 1. 100  2a. - 2.21, - 6.79  b. No, there are no
factors of 15 with a sum of 9.  3a. (- 2, 6) b. (- 6, 2)  
- b = - -6 =- -6 = - 3.  35a. 0.4 s  b. No, the 4. 5.77 ft
2a 2( - 1) -2

ball does not start at height 0 m. Lesson Check 1. - 18, 10 2. - 11, 15 3. - 21, 14 

Lesson 9-3 pp. 561–566 4. - 9, 7.5 5. Answers will vary. Samples are given. 
a. factoring; k2 - 3k - 304 = (k - 19)(k + 16) 
Got It? 1a. { 4  b. no solution  c. 0 2a. { 6  b. no b. completing the square 6. Answers will vary. Sample:
solution  c. 0 3a. 7.9 ft  b. The solutions of the equation
You have to know how to solve using square roots in
in Problem 3 are irrational numbers, which are difficult to
order to solve by completing the square. There are more
approximate on a graph.
Lesson Check 1. { 5 2. { 2  3. { 12 4. { 15 5. The steps involved in completing the square.
zeros of a function are the x-intercepts of the function.
Example: y = x2 - 25 has zeros { 5. 6. Answers will Exercises 7. 81 9. 225 11. 289  13. - 16, 9 
vary. Sample: When an equation has noninteger solutions, 4
15. - 10.24, - 5.76 17. - 10.12, - 1.88 19. ( - 2, - 20) 

Selected Answers i 905

21. (1, - 324) 23. (- 1, - 29) 25. - 1.65, 3.65  60. 12 y 61. 8 y
27. - 1.96, 2.56 29. - 7, 1 31. about 13.3 
33a. 75 - 2w  b. 11.6 ft or 25.9 ft  c. 51.9 ft or 23.1 ft  10 7
35. no solution 37. 2.27, 5.73 39. no solution  8 6
41. - 0.11, 9.11 43. She forgot to divide each side by 4 to 6 5
make the coefficient of the x2-term 1.  4 4
3
Selected Answers x 2
Ϫ2 O 1 2 3 1x
Ϫ3Ϫ2 O 1 2 3 4
47. - 0.45, 4.45  49a. 3 { 25  b. (3, - 5)  c. Answers
will vary. Sample: p is the x–coordinate of the vertex and

- q is the y-coordinate of the vertex. 51. 0.0215 53. 2
--61b, -625. t5183. 6{383. - 61, 5
55. 4.5  57.  59. 2   Lesson 9-7 pp. 589–594
60. m12  61.
y 29  64. 81 65. 0  66. - 15 Got It?
1a. 4 y
Lesson 9-6 pp. 582–588 b. 12 y
3
Got It? 1. - 3, 7 2. 144.8 ft 3a. Factoring; the 2 10
equation is easily factorable.  b. Square roots; there is no 1x 8
x-term.  c. Quadratic formula, graphing; the equation Ϫ2 Ϫ1 O 2 6
4
cannot be factored. 4a. 2  b. 2; if a 7 0 and c 6 0, then     exponential 2O x
- 4ac 7 0 and b2 - 4ac 7 0. Ϫ2Ϫ1 1 2
dLiescsrsimoninaCnhteisckp o1si.tiv-e4, ,th13e r2e.a-re02.9x4-,in1t.e2r2ce p3t.s2.  If4t.hIef the
discriminant is 0, there is 1 x-intercept. If the discriminant     quadratic
is negative, there are no x-intercepts. 5. Factoring
because the equation is easily factorable; quadratic 2. exponential  3. Answers will vary. Sample: linear;
formula or graphing because the equation cannot be
factored. 6. If you complete the square for y = 480.7x + 18,252.4
ax2 + bx + c = 0, you will get the quadratic formula. Lesson Check 1. quadratic 2. linear 3. exponential
4. No, a function cannot be both linear and exponential.
5. Graph the points, or test ordered data for a common

difference (linear function), a common ratio (exponential

Exercises 7. - 1.5, - 1 9. - 3, 1.25  11. - 65, 10   function), or a common second difference (quadratic
- 2.56, 0.16  3
13. - 11, 2  15. - 2.6, 12 17. function).
4 3 Exercises

