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d.Precalculus with Limits, Answers to Section 7.1 1
Chapter 7Section 7.1 (page 503)
Vocabulary Check (page 503)1. system of equations 2. solution3. solving 4. substitution5. point of intersection 6. break-even
1. (a) No (b) No (c) No (d) Yes2. (a) Yes (b) No (c) No (d) Yes3. (a) No (b) Yes (c) No (d) No4. (a) No (b) Yes (c) Yes (d) No5. 6. 7.
8.9. 10.
11. 12.13. 14.15. 16. 17. 18.
19. 20. 21. 22.23. No solution 24. No solution 25.26. 27. No solution 28.29. 30. 31. 32.33. 34. 35.36. 37. 38.39. No solution 40. No solution 41.42.
43. 44.
45. 46.
47. 48.
49. 50. No solution 51.
52. 53. No solution 54. No solution
55. 56.57. 58.
59. 60. 61. 192 units
62. 3133 units 63. (a) 781 units (b) 3708 units64. (a) 3760 items (b) 10,151 items65. (a) 8 weeks
(b)
66. (a) 5 weeks(b)
67. More than $11,666.67
68.
69. (a)
(b)
Decreases; Interest is fixed.(c) $5000
70. (a)
(b) 24.7 inches(c) Doyle Log Rule
00
40
V1
V2
1500
0 10,00012,000
27,000
� x0.06x
�
�
y0.085y
�
�
25,0002,000
�99.99, 2.85�
00
150
10
�1, 0�, �5, 2�� 12, 2�, ��4, �1
4��0, �1�, �2, 1�, ��1, �5���1, 0�, �0, 1�, �1, 0���1.96, 0.14�, �1.06, 2.88��0.287, 1.751�
�3, 4�, �5, 0���2, 0�, � 29
10, 2110��1, 2�
�0, �2�, �±1.32, 1.50��0, �13�, �±12, 5�
−6
−4
6
4
−16
−24 24
16
�5.31, �0.54��4, 2�
−1
−6
4
14
−2 10
−3
5
��0.49, �6.53��0, 1�
−7
−10
80
−2
6−6
6
�3, �4��3, 4�,�4, 3�, ��4, 3��2, 2��4, �1
2��15, 7��3, 1�,�1, 4�, �4, 7��3, 6���3, 0�,�2, 2�, �4, 0��5, 3�� 5
2, 32��2, �2��4, 3��0, 0��12, 6��0, 0�,��2, 4�, �0, 0�
�20817 , 88
17�� 203 , 40
3 ��2, 52��1, 1��4
3, 43�� 12, 3���3, 2��5, 5�
�0, 4�, �1, 2�, �2, 0��0, 1�, �1, �1�, �3, 1��0, 2�, �1, 0�, ��1, 0��0, 0�, �2, �4��0, 0�, �2, �2�, ��2, 2��0, �5�, �4, 3�
��3, 2 � 3�3 ��0, 2�,���3, 2 � 3�3 �,�2, 6�, ��1, 3���1, 3��2, 2�
1 2 3 4
336 312 228 264
42 60 78 9624 � 18x
360 � 24x
5 6 7 8
240 216 192 168
114 132 150 16824 � 18x
360 � 24x
1 2 3 4 5
125 150 175 200 225
425 375 325 275 225�50x � 475
25x � 100
333202CB07_AN.qxd 4/13/06 5:30 PM Page 1
Precalculus with Limits, Answers to Section 7.1 2
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d.
(Continued)
71. (a) Solar:Wind:
(b)
(c) Point of intersection: Consumption ofsolar and wind energy are equal at this point in time inthe year 2000.
(d)(e) The results are the same, but due to the given parame-
ters, is not of significance.(f) Answers will vary.
72. (a) Alabama:Colorado:
(b) Point of intersection: Colorado’spopulation exceeded Alabama’s just after this point.
(c) so 73.74.75. 76.77.78.79. False. To solve a system of equations by substitution, you
can solve for either variable in one of the two equations andthen back-substitute.
80. False. The system can have at most four solutions becausea parabola and a circle can intersect at most four times.
81. 1. Solve one of the equations for one variable in terms ofthe other.
2. Substitute the expression found in Step 1 into the otherequation to obtain an equation in one variable.
3. Solve the equation obtained in Step 2.4. Back-substitute the value obtained in Step 3 into the
expression obtained in Step 1 to find the value of theother variable.
5. Check that the solution satisfies each of the originalequations.
82. For a linear system, the result will be a contradictoryequation such as , where is a nonzero real num-ber. For a nonlinear system, there may be an equation withimaginary solutions.
83. (a) (b) (c)84. (a)
(b) There are three points of intersection when b is even.
85. 86.87. 88.89. 90.91. Domain: All real numbers except
Horizontal asymptote: Vertical asymptote:
92. Domain: All real numbers except
Horizontal asymptote:
Vertical asymptote: 93. Domain: All real numbers except
Horizontal asymptote: Vertical asymptotes:
94. Domain: All real numbers except Horizontal asymptote: Vertical asymptote: x � 0
y � 3x � 0x
x � ±4y � 1
x � ±4xx � �
23
y �23
x � �23x
x � 6y � 0
x � 6x45x � 29y � 127 � 030x � 17y � 18 � 0
x � 4 � 0y � 3 � 0
4x � 13y � 38 � 02x � 7y � 45 � 0
−6
−2
6
6
−6
−2
6
6
b � 4b � 3
−6
−2
6
6
−6
−2
6
6
b � 2b � 1y � x � 2y � 0y � 2x
N0 � N
�2 inches � �2 inches � 2 inches8 kilometers � 12 kilometers
42 feet � 63 feet9 inches � 12 inches 60 centimeters � 80 centimeters6 meters � 9 meters
t � 11.9317.4t � 4273.2 � 84.9t � 3467.9,
�11.93, 4480.79�.
94000
13
4800
84.9t � 3467.917.4t � 4273.2
t � 135.47
t � 10.3, 135.47
�10.3, 66.01�.
80
13
150
16.371t � 102.70.1429t2 � 4.46t � 96.8
333202CB07_AN.qxd 4/13/06 5:30 PM Page 2
Precalculus with Limits, Answers to Section 7.2 3C
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pany
. All
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ts r
eser
ved.
Section 7.2 (page 515)
Vocabulary Check (page 515)1. elimination 2. equivalent3. consistent; inconsistent 4. equilibrium point
1. 2.
3. 4.
5. No solution 6. No solution
7. 8.
9. 10.
11. 12. 13. 14.
15. 16. 17. 18.
19. No solution 20. Infinitely many solutions:
21. 22. Infinitely many solutions:
23. Infinitely many solutions:
24. Infinitely many solutions:
25. 26. 27.
