Coburn J.W., Herdlick J.D. College Algebra: Graphs and Models
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75. a. 5 b. 18 c. The horizontal asymptote at means her
average grade will approach 95 as the number of tests taken increases; no
d. 6 77. a. 16.0, 28.7, 65.8, 277.8 b. 12.7, 37.1, 212.0
c. a. 22.4, 40.2, 92.1, 388.9 b. 17.8, 51.9, 296.8; answers will vary.
79. 81.
Exercises 4.5, pp. 454–458
1. slant 3. two 5. Answers will vary.
7.
9.
11.
13.
15.
17.
19. 21. 23.
25. 27. 29.
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y x
(1, 0)(2, 0)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y x 3
(1, 0)(2, 0)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y x 2
(1, 0)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y x
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y x
(
兹
3, 0) (
兹
3, 0)
x
y
(2, 0)
(2, 0)
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y x
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
(3, 2)
(1, 2)
R1x2 μ
x
3
3x
2
x 3
x
2
2x 3
x 3, x 1
2 x 3
2 x 1
x
y
54321
5
4
3
2
1
2
4
6
8
10
4
6
8
10
2
(1, 4)
Q1x2
•
x
3
7x 6
x 1
x 1
4 x 1
x
y
84
8
4
2
12
16
8
4
(2, 12)
P1x2 •
x
3
8
x 2
x 2
12 x 2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
冢
w,
w
冣
H1x2 μ
3x 2x
2
2x 3
x
3
2
3
2
x
3
2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
(1, 4)
G1x2 •
x
2
2x 3
x 1
x 1
4 x 1
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
(2, 4)
F1x2 •
x
2
4
x 2
x 2
4 x 2
16
3
,
3
4
; 13x 16214x 32 0y
4
3
x
1
3
y 95
31. 33. 35.
37. 39. 41.
43. 45. 47.
49. 51. 119.1
53. a. b. 60.5 c. 10
55. a.
b. cost: $307, $372, $445; Avg. cost: $307, $186, $148.33
c. 8, $116.25
d.
57. a. b.
c. S(x) is asymptotic to d. 3.5 in.; 3.5 in.
59. a. b. ;
c. A(x) is asymptotic to
d. in.; in. 61. a. b.
c. d. cm, cm;
63. Answers will vary. 65.
67.
69. a. cm, b. cm, c. 30 cm
2
,
d. cm
2
, and cm
2
Exercises 4.6, pp. 465–469
1. vertical, multiplicity 3. empty 5. Answers will vary.
7. 9.
11. 13. x 僆 12 13
, 2 132x 僆 1q, 24 ´ 526 ´ 34, q2
x 僆 34, q2 ´ 516x 僆 13, 52
A
4320
169
A
750
169
CD
60
13
P 30
y
3
4
x 4, m
3
4
, 10, 42
S
r
3
2V
r
; r ⬇ 3.1 in., h ⬇ 3 in.
S ⬇ 625.13 cm
2
h ⬇ 11.51r ⬇ 5.76S
2r
3
2V
r
S 2r
2
2V
r
h
V
r
2
y ⬇ 8.93x ⬇ 11.16
y 2x 60A1x2
2x
2
55x
x 2.5
y
2x 55
x 2.5
R1x, y2 1x 2.521y 22A1x, y2 xy;
y ⬇ 2 ftx ⬇ 2 fty 2x
2
.
S1x2
2x
3
48
x
y
12
x
2
;S1x, y2 2x
2
4xy; V1x, y2 x
2
y
0
300
200
x 0, y 4x 53A1x2
4x
2
53x 250
x
;
a 5, y 3a 15
x
y
642
6
4
2
4
8
12
16
12
16
4
8
y 14 x
2
(3.2, 0)
(3.2, 0)
(0, 2)
x
y
54321
5
4
3
2
1
1
2
5
6
7
8
4
3
2
1
y x
2
1
(0, 4)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y
x
x 3
x 3
(2, 0)
(0, 0.2)
(1, 0)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y x
(4, 0)
(4, 0)
(0, 0)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y x
x 1
x 1
(2, 0) (2, 0)
(0, 0)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y x 1
x 1
(2, 0)
(2, 0)
(0, 4)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y x 1
x 1
(0, 1)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y x 1
x 3
(2, 0)
(
0, d
)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y x 1
(2, 0)
(2, 0)
(1, 0)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y x 5
(1, 0)
(4.8, 0)
(0.8, 0)
SA-26 Student Answer Appendix
cob19545_saa_018-038.qxd 11/26/10 9:59 PM Page SA-26
15. 17.
19.
21. 23.
25. 27.
29. 31.
33. 35.
37. 39.
41. 43.
45. 47. 49.
51. 53.
55. 57. d 59. b 61. a. verified
b.
c. d. verified
63. a. b. 320k units
c. d. 2 ft 65. a. verified b. horizontal: , as r
1
increases, r
2
decreases to maintain ; vertical: , as r
1
decreases, r
2
increases to maintain c.