19. - 0.47, 1.34 21. - 2.26, 0.59  23. Quadratic 7. 8y 9. 5y
6 4
formula, completing the square, or graphing; the Ϫ2 4 Ϫ3Ϫ2 3
2x 2
coefficient of the x2-term is 1, but the equation cannot be O 12345 1O

factored. 25. Quadratic formula, graphing; the equation x
23
cannot be factored. 27. Factoring; the equation is easily Ϫ4
Ϫ6
factorable. 29. 0 31. 0 33. 2 35. { 4 37. { 1.73  Ϫ8 Ϫ2
39. 2 41. No, there are no real-number solutions of the Ϫ3

equation (14 - x)(50 + 5x) = 750. 43. Find values of a,    linear quadratic
b, and c such that b2 - 4ac 7 0. 45a. 16; 1, 5 
b. 81; - 5, 4  c. 73; - 0.39, 3.89  d. Rational; if the 11. 10 y 13. linear 
discriminant is a perfect square, then its square root is an q uadratic;
8 15. y = 3x2 
integer, and the solutions are rational.  47. never  64 17. linear; y = - 0.5x + 2 

49. always  51. I  53. G  55. 1.54, 8.46 2 x 19.

56. - 2, - 1 57. - 6.06, 0.06 Ϫ3Ϫ2 O 1 2 3 exponential;
y = 540(1.03)x
58. 8 y 59. 24 y
  linear
7 21
6 18 21b. The second common difference is twice the
5 15 coefficient of the x2-term.  c. When second differences
4 12 are the same, the data are quadratic. The coefficient
39 of the x2-term is one-half the second difference. 
26

x 3x

Ϫ3Ϫ2 O 1 2 3 O 123

906

23. Answers will vary. Sample: (0, 5), (2, 13), (4, 29), (6, 53) Exercises
25a. P linear
9. 9y (2, 8)
6000 8
Population 7 (2, 8)
6
4000 5 Selected Answers

2000

00 4 t 3
8 12 16 2
1x
Year Ϫ4Ϫ3Ϫ2 O 1 2 3 4

b. The population changes by 600 every 5 years; the 11. 6y (0, 1), ( - 1, 0)

y-values have a common difference, so a linear model (؊1, 0) 5
works best.  c. p = 120t + 5100  d. 8700  Ϫ4Ϫ3 4
e. 70t + 3800  27a. 6, 12, 18, 24; 6, 6, 6  b. 6  c. Yes, 3
the first differences are constant for linear functions, the 2
1 (0, 1)
second differences are constant for quadratic functions, x

and the third differences are constant for cubic functions.  O 12345
29. I  31. (5x + 2)(2x - 1)  32. - 1.5, 0.5 
33. - 3.83, 1.83 34. 0.13, 2.54 35. (6, 4) 36. (2, 7)  13. y (0, 4) (0, 4), ( - 3, - 5) 
37. (1, - 2)

Lesson 9-8 pp. 596–601 15. (2, 4), ( - 1, 1) 
17. Day 13, 2451 players of
Got It? 1a. ( - 2, 9), (1, 3)  b. no solution  2. Day 5; 234 2
people  3. (- 6, - 42), (7, 114)  4a. (- 2, 2), (1, - 1) 1x each type 
b. Substitution; substitute - x for y in the first equation. O 12 34
Ϫ4Ϫ3 19. (6, - 2), ( - 9, - 47) 
( )21. (9, - 71), ( - 11, - 91) 
Lesson Check Ϫ2 23. ( - 4, - 41), 13, 7  
Ϫ3 25. no solution  3
Ϫ4
1. 5y (2, 4), ( - 2, 0) (؊3, ؊5) 27. (2, - 5), ( - 4, 1) 

(؊2, 0) 4 (2, 4) 29. ( - 3, 0), ( - 6, - 3) 
3 31. y = 2x + 2  33. The system has no solution. 
2 35a. 7.4  b. 7.8  c. (1.61, 0), (1.61, 3.22), ( - 1.61, 3.22),
1x ( - 1.61, 0)  d. 10.38  37. B  39. B  41. Given (x, y), where

Ϫ4 O 1 2 3 4

Ϫ3 x is the number of balls and y is the weight of the box,

you have the points (4, 5) and (10, 11). The slope of the

line that passes through these two points is
11 - 5
2. (6, 10), ( - 7, 192)  3. (1, 4), (4, 1) 4. (1, 4)  5. (- 3, - 3), = 6 = 1. An equation of the line is
(- 1.5, - 1.5)  6a. Answers may vary. Sample: 1y0--54 = 6 1. The equation
y = x2 + x - 2, y = - x + 1  b. Answers may vary. 1(x - 4), or y = x + of the line
Sample: y = x2 - x, y = x - 1  c. Answers may vary.
Sample: y = x2 + x - 2, y = x - 5  in standard form is x - y = - 1.  42. quadratic;
7. In both cases, you can use graphing, substitution, or 0.2x 2  75y =474.(21.5.2)x   4484..9l in4e9a.r;0.6 
elimination. If you don’t use graphing, you must know how y= - 4.2 x 43. exponential;
to solve a quadratic equation in order to solve a linear- y= 20 + 7  45. 14  46.
quadratic system. 50.