28. 29. 30.31. b; one solution; consistent32. a; infinitely many solutions; consistent33. c; one solution; consistent34. d; no solutions; inconsistent35. 36. 37. 38.39. 40. 41.42. 43. 550 miles per hour, 50 miles per hour44. First plane: 880 kilometers per hour
Second plane: 960 kilometers per hour45. 46. 47.48.49. Cheeseburger: 310 calories; fries: 230 calories50. Apple juice: 103 milligrams; orange juice: 82 milligrams51. (a)
(b) (c) 20% solution:
50% solution:
Decreases
52. (a)
(b) (c) 87 octane: 300 gallons;92 octane: 200 gallons
Decreases53. $6000 54. $20,000 55. 400 adult, 1035 student
00
500
500
� x �
87x �
y �
92y �
500
44,500
313 liters
623 liters
−6 18
−4
12
� x �
0.2x �
y � 10
0.5y � 3
�250,000, 350��2,000,000, 100��500, 75��80, 10�
�3, 2��43
6 , 256 ���23, 61��6, �3�
�1, 3��2, �1���2, 5��4, 1�
�7, 1��5, �2���149 , 20
9 ��� 6
35, 4335 ��101, 96�� 90
31, �6731 �
�a, 34 �78a�
�a, �12 �
56a�
�a, 4 � 4a�� 185 , 35�
�a, 18 �34a�
��17, 5��127 , 18
7 ��56, 56��4, �1�
�5, 1��3, 4��3, 75�� 52, 34�
x
5x + 3y = −18
2x − 6y = 1
2−4
−2
−6
4
2
y
x
−4
−3
−2
3
4
y
−1 2 3 4−2−3−4
9x + 3y = 1
3x − 6y = 5
��3512, �41
36�� 13, �2
3�
x
6
8
−4
−6
−8
42−4−6−8 86
y −3x + y = 5
9x − 3y = −15
x
y
−1 2 3 4 5−2
−2
1
2
3
4
−3
−6x + 4y = −10
3x − 2y = 5
�a, 3a � 5��a, 32 a �52�
x
6x + 4y = 14
−2 2
−2
−4
4
y
3x + 2y = 3
x
y
−1
−2
1
4
−4
2 3 4−2−4
−2x + 2y = 5
x − y = 2
x
2x − y = 3
4x + 3y = 21
−2
2
4
6
42
y
x
2
3
4
y
−1 2 3 4−2
−4
−3
−2
−3−4
3x + 2y = 1x + y = 0
�3, 3��1, �1�
x−2
−2
−4−6
4
y
−x + 2y = 4x + 3y = 1
x65421−1−2
−4
−3
1
2
3
4
2x + y = 5
x − y = 1y
��2, 1��2, 1�
333202CB07_AN.qxd 4/13/06 5:30 PM Page 3
Precalculus with Limits, Answers to Section 7.2 4
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d.
(Continued)
56. Before noon: 81 jackets; After noon: 133 jackets57. 58.59. 60.
61. 62.63. (a) (b) 41.4 bushels per acre64. (a) and (b)
(c)
(d) $92.54 (e) 200465. False. Two lines that coincide have infinitely many points
of intersection.66. False. Solving a system of equations algebraically will
always give an exact solution.67. No. Two lines will intersect only once or will coincide, and if
they coincide the system will have infinitely many solutions.68. (a) (b)
69. (39, 600, 398). It is necessary to change the scale on theaxes to see the point of intersection.
70. It is necessary to change the scale on the axesto see the point of intersection.
71. 72.
73. 74.
75. 76.
77. 78. All real numbers x
79. 80.
81. 82. 83.
84. 85. No solution 86.
87. Answers will vary.
�32, 3
10�log6 4�3x
log9 12x
ln x
�x � 3�5ln 6x
x
420−2−4−6−8x
72
−6 −5 −4 −3 −2 −1 0 1 2 3 4
x > 0x < �4,�5 < x < 72
x
3210−1−2−3x
1815129630
−2
−3
�2 < x < 18
x
7654321
163
43
x
3210
1916
−1
43 ≤ x < 16
3x ≤ 1916
x
43210
−5−6−7−8−9
x
223
−
x > 1x ≤ �223
k � �2k � �4
�300, 315�.
� x � y � 3
2x � 2y � 6�x � y � 10
x � y � 20
y � 3.6t � 49.343y � 14x � 19
y �12 x �
34y � �2x � 4
y � �0.58x � 5.4y � 0.32x � 4.1y � 0.22x � 1.9y � 0.97x � 2.1
Year 1995 1996 1997 1998
y $67.34 $70.94 $74.54 $78.14
Year 1999 2000 2001
y $81.74 $85.34 $88.94
333202CB07_AN.qxd 4/13/06 5:30 PM Page 4
Precalculus with Limits, Answers to Section 7.3 5C
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ved.
Section 7.3 (page 527)
Vocabulary Check (page 527)1. row-echelon 2. ordered triple3. Gaussian 4. row operation5. nonsquare 6. position
1. (a) No (b) No (c) No (d) Yes
2. (a) No (b) Yes (c) No (d) No
3. (a) No (b) No (c) Yes (d) No
4. (a) Yes (b) No (c) No (d) Yes
5. 6. 7.
8. 9. 10.
11. 12.
First step in putting the Eliminated the x-termsystem in row-echelon form from the 3rd equation.
13. 14. 15.
16. 17. 18.
19. No solution 20. No solution 21.
22. 23.
24. 25.
26. 27.
28. 29.
30. 31.
32. 33. No solution 34.
35. 36. 37.
38. 39.
40. 41.
42.
43. 44.
45. 46.
47. 48.
49. 50.
51. 6 touchdowns, 6 extra-point kicks, and 1 field goal
52. 17 two-point baskets, 7 three-point baskets,15 one-point free throws
53. $300,000 at 8% 54. $625,000 at 8%$400,000 at 9% $50,000 at 9%$75,000 at 10% $125,000 at 10%
55. in certificates of deposit
in municipal bondsin blue-chip stocks
s in growth stocks56. in certificates of deposit,
in municipal bonds,
in blue-chip stocks,in growth stocks
57. Brand 58. 20 liters of spray XBrand 18 liters of spray YBrand 16 liters of spray Z
59. 60.
61. 62.
63. (a) Not possible(b) No gallons of 10%, 6 gallons of 15%, 6 gallons of 25%(c) 4 gallons of 10%, No gallons of 15%, 8 gallons of 25%
64. (a) 1 liter of 10%, 7 liters of 20%, 2 liters of 50%
(b) No liters of 10%, liters of 20%, liters of 50%
(c) liters of 10%, No liters of 20%, liters of 50%
65.