67. a. b.
c. 69. a. b. c. 13
71. a. yes, b. yes,
73.
75. for
77. 79.
Making Connections, p. 470
1. e 3. b 5. a 7. h 9. d 11. a 13. g 15. c
Summary and Concept Review, pp. 470–474
1. 2.
3. 213 914
7
2120
Since is a root and is a factor.
4.
5. 6.
7. 48
251
410 2 0
Since is a root and is a factor.
8. 3i 19
3i 18
10
Since 3i is a zero
9. 1913
7
12
10. 11.
12. a. customers b. more at 2
P
.
M
., 170
c. busier at 1
P
.
M
., 13.
14. 15. 16. only
possibilities are none give a remainder of zero 17. [1, 2], [4, 5];
verified 18. one sign change for positive zero; three sign changes
for or 1 negative zeroes; 1 positive, 3 negative, 0 complex, or 1
positive, 1 negative, 2 complex; 1 positive, 1 negative, 2 complex, verified
g1x2S 3
g1x2S 1
1, 3,
P1x2 12x 321x 421x 12x
1
2
, 2,
5
2
51, 10, 2, 5,
1
2
,
5
2
,
1
4
,
5
4
6760 7 710
C102 350
C1x2 x
4
2x
3
5x
2
8x 4P1x2 x
3
x
2
5x 5
h1723
31
147
107
r 0,
6i2 3i
9 6i
182
1x
1
2
2
1
2
r 0,
13
1
2
h1x2 1x 121x 421x
2
2x 221x 421x 121x 32
x
3
4x 5 1x 221x
2
2x2 5
x 7r 0, 7
1
14714
67
q1x2 x 1; r 3x 4q1x2 x
2
6x 7; r 8
x 僆 33, 94F1x2 e
f 1x2 x 4
6 x 4
x
y
54321
5
4
3
2
1
5
6
7
4
3
2
1
3
2
1
x 僆 12, 82 ´ 18, 142R1x26 0
x1x 221x 12
2
7 0;
x1x 22
1x 12
2
7 0
x
2
x
2
1
0x
2
0
n 9n 4150°, q2
120°, q230°, 30°2R1t2 0.01t
2
0.1t 30
r
1
僆 120, 402R 40
r
1
20R 40
r
2
20x 僆 30, 32
x 僆 15, 84d1x2 k1x
3
192x 10242
1q, 32 ´ 13,
3
4
2
D 41p
3
4
21p 32
2
; p 3, q 2; p
3
4
, q
1
4
x 僆 33, 04 ´ 33, q2
x 僆 1q, 34 ´ 35, q21q, 32 ´ 13, q2
x 僆 11, q2x 僆 12, q2
x 僆 13,
7
4
4
´ 12, q2
x 僆 1q, 172 ´ 12, 12 ´ 17, q2x 僆 1q, 24 ´ 10, 22
x 僆 17, 32 ´ 12, q2x 僆 14, 24 ´ 11, 24 ´ 13, q2
x 僆 1q, 52 ´ 10, 12 ´ 12, q2x 僆 1q, 22 ´ 32, 32
x 僆 1q, 22 ´ 12, 12x 僆 33, 22
x 僆 1q, 24 ´ 11, 12 ´ 33, q2x 僆 1q, 22 ´ 12, 32
x 僆 31, 14 ´ 536x 僆 1q, 22 ´ 12, 12 ´ 13, q2
x 僆 1q, 32 ´ 11, 12 ´ 13, q2
x 僆 13, 12 ´ 12, q2x 僆 1q, 34 ´ 516 19. degree 5; up/down; 20. degree 4; up/up;
21. 22. 23.
24. a. even b. odd; even; odd c. deg 6:
25. a. b. HA: VA:
c. (y-intercept); (x-intercepts) d.
26. No—even multiplicity; yes—odd multiplicity
27. 28.
29.
30. a. as As production increases, average
cost decreases and approaches 15. b.
31. removable discontinuity at ;
32.
33. 34.
35. a.
b. about 2450 favors c. about $2.90 ea.
36. factored form
outputs are positive for
37.
outputs are positive or zero for
38.
outputs are negative or zero for
x 僆 32, 02 ´ 31, 22
1
Pos Pos Neg PosNeg
02 1 2
1x 221x 12
x1x 22
0
x 僆 32, 22 ´ 35, q2
2
Neg Neg PosPos
02 5
x
2
3x 10
x 2
1x 521x 22
x 2
0
x 僆 14, 12 ´ 12, q2
1
Neg Neg PosPos
04 2
1x 421x 121x 227 0
x
y
810462
8
10
4
6
2
4
6
2
8
10
4
6
2
8
10
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
108642
10
8
6
4
2
4
8
12
16
20
8
12
16
20
4
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
H1x2 •
x
2
3x 4
x 1
x 1
5 x 1
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
12, 52
x 7 2000
A1x2S 15
.