Chapter Review pp. 603–606

1. parabola 2. axis of symmetry 3. discriminant 4. vertex

5. 6 y 6. (0, 1) y x
5 x‫؍‬0

4 Ϫ3Ϫ2 O 1 2 3

3 Ϫ2
2
1x Ϫ3
Ϫ4
Ϫ3 (0, 0) 1 2 3 Ϫ5 x‫؍‬0

Selected Answers i 907

7. y 8. 18 y Chapter 10
x‫؍‬0 x
Ϫ3 16 Get Ready! p. 611
O1 3 14
12 1. 6 2. 18 3. 4.5 4. 8 5. 10 6. 4 7. 12 8. 14
Ϫ2 9. - 2h2 + 5h + 12 10. 9b4 - 49 
Selected Answers Ϫ3 8 (0, 8) 11. - 15x 2 - 11x - 2
6
(0, ؊4) 4
Ϫ5 2

x‫؍‬ 0 x 12. 12 y 13. y

Ϫ3Ϫ2 O 123

9. 10 y x‫؍‬4 ؊43( )10.,111 y 8 2 x
(4, 9) 8 4 Ϫ4 O 4
8 3
6 x 8 x ‫؍‬ ؊ 4 Ϫ2 O x
4 6 8 10 2
2O 6
Ϫ4 2 4
2O x
1 4. 8 y 1158.. 2 16. 2 17. 0 
Ϫ3Ϫ2 123 1 19. 2 20. 2 

Ϫ4 2 x 21. T hey both contain the
same radical expression,
11. x ‫ ؍‬؊2 2y x 12. 6 y O2
O 12 4 13. 
Ϫ5Ϫ4Ϫ3 2 x ‫؍‬ ؊ 1
6 22. I would be rich.

(؊2, ؊5) Ϫ6 Ϫ2 Ϫ2 O 2 3 4 x Lesson 10-1 pp. 614–618

( )؊1 , ؊1621 Got It? 1. 15 cm 2. 9 3a. no; 202 + 472 ≠ 522
6
b. yes; (2a)2 + (2b)2 = 4a2 + 4b2 = 41a2 + b22 =
13. Answers will vary. Sample: y = - x2  14. Answers will 4c2 = (2c)2
vary. Sample: y = x2  15. Answers will vary. Sample: Lesson Check 1. 39 2. 7 3. yes; 122 + 352 = 372 
12y-894=.. x2{22.43 51. in061.,.9 2A3. n002s .w52-.0e64r.s.,n7w5o4 i,ls2lo0v6l.au7.rt4yi-o. n3S3a ,1m221.1 p02.l.e73{:8.y,23- =2232.60,22.23.5  x{32228 4.1. 172-,.324.{, -23 , 4. If you are a student, then you study math. 5. The
- 1.5 33. - 9.12, - 0.88 34. - 1.65, 3.65  35. 1.26,
12.74 36. 7.6 ft by 15.8 ft 37. 6.4 in. by 13.8 in.  38. two  value of 13 should have been substituted for c since it is
39. two 40. - 1.84, 1.09 41. - 2.5, 4  42. 7.87, 0.13 
43. - 0.25, 0.06 44. { 5; square roots because there is no the hypotenuse. The correct equation is
x-term 45. 3; factoring because it is easy to factor 46. 1.5 s 122 + x2 = 132; x = 5.
Exercises 7. 8 9. 12 11. 17  13. 4.5 15. 6.1 17. 41 

19. 8.5 21. 1.2 mi 23. yes  25. no 27. yes 29. 10 ft 

31. yes 33. yes 35. yes  37. 719 ft 39. Yes;