66. (a)
(b)
The system is stable.a � 0 feet per second squaredt2 � 64 poundst1 � 128 poundsa � �16 feet per second squaredt2 � 48 poundst1 � 96 pounds
I3 � 1I2 � 2,I1 � 1,
33461
4
12381
3
Pop � 9Newspaper � 20 adsDance � 5Radio � 10 adsRock � 18Television � 30 ads
Irises � 3French Roast � 4 lbLilies � 1Hazelnut � 4 lbRoses � 8Vanilla � 2 lb
Z � 9 lbY � 9 lbX � 4 lb
s125,000 � s
�31,250 �12s
406,250 �12s
125,000 � s125,000 �
12s
250,000 �12s
−2
−3
4
1
−12
−2
6
10
x2 � y 2 � 3x � 2y � 0x2 � y 2 � 6x � 8y � 0
−6
−1
6
7
−3 6
−3
3
x2 � y 2 � 6y � 0x2 � y 2 � 4x � 0
−4 8
4
−4
−6
−2
12
10
y � �2x 2 � 5xy � x2 � 6x � 8
−5
−3
7
5
−4 8
−3
5
y � �x 2 � 2x � 3y �12x 2 � 2x
s � �16t 2 � 16t � 132
s � �16t 2 � 32t � 500s � �16t 2 � 64t
s � �16t 2 � 144�15a �
15, �3
5a �25, a�
�9a, �35a, 67a��0, 0, 0��0, 0, 0�
�3, 72, 12��1, 0, 3, 2�
�1, 1, 1, 1���38a �
14, �3
4a �52, a�
��32a �
12, �2
3a � 1, a���5a � 3, �a � 5, a��2a, 21a � 2, 8a���2a � 5, �7a � 14, a�
��a � 3, a � 1, a���12a �
52, 4a � 1, a�
��3a � 10, 5a � 7, a�� 310, 25, 0�
��12, 1, 32�
�1, 12, �3��5, �2, 0��5, �3, 3���4, 8, 5��5
3, 13, 1��1, 2, 3�
�x � 2y � 3z �
�x � 3y � 5z �
4y � 9z �
5
4
�10�
x
2x
� 2y
y
� 3z � 5
� 2z � 9
� 3z � 0
��2, �103 , �4�� 1
2, �2, 2��17, �11, �3��3, 10, 2��2, �3, �2��1, �2, 4�
333202CB07_AN.qxd 4/13/06 5:30 PM Page 5
Precalculus with Limits, Answers to Section 7.3 6
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d.
(Continued)
67. 68.
69. 70.
71. (a)
(b) (c)
The values are the same.
(d) 24.25% (e) 156 females
72. (a)
(b) (c) 453 feet
73.
74.
75. 76.
77. or 78.
79. False. Equation 2 does not have a leading coefficient of 1.
80. True. If a system of three linear equations is inconsistent,then it has no points common to all three equations.
81. No. Answers will vary.
82. There will be a row representing a contradictory equationsuch as where is a nonzero real number.
83.
84.
85.
86.
87. 6.375 88. 150% 89. 80,000 90. 275
91. 92. 93.
94. 95. 96.
97. (a)
(b)
98. (a)
(b)
99. (a)
(b)
100. (a)
(b)
x8642−2−4
20
y
�12, 13, 5
x1−2−3−5 2 4
30
20
10
−30
−40
−50
−60
y
�4, �32, 3
x
36
30
24
18
−631−1−3
y
±2, 0
x1−1−2−3−5 2 4
25
20
15
−10
−15
−20
y
�4, 0, 3
1751241 �
201241i7
2 �72i11 � 2i
22 � 3i�7 � 3i11 � i
� 4x � y � 2z � 124y � 2z � 2
�2x � y � z � 0�
2x � y � 3z �
�6x � 4y � z �
�4x � 2y � 3z �
�28
18
19
�x � 2y � 4z � 9
y � 2z � 3
x � 4z � �4�
x � 2y � 4z �
�x � 4y � 8z �
x � 6y � 4z �
�5
13
7
� 2x � y � z � �9�x � 2y � 2z � 3
�3x � y � 2z � 11�
x � y � z �
�2x � y � 3z �
x � 4y � z �
�6
15
�14
�x � y � z � 5
x � 2z � 0
2y � z � 0�
3x � y � z � 9
x � 2y � z � 0
�x � y � 3z � 1
N0 � N,
� � �51� � 0� � 1
y � 50y � 0y �12
x � 25x � 0x � ±�2� 2
� � �4� � �5
y � 2y � 5
x � 2x � 5
Safeties � 1Field goals � 3;
Extra-point kicks � 9;Touchdowns � 9;
Extra-point kicks � 5Two-point conversions � 1;
Field goals � 2;Touchdowns � 8;
Speed(in miles per hour)
Stop
ping
dis
tanc
e(i
n fe
et)
x10 7050403020
50100150200250300350400450
60
y
y � 0.165x2 � 6.55x � 103
750
100
175
y � �0.0075x2 � 1.3x � 20
y �37 x 2 �
65 x �
2635y � �
524 x2 �
310x �
416
y � �54 x 2 �
920 x �
19920y � x2 � x
x 100 120 140
y 75 68 55
333202CB07_AN.qxd 4/13/06 5:30 PM Page 6
Precalculus with Limits, Answers to Section 7.3 7C
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. All
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ved.
(Continued)
101.
102.
103.
104.
105. 106. 107. Answers will vary.�12, 0��40, 40�
1 2 3 4−1
18
12
6
x
−6
y
x654321−1−2−3
7
6
5
4
2
2
1
−2
y
x4321−1−2−3−4
12
10
8
6
4
2
−4
−6
y
x64321−1−2−3
12
10
8
6
4
2
−4
−6
y
0 2 4 5
�1�4�4.938�4.996�5y
�2x
x 0 1 2
y 11.625 2.25 �3.6�3�1.5
�1�2
0 1 2
5.793 4.671 4 3.598 3.358y
�1�2x
x 0 1 2
y 28.918 18.25 12.548 9.5 7
12�
12
333202CB07_AN.qxd 4/13/06 5:30 PM Page 7
Precalculus with Limits, Answers to Section 7.4 8
Cop
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Hou
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d.
Section 7.4 (page 539)
Vocabulary Check (page 539)1. partial fraction decomposition 2. improper3. linear; quadratic; irreducible 4. basic equation
1. b 2. c 3. d 4. a
5. 6.
7. 8.
9.
10.
11. 12.
13.
14.
15. 16.
17. 18. 19.
20. 21.
22. 23.
24. 25.
26. 27.
28. 29.
30. 31.
32.
33.
34.
35.
36. 37.
38. 39.
40. 41.
42.
43.
44.
