A102 Answers to Odd-Numbered Exercises and Tests 21. (a) (b) Reflection in the axis (no effect), vertical stretch, and a vertical shift seven units downward (c) 22. (a) (b) (c) (d) 23. 24. No inverse 25. Chapter 2 Section 2.1 (page 172) Vocabulary Check (page 172) 1. equation 2. solve 3. identities, conditional equations 4. 5. extraneous 6. Mathematical modeling 7. formulas 1. (a) Yes (b) No (c) No (d) No 3. (a) Yes (b) No (c) No (d) No 5. (a) No (b) No (c) No (d) Yes 7. Identity 9. Identity 11. Conditional equation 13. 15. 17. 12 19. 1 21. 23. 25. 27. 29. 10 31. 4 33. 5 35. 37. 39. No solution 41. 43. 45. 47. 49. 51. 53. 55. 57. 61.2 inches 59. (a) (b) (c) 7.5 meters long 5 meters wide 61. (a) (b) 97 63. 3 hours 65. miles per hour 67. (a) (b) 91.4 feet 69. $1950 71. $4000 73. $40,000 in DVD players; $10,000 in VCRs 75. 50 pounds of each kind 77. feet 79. (a) (b) 81. 83. feet 85. False. It is quadratic; 87. 89. Equations with the same solution set 91. 93. 95. 14 12 10 8 6 4 2 -4 -2 16 14 12 10 8 6 4 2 x y 5 4 3 2 1 -3 -4 -5 7 8 6 5 4 3 1 -1 -2 x y 5 8 4 x 16 0, 2x 8 0 9x 27 0 3x x 2 10. ⇒ x 3 x10 x 6 25 20 15 Time Temperat u re ( C) ° 10:00 A.M. 11:00 A.M. 12:00 P.M. 1:00 P.M. 2:00 P.M. 3:00 P.M. 4:00 P.M. 5:00 P.M. 6:00 P.M. 24 12 8 inches h w l h 27 h 3 ft 1 2 4 ft 80 ft Not drawn to scale 46.3 Test average test 1 test 2 test 3 test 4 4 l 1.5w; P 5w w l R PV nT r S 2 h h V r 2 w P 2l 2 b 3V 4 a 2 r S a S L P A 1 r n n t h 2A b 5 3 11 6 17 48 6 5 10 9 20 81 96 23 ax b 0 f 1 x8 3 x23 , x ≥ 0 f 1 x3 x 8 2 x 2 , 2 , 2 2 x, , 2x 2 2 x , , 2x 2 2 x , , 22 1 1 2 3 4 5 -7 -2 -3 -4 -5 -8 x y y- f xx 333370_02_ans_odd.qxp 1/3/07 2:28 PM Page A102
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A102 Answers to Odd-Numbered Exercises and Tests
21. (a)
(b) Reflection in the axis (no effect), vertical stretch, anda vertical shift seven units downward
(c)
22. (a) (b)
(c) (d)
23. 24. No inverse
25.
Chapter 2Section 2.1 (page 172)
Vocabulary Check (page 172)1. equation 2. solve
3. identities, conditional equations 4.
5. extraneous 6. Mathematical modeling
7. formulas
1. (a) Yes (b) No (c) No (d) No
3. (a) Yes (b) No (c) No (d) No
5. (a) No (b) No (c) No (d) Yes
7. Identity 9. Identity 11. Conditional equation
13. 15. 17. 12 19. 1 21.
23. 25. 27. 29. 10 31. 4
33. 5 35. 37. 39. No solution
41. 43. 45.
47. 49. 51.
53. 55. 57. 61.2 inches
59. (a) (b)
(c) 7.5 meters long 5 meters wide
61. (a)
(b) 97
63. 3 hours 65. miles per hour
67. (a) (b) 91.4 feet
69. $1950 71. $4000
73. $40,000 in DVD players; $10,000 in VCRs
75. 50 pounds of each kind 77. feet
79. (a) (b)
81. 83. feet
85. False. It is quadratic;
87.
89. Equations with the same solution set
91.
93. 95.
1412108642−4 −2
16
14
12
10
8
6
4
2
x
y
5
43
21
−3
−4−5
7 865431−1−2x
y
58
4x � 16 � 0, 2x � 8 � 0
9x � 27 � 0
3x � x2 � 10.⇒x�3 � x� � 10
x � 6
25
20
15
Time
Tem
pera
ture
(C
)°
10:0
0 A
.M.
11:0
0 A
.M.
12:0
0 P.
M.
1:00
P.M
.
2:00
P.M
.
3:00
P.M
.
4:00
P.M
.
5:00
P.M
.
6:00
P.M
.
24 � 12 � 8 inchesh
wl
h � 27
h
3 ft12
4 ft
80 ft
Not drawn to scale
�46.3
Test average �test 1 � test 2 � test 3 � test 4
4
�
l � 1.5w; P � 5w
w
l
R �PVnT
r �S
2�h
h �V
�r 2w �P � 2l
2b �
3V4�a2
r �S � aS � L
P � A�1 �rn�
�nth �
2Ab
53
116
1748�
65�10
�92081�
9623
ax � b � 0
f �1�x� � �83 x�2�3
, x ≥ 0
f �1�x� � 3�x � 8
�2 � x2, ��2, �22 � x, ���, 2
x2
�2 � x, ���, 2�x2 � �2 � x, ���, 2
21
1 2 3 4 5
−7
−2−3−4−5
−8
x
y
y-
f �x� � �x�
333370_02_ans_odd.qxp 1/3/07 2:28 PM Page A102
x 1.5 1.6 1.7 1.8 1.9 2
3.2x � 5.8 �1 �0.68 �0.36 �0.04 0.28 0.60
x �1 0 1 2 3 4
3.2x � 5.8 �9 �5.8 �2.6 0.6 3.8 7
97.
99. 101. 103.
Section 2.2 (page 183)
Vocabulary Check (page 183)1. -intercept, -intercept 2. zero
3. point of intersection
1. 3.
5. 7. No intercepts 9.
11. 13.
15–19. Answers will vary.
21.
23. 25. 6;
27.
29. 31.
33. 35. 2.172, 7.828
37. 39. 41.
43. 45. 47.
49. 51. 11 53. 21
55. (a)
Answers will vary.
(b)
Answers will vary. Sample answer:Use smaller intervals of to increase accuracy.
57. 59. 61. 63.
65. 67.
69.
71. (a) 6.46
(b) The second method decreases the accuracy.
73. (a)
(b)
(c) 164.5 miles
75. (a)
(b)
(c) 22.2 gallons
77. (a)
(b) (c) 16.7 units
79. (a) (b) $6800
(c) $7600 (d) $7500
81. (a)
In 1986, both states had the same population.
(b) In 1986, both states had the same population.
(c) Change in population per year; Arizona’s populationis growing faster.