47. 8 y 48. y 502 + 1202 = 1302, so the triangle formed by the forces
a2 b2  c2  1
6 6 a right triangle.  41a. + 2ab + b. c. 2 ab 
4 ( )is
2x 4 d. a2 + 2ab + b2 = 4 12ab + c2; a2 + b2 = c2; it is the
Ϫ3Ϫ2 O 1 2 3
2 Pythagorean Theorem.
quadratic x
     Lesson 10-2 pp. 619–625
O 2468
Got It? 1. 6 12 2. - 4m5 15m 3a. 18 13  b. 3a2 12
exponential
c. 210x3  d. yes; 214t2 = t 114 4. w 117 5a. 4
49. y = 3x - 2 50. y = 5(2)x  51. ( - 1, 8), (2, - 1)  bLe. s3as oc.n5Cy zh1ey c6ka 1. .13761  b2. 21.61m40mb2  1c.b1 3321.s12m2 4.
52. (0, - 1), (1, - 2) 53. ( - 1, - 1), (1, 1) 54. ( - 2, - 4), 115
(3, 6) 55. ( - 8, 3), (12, 123) 56. (7, - 2), (9, 6)  5fa.ct1o31rs5 13n x
57. ( - 7, - 45), ( - 4, - 21) 58. ( - 13, 64), (3, - 16) n
59. (6, 69) (10, 145) 60. ( - 9, 33), ( - 12, 63) 61. If you  6.  7a. Yes; there are no perfect-square
look at the graph and see how many times the graphs in the radicand, and
intersect, that is how many solutions the system will have. in 31, there are no fractions

there are no radicals in the denominator.  b. No; there is a

fraction in the radicand.  c. No; 25 is a perfect-square

#factor of 175. 8. Answers may vary. Sample:3=313=3 13=13;
112 213 13 6 2

908

#3 = 3 112 = 3 112 = 112 = 2 13 = 13 because no matter what value of x you input, the output
112 112 12 4 4 2
112 will always be nonnegative. 68. 6 13 69. 15 16 
9. A radical expression is in simplified form if the radicand
70. 2-311c2  7771..-145, 732 7. 88.16- 57,33.  27191 . 7-43.,5232 78 07.5-. 323,  21 
has no perfect-square factors other than 1, the radicand 76. 81. -7

contains no fractions, and no radicals appear in the

denominator of a fraction. Lesson 10-4 pp. 633–638 Selected Answers

Exercises 11. 3 111  13. - 2 115 15. 50 17  Got It? 1. 9 2. 0.825 ft 3. 7 4. - 2 5a. no solution
17. 5t2 12t 19. - 63x 4 13x  21. - 18y 13y 23. 4  b. The principal root of a number is never negative.
25. 30 27. 42n2 29. 16y3  31. - 126a 1a 33. 24c7 
Lesson Check 1. 12 2. 3 3. 1 4. no solution 5. C
35. 2w111216 4 377. .4s  741493. 2391.61i8n3x.   41. 77a  43. 110x   6. If x 2 = y 2, then x = y; no, if x = - 1 and y = 1, then
45. 51. 2 4x x 2 = y 2, but x ≠ y.
not simplest form; Exercises 7. 4 9. 36 11. 8 13. 16 15. - 2 17. about
5.2 ft 19. 4.5 21. 7 23. 4  25. 2 27. none 29. - 7 
radical in the denominator of a fraction 53. Simplest 31. 3 33. no solution  35. no solution 37. The student

form; radicand has no perfect-square factors other than 1. 
#55a. f13f   b.
#1180 = 136 x121  c5. 12a   d. 12m  57a. 118 10 = did not check the solutions in the original equations. Both
2a 4m may vary.
= 6 15  b. Answers
7S6a35m.. Ap4ln1es:5w4 e6arns7dm. a4ab5y2 vc5a19ry.a. b2Sca1 m61p39le . :6811132.a6,a-2 2a7721,1a4. 816  37{.5x.1y11250y b  2 of those solutions are extraneous, so the equation has no

solution.  39a. 25  b. 11.25 41. Add 1y + 2 to each side

of the equation. Square each side of the equation. Solve

for y. Check each apparent solution in the original

( ) ( )77a. 512p 12p equation.  43. 3 45. no solution 47. 1.5 49. 1600 ft 
p ft, 3.99 ft  b. 4 p , 3.19 in. 
51. The square of 1x - 1 will have only two terms, while
( )c. the square of 1x - 1 will have three terms. 
110p m, 1.78 m
p

Lesson 10-3 pp. 626–631 53. D 55. B 57. 5 12  58. - 24 59. - 2 13 - 4 12  
60. no solution 61. - 2, 2  5
62. - 3 , - 2
Got It? 1a. - 12  b. 7 15 2a. 8 17  b. 8 12 2 3
c. No; if they are unlike and have no common factors
63. 3 y 64. 2 y

other than 1, even if they can be simplified, they still will x O1 x
2 Ϫ4
not be like. 3a. 2 13 + 5 12  b. 15 - 4 111 Ϫ2 O
- 3 110 + 3 15 5. Ϫ2
c. - 6 12 - 6 4. 5 (6 15 - 6) in., or

about 7.4 in.