45. 46.
47. 48.
49.
50.
51.
52.
53. (a)
(b)
(c) The vertical asymptotes are the same.
54. (a)
(b)
(c) The vertical asymptotes are the same.
−1 1 2 3 4
1
2
4
x
y = 2x
y = 4x2 + 1
y
–1–2–3–4 1 2 3 4
–4
1
2
3
4
x
y
y �2x, y �
4x2 � 1
y �2�x � 1�2
x�x2 � 1�
2x
�4
x2 � 1
−6 2 8 10
−8
2
8
x
y = 3x
y = 3x
y = 2x − 4
−
y = 2x − 4
−
y
−6 −4 2 8 10
−8
2
4
6
8
x
y
y �3x, y � �
2x � 4
y �x � 12
x�x � 4�
3
x�
2
x � 4
x � 1 �1
x � 2�
1
x � 1
2x �12�
3x � 4
�1
x � 2�
1
21
x � 2�
1
�x � 2�2�
1
x � 2�
1
�x � 2�2
1
x2 � 2�
x
�x2 � 2�2
1
2�1
x�
5
x � 1�
3
�x � 1�22
x�
1
x2�
2
x � 1
2
x�
4
x � 1�
3
x � 1
3
2x � 1�
2
x � 1
2x � 3 �6
2x � 1�
4�2x � 1�2 �
1�2x � 1�3
x � 3 �6
x � 1�
4
�x � 1�2�
1
�x � 1�3
x � 1 �15�
27x � 4
�3
x � 1�2x � 7 �
17x � 2
�1
x � 11 �
5x � 6x2 � x � 6
1 �2x � 1
x2 � x � 12
x � 1�
x � 1
x 2 � 2x � 3
1
x � 1�
2
x2 � 2x � 3
1
x�
x � 1
x2 � 1
1
8 �1
2x � 1�
1
2x � 1�
4x
4x2 � 1�
2
x 2 � 4�
x
�x 2 � 4�2
1
6 �2
x2 � 2�
1
x � 2�
1
x � 2�
15�
9x � 3
�1
x � 2�
10x � 2�
�1
x � 1�
x � 2x2 � 2
1
3�1
x � 1�
x � 1
x 2 � x � 1��
1
x�
2x
x2 � 1
2
x�
1
x 2�
2
x � 1�
7
�x � 1� 2
3
x � 3�
9
�x � 3�2
2
x � 1�
1
�x � 1�2
3
x�
1
x2�
1
x � 1
1
2�3
x � 4�
1
x��
3
x�
1
x � 2�
5
x � 21
x � 3, x � �1
1
x � 1�
1
x � 2
1
x � 2�
1
x � 3
1
x�
2
2x � 1
1
x � 3�
1
x
1
x�
1
x � 1
1
6�1
2x � 3�
1
2x � 3�12�
1x � 1
�1
x � 1�
Ax
�Bx2 �
C3x � 1
�D
�3x � 1�2
Ax
�Bx � Cx2 � 1
�Dx � E
�x2 � 1�2
A2x
�Bx � Cx2 � 4
A
x�
Bx � C
x2 � 10
Ax � 2
�B
�x � 2�2 �C
�x � 2�3 �D
�x � 2�4
Ax � 5
�B
�x � 5�2 �C
�x � 5�3
Ax
�Bx2 �
C4x � 11
A
x�
B
x2�
C
x � 10
A
x � 3�
B
x � 1
A
x�
B
x � 14
333202CB07_AN.qxd 4/13/06 5:30 PM Page 8
Precalculus with Limits, Answers to Section 7.4 9C
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pany
. All
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ved.
(Continued)
55. (a)
(b)
(c) The vertical asymptotes are the same.
56. (a)
(b)
(c) The vertical asymptotes are the same.
57. (a)
(b) Ymax
Ymin
(c) (d) Maximum: Minimum:
58. Answers will vary. Sample answer: You can substitute anyconvenient values of that will help determine constants.You can also find your basic equation, expand it, thenequate coefficients of like terms.
59. False. The partial fraction decomposition is
60. False. The expression is an improper rational expression,so you must first divide before applying partial fractiondecomposition.
61. 62.
63. 64.
65. 66.
67. 68.
69. 70.
x−2−4
2
64
−8
−10
−4
8
4
6
−6
y
x
5
5−10−15−20 10 15 20
y
x−1−2−3
1
32
−2
−3
−4
2
y
x
3
4
5
−1 1 2 4 5−2−3−1
−2
−3
y
x−2−4−6 2
−4
−6
−8
−10
−12
−14
−16
4 6 8 10 12
y
x
2
4
6
8
−2 2 4 8 10−2
−4
y
1a � 1�
1x � 1
�1
a � x�1a �
1y
�1
a � y�
1a�
1x
�1
x � a�12a �
1a � x
�1
a � x�
Ax � 10
�B
x � 10�
C�x � 10�2.
x
266.7�F400�F
0
−100
1
Ymax
Ymin
1000
� � �200011 � 7x�
� � 20007 � 4x�
2000
7 � 4x�
2000
11 � 7x, 0 < x ≤ 1
−2−4 2 4 6 8 10 12
−4
10
12
x
y =
y = 5x2 − 10x + 26
3x2
y
−2−4 2 4 6 8 10 12
−4
10
12
x
y
y �3x2, y �
5x2 � 10x � 26
y �2�4x2 � 15x � 39�x2�x2 � 10x � 26�
3x2 �
5x2 � 10x � 26
−4 2 4 6 8
−8
−6
−4
6
8
x
y = 5x + 3
y = 5x + 3
y = 3x − 3
y = 3x − 3
y
−4 4 6 8
−8
−6
−4
4
6
8
x
y
y �3
x � 3, y �
5x � 3
y �2�4x � 3�
x2 � 9
3
x � 3�
5
x � 3
333202CB07_AN.qxd 4/13/06 5:30 PM Page 9
Precalculus with Limits, Answers to Section 7.5 10
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erve
d.
Section 7.5 (page 548)
Vocabulary Check (page 548)1. solution 2. graph 3. linear4. solution 5. consumer surplus
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. 12.
13. 14.
15. 16.
17. 18.
19. 20.
21. 22.
23. 24.
25. 26.−8
−10
8
2
−50
4
6
−6
−4
6
4
−9
−9
9
3
−18
−22
18
2
−3
−2
3
2
−6
−1
9
9
−6
−4
6
4
−12
−8 4
4
−2
−8 1
4
−2
−9 9
10
−2
0 6
2
x321−1−2−3
3
2
1
−2
−3
−5
y
−3 −2 −1 1 2 3
−3
−2
2
3
x
y
y
x−1−2−3−4 1 2 3 4
−1
1
2
3
4
5
6
7
−5 −4 2 3
−2
1
2
3
4
6
x
y
−6 −4 2 4
−8
−6
2
x
y
−4 −3 −2 −1 1
−2
1
3
4
x
y
−3 −2 −1 1 3 4 5
−4
−3
−2
1
2
x
y
−2 −1 1 2 3 4
−2
1
2
3
4
x
y
−3 −2 −1 1 2 3
−2
−1
1
2
4
x
y
1−1−2−3 2 3
−2
1
2
3
4
x
y
−1 1 2 3 5
−3
−2
−1
1
2
3
x
y
−1 1 3 4 5
−3
−2
−1
1
2
3
x
y
−1 1 2 3 4 5
−3
−2
−1
1
2
3
x
yy
x−1−2−3 1 2 3
−1
−2
−3
1
3
333202CB07_AN.qxd 4/13/06 5:31 PM Page 10
Precalculus with Limits, Answers to Section 7.5 11C
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ved.
(Continued)
27.
28.
29.30.31. (a) No (b) No (c) Yes (d) Yes32. (a) Yes (b) No (c) No (d) No33. (a) Yes (b) No (c) Yes (d) Yes34. (a) No (b) No (c) No (d) Yes35. 36.
37. 38.
39. 40.
No solution
41. 42.
43. 44.
45. 46.
47. 48.
49. 50.
51. 52.
53. 54.
55. 56. 57.
58. x2 � y2 > 4
�y ≥ 4 � x
y ≥ 2 �14 x
x ≥ 0, y ≥ 0�
y < 6 � 2x
y ≥ x � 3
x ≥ 1�
y ≤ 4 � x
x ≥ 0
y ≥ 0
−3
−1
3
3
−2 7
−1
5
−3
−2
3
2
−6 6
−3
5
−4
−3
8
5
−5
−1
7
7
−3 −2 1
−1
1
3
x
(0, 0)
(−3, 3)
y
x54321
4
3
2
1
−3
−4
(4, 4)
y
(−1, −1)
x2−2−6 4 6
−6
−4
2
4
6
(3, 4)
(−3, −4)
y
−4 −2 2 4
−4
−2
2
4
x
y
1 2 3 4
−2
−1
1
2
x
(4, 2)
(1, −1)
y
−1 1 2 3 4 5
−3
−2
1
2
3
x
(4, 2)
(1, −1)
y
2 4 6
–2
4
6
x
(0, 3)
y
( (
−3 −1 1 3 4
−3
−2
1
3
5
x(−2, 0)
,
y
109
79
x
(6, 6)
(1, 0)
y
2 4 6
2
6
−2 −1 2 3 4
−2
−1
1
4
x
y
x4−2−4
(2, 1)
−2
−4
−6 (2, −6)
, 1 22( (
, 1 − 22( (
y
x4321−3−4
6
4
3
2
1
(−1, 4)
(−1, 0) 5, 0( (
y
1 3
1
2
3
x(0, 0) (2, 0)
(0, 3)
y
−2 1 2
−1
2
3
x(−1, 0) (1, 0)
(0, 1)
y
x2 � y2 ≤ 9y ≥ �
23 x � 2
y ≥ x2 � 4
y ≤ 12 x � 2
333202CB07_AN.qxd 4/13/06 5:31 PM Page 11
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d.
(Continued)
59. 60. 61.
62. 63.
64.
65. (a) (b) Consumer surplus: $1600Producer surplus: $400
66. (a) (b) Consumer surplus: $6250Producer surplus: $12,500
67. (a)
(b) Consumer surplus: $40,000,000Producer surplus: $20,000,000
68. (a)
(b) Consumer surplus: $6,250,000Producer surplus: $15,625,000
69.
70.
71.
72.
73.
74.
1 2 4 5
1
2
5
6
y
x
�6x
3x
x
�
�
4y ≥6y ≥
≥y ≥
15
16
0
0
100
120
80
60
40
20
x20 40 60 80 100 120
y
�55xx
� 70y ≤≥
y ≥
75005040
500
1500
2500
x500 1500 2500 3500 4500
3500
4500
y
�x
30x
x
x
�
�
y ≤20y ≥
≤≥
y ≥
3000
75,000
2000
0
0
10,000 15,000
10,000
15,000
x
y
�x
x
� y
y
y
≤≥≥≥
20,000
2x
5,000
5,000
8 12 16 20 24
4
8
12
16
20
24
x
y
�x
8xx
� 12y
y
≥ 2y
≤ 200
≥ 4
≥ 2
2 4 6 8 10
2
4
6
10
12
x
y
�x
43 x
x
�32 y
�32 y
y
≤ 12
≤ 15
≥ 0
≥ 0
x
600
500
400
300
200
100
200,000 400,000
(250,000, 350)
p = 400 − 0.0002x
p = 225 + 0.0005x
Consumer SurplusProducer Surplus
p
x1,000,000 2,000,000
80
100
120
140
160
p = 80 + 0.00001x
p = 140 − 0.00002x
(2,000,000, 100)
Consumer SurplusProducer Surplus
p
x
200
150
100
50
200 400 600
(500, 75)
p = 25 + 0.1x
p = 100 − 0.05x
Consumer SurplusProducer Surplus
p
x10 60 70 80504020 30
10
20
30
40
50
(80, 10)
Consumer SurplusProducer Surplus
p
p = 50 − 0.5x
p = 0.125x
�y ≤ x � 1
y ≤ �x � 1
y ≥ 0
� y ≤ 32 x
y ≤ �x � 5y ≥ 0�
4x � y ≥ 0 4x � y ≤ 16
0 ≤ y ≤ 4
�2 ≤ x ≤ 5
1 ≤ y ≤ 7�x2 � y2 ≤ 16
x ≤ y
x ≥ 0 �
x2 � y2 ≤ 16
x ≥ 0
y ≥ 0
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Precalculus with Limits, Answers to Section 7.5 13C
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pany
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ved.
(Continued)
75. (a) (b)
(c) Answers will vary.
76. (a)
(b)
(c) Answers will vary.77. (a)
(b)
(c)
78. (a) (b)
79. True. The figure is a rectangle with a length of 9 units anda width of 11 units.
80. False. The graph shows the solution of the system
81. The graph is a half-line on the real number line; on therectangular coordinate system, the graph is a half-plane.
82. Test a point on either side.
83. (a) (b)
(c) The line is an asymptote to the boundary. The largerthe circles, the closer the radii can be and the constraintwill still be satisfied.
84. (a) The boundary would be included in the solution.
(b) The solution would be the half-plane on the oppositeside of the boundary.
85. d 86. b 87. c 88. a
89. 90.
91. 92.
93. 94.