Lesson Check 1. 5 13 2. 16  3. 121 - 2 17 
4. 41 - 12 15 5. 3 15 - 110  6. 2 17 - 4  65. y
#7a. 113 + 2  b. 16 - 13  c. 15 + 110 
8. 13 13 ≠ 9; 13 + 1 = 13 + 1
3-1 2
2
Exercises 9. 7 15 11. 8 13 13. 0 15. - 7 15
19 15 x
17. 9 110 19. 2  21. 2 13 + 3 12 23. 3 17 - 21 O 24

25. 5 133 - 15 122 27. - 6 29. 62 - 20 16 
+ 7 113 -
31. 3 17 4 3 13 33. - 2 15 - 5 35. 8 7 15 Lesson 10-5 pp. 639–644

37. 23 15 - 23 ft, or about 14.2 ft 39. - 43; - 1.3 Got It? 1. x … 2.5 2a. when the power is more than
2 56.25 watts  b. 4
-1 + 17;
41. 4 - 0.4 43. 9 + 6 12 + 4 15 + 3 110; 3. 1 y

35.9 45. No; yes; you can simplify 112 to 2 13 and

then combine the like radicals. 47. 5 110 O2 x

49. 22 13 - 6 51. 13 + 165 + 1130 + 5 12  53. - 24  Ϫ2
55. 4 13 + 4 12 + 8
3 16 n
+ 6  57. s 13 59a. x 2  

b. x n-1 1x  61. n 15 - n  63a. 3 12  b. 2 17  4. y
2 2
2
c. 12(p + q)  65. H  67. The graph of the function
y = 0 x 0 is V–shaped with the vertex at the origin. The x
domain is all real numbers and the range is 5y 0 y Ú 06, O 2 4 6 8 10

Selected Answers i 909

Lesson Check  1. x Ú - 3 3. y 31. y x 33. y
2. 4 y
O2 x O2 2
Ϫ2 4 Ϫ2 Ϫ2 O x
2
2 x Ϫ4 Ϫ4
24
Selected Answers Ϫ2 O Ϫ6
Ϫ2 35. f(x) 37. y

4. No; there is no variable in the radicand. 5. The graph 2 x 2 x
6 4
of y = 1x - 1 is the graph of y = 1x shifted to the O 24 O2
right 1 unit. 6. Yes; the domain includes all the values
39. x Ú 4; y Ú 0
of x such that the radicand has a value greater than or 41a. 800 f b. about 45 lb>in.2

equal to zero, so for b 7 0, the domain of y = 1x + b
is x Ú - b, which includes negative values.
Exercises 7. x Ú 0 9. x Ú 7 11. x Ú - 2  600

13. x … 18 15. x Ú 4 400

17.   f(x) 200
p
x f(x) 6
O 20 40
00
43. about 2800 m>s
14 4 45.  

48 2 x f(x)

x 00 f(x)
O 24 6
14
19.   x y 4y 2 x
0 0 2 2 5.7 O2 4
3 3
5.3 4 O2 48

x 47.   x y y
4
00 2
21.   x y yx 21 x
O2 4 1.4
00 Ϫ2 82 O 246
1 −3 Ϫ4
4 −6 49.   x f(x) f(x) x
y Ϫ2 O 2
23.   x y 2 −2 −4
0 0 −1 −3 Ϫ2
2 1 x
8 2 O 246 2 −2 Ϫ4

v 51.   x y 4y
8 1
25.   h v 4 −3 2.4 2 x
−2 3 Ϫ2 O
00 h −1 3.4
1 4.4 O4
6 10.8 0

    h 7 5.1 m 53a. No; the graph does not pass the vertical-line test.
27. A 29. B b. The graph of y = 1x is the first-quadrant portion of
the graph of x = y 2.  c. y = - 1x

910