95. (a)
(b)
(c) The quadratic model is the best fit for the data.(d) $48.66
y1
y2
y3
530
18
60
y3 � 27�1.05t�
y2 � �0.241t2 � 7.23t � 3.4
y1 � 2.17t � 22.5
60x � 35y � 113 � 0x � y � 1.8 � 0
2x � y � 1 � 028x � 17y � 13 � 0
x � 11y � 8 � 05x � 3y � 8 � 0
−6 6
−4
4
�y2 � x2 ≥y >x >
10x0
� y < 6�4x � 9y < 6
3x � y2 ≥ 2.
10 20 30 40 50 60
10
20
30
50
60
x
y
�2x
x
�
xy ≥y ≥
≥y ≥
500
125
0
0
Total retail sales �h2
�a � b� � $821.3 billion
80
14
225
y � 19.17t � 46.61
y
x25 50 75 100
25
50
75
100
125
150
175
y ≥ 0.5�220 � x�y ≤ 0.75�220 � x�x ≥ 20x ≤ 70
30
30
x
y
�20x
15x
10x
x
�
�
�
10y
10y
20y
y
≥ 300
≥ 150
≥ 200
≥ 0
≥ 0
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erve
d.
Precalculus with Limits, Answers to Section 7.6 14
Section 7.6 (page 558)
Vocabulary Check (page 558)1. optimization 2. linear programming3. objective 4. constraints; feasible solutions5. vertex
1. Minimum at 0 2. Minimum at 0
Maximum at 20 Maximum at 32
3. Minimum at 0 4. Minimum at 0
Maximum at 40 Maximum at 14
5. Minimum at 0 6. Minimum at 10
Maximum at 17 Maximum at 31
7. Minimum at 0 8. Minimum at 2
Maximum at Maximum at 11
9. Minimum at 0
Maximum at
10. Minimum at 11,250
Maximum at 28,000
11. Minimum at
Maximum at any point on the line segment connectingand
12. Minimum at 6750
Maximum at 16,000
13. 14.
Minimum at Minimum at Maximum at Maximum at 15. 16.
Minimum at Minimum at Maximum at Maximum at 17. 18.
Minimum at Minimum at No maximum Maximum at 19. 20.
Minimum at Minimum at No maximum Maximum at 21. 22.
Minimum at Minimum at any point onMaximum at the line segment connecting
and Maximum at
23. 24.
Minimum at Minimum at any point onMaximum at the line segment connecting
and Maximum at
25. Maximum at 26. Maximum at
27. Maximum at
28. Maximum at any point on the line segment connectingand �5, 0�: 15�3, 6�
�0, 10�: 10
�5, 0�: 25�3, 6�: 12
�0, 20�: 20�12, 0�: 0�0, 0�
�24, 8�: 56�36, 0�: 36
−5
−5
40
25
20
−5
50
15
�12, 0�: 12�0, 20�: 0�0, 0�
�40, 0�: 160�24, 8�: 104
−5
−5
40
25
20
−5
50
15
�5, 0�: 10�0, 3�: �3�10, 0�: 20
2 3
1
2
4
x
(0, 3)
(0, 0)
(4, 1)
(5, 0)
y
2 4 6 8
2
4
10
x
(0, 8)
(5, 3)
(10, 0)
y
�4, 1�: 21�0, 0�: 0�5, 3�: 35
2 3
1
2
4
x
(0, 3)
(0, 0)
(4, 1)
(5, 0)
y
2 4 6 8
2
4
10
x
(0, 8)
(5, 3)
(10, 0)
y
�4, 0�: 28�0, 2�: 48�0, 0�: 0�0, 0�: 0
2 6 8
2
4
6
8
x
(0, 8)
(4, 0)
(0, 0)
y
2 3 4 5
−1
1
3
4
x
(0, 2)
(5, 0)
(0, 0)
y
�0, 8�: 64�5, 0�: 30�0, 0�: 0�0, 0�: 0
2 6 8
2
4
6
8
x
(0, 8)
(4, 0)
(0, 0)
y
2 3 4 5
−1
1
3
4
x
(0, 2)
(5, 0)
(0, 0)
y
�0, 800�:�450, 0�:�30, 45�: 2100�60, 20�
�0, 0�: 0�0, 800�:�450, 0�:�60, 20�: 740
�0, 0�:�4, 3�:�4, 0�: 20
�0, 2�:�0, 0�:�4, 3�:�3, 4�:�0, 2�:�0, 0�:�2, 0�:�0, 5�:�0, 0�:�0, 0�:�0, 4�:�5, 0�:�0, 0�:�0, 0�:
333202CB07_AN.qxd 4/13/06 5:31 PM Page 14
Precalculus with Limits, Answers to Section 7.6 15C
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. All
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ved.
(Continued)
29. Maximum at 30. Maximum at
31. Maximum at 32. Maximum at
33.
The maximum, 5, occurs at any point on the line segmentconnecting and
34.
The constraints do not form a closed set of points. There-fore, is unbounded.
35.
The constraint is extraneous. Maximum at
36.
The feasible set is empty.
37.
The constraint is extraneous. Maximum at
38.
The maximum, 4, occurs at any point on the line segmentconnecting and
39. 750 units of model A 40. 1000 units of model A1000 units of model B 500 units of model BOptimal profit: $83,750 Optimal profit: $76,000
41. 216 units of $300 model 42. 60 acres of crop A0 units of $250 model 90 acres of crop BOptimal profit: $8640 Optimal profit: $29,550
43. Three bags of brand XSix bags of brand YOptimal cost: $195
44. (a)(b) (c)
(d) gallon of 87 octane and gallon of 93 octane(e) $1.90 per gallon(f) Yes, the cost is lower than the national average of
$1.96 for mid-grade unleaded gasoline.45. 0 tax returns
12 auditsOptimal revenue: $30,000
13
23
y ≥ 0 x ≥ 0
87x � 93y ≥ 89
12
14
14
12
34
34
( (23
13
,
y
x
x � y ≥ 1C � 1.84x � 2.03y
�43, 43�.�0, 2�
x
(0, 2)
(0, 0)
(2, 0)
( (43
43
1
1
,
y
�0, 1�: 42x � y ≤ 4
x
(0, 1)
(1, 0)
(0, 0) 3 4
2
3
y
−2−3 1 2
−2
−1
3
x
y
�0, 7�: 14x ≤ 10
x
(0, 7)
(0, 0)
(7, 0)
2 4 6
2
4
6
10
y
z � x � y
1 2 3 4
3
4
x
(0, 1)
(2, 3)
(0, 0)
y
�2019, 45
19�.�2, 0�
(0, 0)x
1 3
1
2
( (2019
4519
(2, 0)
(0, 3) ,
y
�212 , 0�: 42� 22
3 , 196 �: 271
6
823�22
3 , 196 �:�0, 5�: 25
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Precalculus with Limits, Answers to Section 7.6 16
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d.
(Continued)
46. 42 tax returns5 auditsOptimal revenue: $24,700
47. $62,500 to type A 48. $225,000 to type A$187,500 to type B $225,000 to type BOptimal return: $23,750 Optimal return: $36,000
49. True. The objective function has a maximum value at anypoint on the line segment connecting the two vertices.
50. True. If an objective function has a maximum value atmore than one vertex, then any point on the line segmentconnecting the points will produce the maximum value.
51. (a) (b)
52. (a) (b)
53. 54. 55.
56. 57.
58. 59.
60. 61.
62. 63.
64. 65.
66. 67.
68. ��1, 2, �3���4, 3, �7�e � 9 � �6.282
13 e12�7 � 1.851�ln 6 � �1.792
4 ln 38 � 14.550ln 6 � 1.792ln 4 � 1.386,
ln 3 � 1.099�x � 1��x � 3�
3, x � �1
x2 � 2x � 13
x�x � 2�, x � ±3
1
x � 2, x � 0, �2
9
2�x � 3�, x � 0z � �10x � y
z � 4x � yz � x � yz � x � 5y
t ≥ 6�3 ≤ t ≤ 6
34 ≤ t ≤ 9t ≥ 9
333202CB07_AN.qxd 4/13/06 5:31 PM Page 16
Precalculus with Limits, Answers to Review Exercises 17C
opyr
ight
©H
ough
ton
Mif
flin
Com
pany
. All
righ
ts r
eser
ved.
Review Exercises (page 563)1. 2. 3. 4.5. 6. 7.8. 9. 10.
11. 12.13. 14.
15. 3847 units 16. Sales greater than $500,00017. 18.19. 20. 21. 22.23. 24. 25.
26. No solution 27. d, one solution, consistent28. c, infinite solutions, consistent29. b, no solution, inconsistent30. a, one solution, consistent
31. 32.
33. 34. 35.
36. 37.
38. 39.
40. 41.42.43.44.45. (a)
(b) (c) 195.2; yes.
The model is a good fit46. 10 gallons of spray X 47. $16,000 at 7%
5 gallons of spray Y $13,000 at 9%12 gallons of spray Z $11,000 at 11%
48. (a)(b)
49. 50.
51. 52.
53. 54.
55. 56.
57. 58.
59. 60.
61. 62.
63. 64.
65. 66.
67. 68.
69. 70.
−6 −2 4
−2
2
4
8
x
(0, 6)
(−3, 3)
y
x
(2, 3)
(−1, 0)
1−3−4 2 3 4
−2
2
3
4
5
6
y
5 15
5
10
15
x(25, 0)
(25, 25)
(18, 0)
(0, 16)
(0, 25)
(6, 4)
y
x4 12
4
8
12
16
(15, 15)
(6, 3)
(2, 9)
(2, 15)
15, − 32( (
y
4 12 16
4
12
16
x(0, 0)(0, 0)
(8, 0)
(0, 8)
(6, 4)
y
x20 40 80 100
20
40
60
100
(0, 80)
(40, 60)
(60, 0)(0, 0)
y
y
x−4 −3 −2 −1 1 2
4
3
2
−1
−2
−3
−4
3 4x
1 2
4
3
2
1
−2
−1−2−3 3
y
x2−2−4−6
8
6
4
−2
y
x108642−2
6
4
2
8
10
−2
−4
y
2� 1x � 1
�x � 1x2 � 1�
3xx2 � 1
�x
�x2 � 1�2
43�x � 1� �
43�x � 1�2
12�
3x � 1
�x � 3x2 � 1�
12�
3x � 3
�3
x � 3�1 �25
8�x � 5� �9
8�x � 3�
1x � 1
�2
x � 23
x � 2�
4x � 4
Ax
�Bx � Cx2 � 2
�Dx � E
�x2 � 2�2
Ax
�Bx2 �
Cx � 5
Ax � 7
�B
x � 4Ax
�B
x � 20
s � �16t 2 � 20t � 220s � �16t 2 � 150
080
6
130
y � 3x2 � 14.3x � 117.6x2 � y2 � 2x � 2y � 23 � 0x2 � y2 � 4x � 4y � 1 � 0y � 3x2 � 11x � 14
y � 2x2 � x � 5��3a � 2, 5a � 6, a��a � 4, a � 3, a���3
4, 0, �54�
�3a � 4, 2a � 5, a��3817, 40
17, �6317�
�245 , 22
5 , �85��5, �8, 3��2, �4, �5�
�250,000, 95��500,0007
, 1597 �
�85 a �
145 , a���3, 7��0, 0�
�13, �1
2���0.5, 0.8�� 310, 25��5
2, 3�16 feet � 18 feet96 meters � 144 meters
�9.68, �0.84��0, �2�−4
120
4
−6
−6 6
2
��3, 3��0, 0�,��1.41, 10.66��1.41, �0.66�,�1.5, 5��4, �2��2, �1��5, 2�,�0, 0�, �2, 8�, ��2, 8��5, 12��13, 0�,�5, 4�
�115 , 7��0.25, 0.625���3, �3��1, 1�
333202CB07_AN.qxd 4/13/06 5:31 PM Page 17
(Continued)
71. 72.
73.
74. (a)
(b)
(c) Answers will vary. Sample answer: and 75. (a)
(b) Consumer surplus: $4,500,000Producer surplus: $9,000,000
76. (a)
(b) Consumer surplus: $4,000,000Producer surplus: $6,000,000
77. 78.
Minimum at 0 Minimum at 600Maximum at No maximum79. 80.
Minimum at Minimum at 0No maximum Maximum at 60,00081. 82.
Minimum at 0 Minimum at
Maximum at No maximum
83. 72 haircuts, 0 permanents; Optimal revenue: $1800
84. 5 walking shoes 85. Three bags of brand X
2 running shoes Two bags of brand Y
Optimal profit: $138 Optimal cost: $105
86. regular unleaded gasoline
premium unleaded gasoline
Optimal cost: $1.70
87. False. To represent a region covered by an isosceles trape-zoid, the last two inequality signs should be
88. False. An objective function can have no maximum value,one point where a maximum value occurs, or an infinitenumber of points where a maximum value occurs.
≤.
�13�
�23�
�3, 3�: 48
�7, 0�: �14�0, 0�:
y
x
100
75
50
25
1007525
(0, 100)
(25, 50)
(75, 0)
y
x
1
2
1 2 3 4 5 6
3
4
5
6
(0, 4)
(3, 3)
(5, 0)(0, 0)
�500, 500�:�0, 0�:�15, 0�: 26.25
y
x
200
200 400 600 800
400
600(500, 500)
(700, 0)
(0, 750)
(0, 0)
y
x3
3 6 9 12 15 18 21 24 27
6
9
12
15
18
21
24
27 (0, 25)
(5, 15)
(15, 0)
�5, 8�: 47�25, 50�:�0, 0�:
y
x
100
75
50
25
1007525
(0, 100)
(25, 50)
(75, 0)
y
x
3
3 6 9 12 15
6
9
12
15
(0, 10)
(5, 8)
(7, 0)(0, 0)
x
200
150
100
50
100,000 300,000
(200,000, 90)
p = 30 + 0.0003x
p = 130 − 0.0002x
Consumer SurplusProducer Surplus
p
x100,000 200,000 300,000
50
75
100
125
150
175
p x= 70 + 0.0002
(300,000, 130)
Consumer SurplusProducer Surplus
p
p = 160 − 0.0001x
�16, 9��15, 8�5 10 20 25
5
10
20
25
y
x
�12x10x20x
x
�
�
�
15y ≥20y ≥12y ≥
≥y ≥
300280300
00
y � food Yx � food X,
−400 1600
−400
1600
�20x12x
x
�
�
30y ≤8y ≤
≥y ≥
24,00012,400
00
x−4 2 4 8
−6
−4
2
4
6
32 2
3 3, −( (
32 2
3 3, ( (
y
x2 4 6 8
−2
2
4
6
8
(0, 0) (4, 0)
(6, 4)
y
Precalculus with Limits, Answers to Review Exercises 18
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Precalculus with Limits, Answers to Review Exercises 19
(Continued)
89. 90.
91. 92.
93. 94.
95. 96.
97. An inconsistent system of linear equations has no solution.
98. The lines are distinct and parallel.
99. Answers will vary.
� x � 2y � 32x � 4y � 9
�4x � y � z �
8x � 3y � 2z �
4x � 2y � 3z �
�7
16
31�
2x � 2y � 3z �
x � 2y � z �
�x � 4y � z �
7
4
�1
�x � 2y � z �
2x � y � 4z �
�x � 3y � z �
�7
�25
12�
x � y � z � 6
x � y � z � 0
x � y � z � 2
��x � 4y �
3x � 8y �
10
�21� 3x � y � 7
�6x � 3y � 1
� x � y � 9
3x � y � 11�x � y �
x � y �
2
�14
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333202CB07_AN.qxd 4/13/06 5:31 PM Page 19
Chapter Test (page 567)1. 2.3.4. 5.
6.
7. 8.9. 10. No solution
11. 12.
13. 14.
15. 16.
17.
18. Maximum at Minimum at 19. 8%: $20,000 20.
8.5%: $30,00021. 0 units of model I
5300 units of model IIOptimal profit: $212,000
y � �12 x2 � x � 6�0, 0�: 0�12, 0�: 240;
x532
5
3
2
1
−2
−5
1, 15
7, −3 ( (
( (
(1, −3)
−1−2−3−5
y
x−3 6 9 12−6−9−12
−18
3(1, 4)
6
y
(−4, −16)
x−1−2
−2
2
3
31
(0, 0)
(1, 2)
4
1
4
y
�2x
�3x
x2 � 2�
5x
�3
x � 1�
3x � 1
2x2 �
32 � x
�1
x � 1�
3x � 2
�2, �3, 1��2, �1��1, 5�
�0.034, 8.619��1, 12�,
(0.034, 8.619)
(1, 12)
1−1 2 3
4
12
16
y
x
��3, 0�, �2, 5��3, 2�
x−6−9 6 9
−3
−6
3
6
9
12
(−3, 0)
(2, 5)
y
x2 4 6 10
−2
−4
2
4
6
8
(3, 2)
y
�8, 4�, �2, �2��0, �1�, �1, 0�, �2, 1���3, 4�
Precalculus with Limits, Answers to Chapter Test 20
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Precalculus with Limits, Answers to Problem Solving 21
Problem Solving (page 569)1.
Therefore, the triangle is a right triangle.2. 3.4. (a)
Answers will vary.(b)
Answers will vary.
5. (a) One (b) Two (c) Four
6.
Kerry: 57,314,544 votesBush: 60,634,544 votesNader: 354,912 votes
7. 10.1 feet high;
8. Carbon: 12.011 u 9. $12.00
Hydrogen: 1.008 u
10.
5 miles from the airport
11. (a) (b)
12.
13. (a)
(b)
(c) (d) Infinitely many
14.
15.
16. (a) (b)
(c) 142.8 pounds ≤ y ≤ 186.2 pounds
00
45
300
�y ≥ 91 � 3.7xy ≤ 119 � 4.8xx ≥ 0y ≥ 0
t
a
−5
5
30252015105−5
10
20
25
30� a �
0.15a 193a �
t ≤≥
772t ≥
321.911,000
x5 � 1x4 � �5;x3 � 3;x2 � �2;x1 � 2;
��a � 3, a � 3, a�
��11a � 3614
, 13a � 40
14, a�
��5a � 166
, 5a � 16
6, a�
a � 12, b � �4, c � 10
� 2�a � 5
, 1
4a � 1,
1a��3, �4�
�1, 30�
d
t
40
30
20
10
12
12
1 232
−
�d1 � 30td2 � 40�t �
14�
� 252.7 feet long
N � 354,912 B � K � 3,320,000
B � K � N � 118,304,000
�32 a �
72, a�
y
x−2
−4
−2
−1
1
2
3
4
−1 1 52 4 6
�5, 2�
y
x−2
−4
−2
−3
−1
1
3
4
−1 1 32 4 6
y
x−2
−4
−2
−3
−1
1
3
4
−1 1 32 4 5 6
y
x−2
−4
−2
−1
1
2
3
4
−1 1 3 4 5 6
ad � bck1 � �103 , k2 �
163
�8�5�2� �4�5 �2
� 202
a � 8�5, b � 4�5, c � 20
y
x−8 −4
−12
−8
−4
8
12
4 8
(−10, 0)(6, 8)
(10, 0)
a bc
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333202CB07_AN.qxd 4/13/06 5:31 PM Page 21
(Continued)
17. (a) (b)
(c) No, because the total cholesterol is greater than 200milligrams per deciliter.
(d) LDL: 140 milligrams per deciliter
HDL: 50 milligrams per deciliter
Total: 190 milligrams per deciliter
(e) answers will vary.�50, 120�; 17050 � 3.4 < 4;
y
x50
50
100
150
200
250
100 150 250
(35,130)
(70, 130)
�xx0
� y
< y
≤ 200≥ 35 ≤ 130
Precalculus with Limits, Answers Problem Solving 22
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