冟
x
冟
Sqy 15;
V1x2
x
2
x 12
x
2
x 6
; V102 2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
V112
4
3
x 3, 3V102
9
4
x 1, x 4y 1;5x
冟
x 僆 ⺢; x 1, 46
P1x2 1x 221x 12
2
1x 12
3
x 1,x 1,x 2,
x
y
54321
5
4
3
2
1
3
6
9
12
15
6
9
12
15
3
x
y
54321
5
4
3
2
1
4
8
12
16
20
8
12
16
20
4
x
y
54321
5
4
3
2
1
2
4
6
8
10
4
6
8
10
2
10, 8210, 42
Student Answer Appendix SA-27
cob19545_saa_018-038.qxd 11/26/10 10:01 PM Page SA-27
Practice Test, pp. 474–475
1. a. b.
2. 3. a. 40 ft, 48 ft b. 49 ft c. 14 sec
4. 5.
6.
✓
7. 8.
9. 2 mult 2, 1 mult 2, mult 1
10. a. b. 1 positive zero, 3 or 1 negative
zeroes; 2 or 0 complex zeroes c.
11. a. 2002, 2004, 2008 b. 4 yr c. deficit of $7.5 million
12. 13. 14.
15. a. removal of 100% of the contaminants b. $500,000; $3,000,000;
dramatic increase c. 88%
16. a. b.
17. 800 18. a. b.
19. a.
b. c. 28.6%, 29.6% d. e. 4 hr, 43.7%
f. The amount of the chemical in the bloodstream becomes neglible.
20.
Strengthening Core Skills, pp. 476–477
Exercise 1. Exercise 2.
Exercise 3. Exercise 4.
Exercise 5. Exercise 6.
Cumulative Review Chapters R–4 pp. 477–478
1. 3. a. b.
5. all reals 7. verified 9. ; 39 min, driving time
increases 11 min every 60 days 11. month 9 13.
15. 17. X 63
x
y
5
5
5
5
f
1
1x2
x
3
3
2
y
11
60
x
1009
60
1x 321x 221x 221x 121x
2
x 12R
R
1
R
2
R
1
R
2
x 僆 33, 14 ´ 33, q2x 僆 1q, 22 ´ 12, q2
x 僆 32, q2x 僆 1q, 42 ´ 11, 32
x 僆 12, 12 ´ 12, q2x 僆 1q, 34
V1x2
x
2
x 6
x
2
2x 3
; V102 2
⬇11.7 hrh 1
3
55; no
2016440812
0.4
0.8
1.2
y
x
x 僆 1q, 42 ´ 10, 22x 僆 1q, 34 ´ 31, 44
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
108642
10
8
6
4
2
10
20
30
40
50
20
30
40
50
10
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
108642
10
8
6
4
2
4
8
12
16
20
8
12
16
20
4
x
y
108642
10
8
6
4
2
100
300
500
300
500
100
C1x2 1x 221x 121x 3i21x 3i2
1, 18, 2, 9, 3, 6
1Q1x2 1x 22
2
1x 12
2
1x 12,
P1x2 x
3
2x
2
9x 181
31 015 10 24
391824
1 3 680r 0
x
2
2x 9
2
x 2
x 5
14x 3
x
2
2x 1
12, 02, y 2x
2
4x
x
y
108642
10
6
8
4
2
14
16
18
12
10
8
6
4
2
(0, 16)
(
4, 8)
x
y
161412108
4
2246
4
8
12
16
20
8
12
16
20
4
(5, 9)
(2, 0)
(8, 0)
(0,
16)
g1x2
1
2
1x 42
2
8f 1x21x 52
2
9
19. 21. 87.91, , 1.99
23. a. b. c.
d. 25. a. Y
6
b. Y
7
c. Y
4
d. Y
3
e. Y
5
f. Y
2
CHAPTER 5
Exercises 5.1, pp. 488–491
1. second, one 3.
5. False, answers will vary. 7. one-to-one 9. one-to-one
11. not one-to-one, fails horizontal line test: , and
are paired with 13. not a function 15. one-to-one 17. not one-
to-one, is paired with and 19. one-to-one
21. not one-to-one; corresponds to two x-values
23. one-to-one 25. not one-to-one; corresponds to more
than one x-value 27.
29.
31. 33. 35.
37.
39. verified
41. verified
43. verified
45. verified
47. a. b.
49. a. b.
51. a. b.
53. 55.
57. 59.
61. 63. 65.
67. 69. 71.
73. D: , R: ;
75. D: , R: ;
77. D: , R: ;
79. D:, R:;
D:, R:
81. D:, R:;
D:, R: y 僆 10, q2x 僆 1q, q2
y 僆 1q, q2x 僆 10, q2
x
y
54321
5
4
3
2
1
1
2
3
4
5
2
3
4
5
1
y 僆 30, q2x 僆 32, q2
y 僆 32, q2x 僆 30, q2
x
y
54321
5
4
3
2
1
1
2
3
4
5
2
3
4
5
1
v
1
1x2 2x 3, D: x 3, R: y 0y 3x 0
p
1
1x2
x
2
4
3, D: x 0, R: y 3y 0x 3
f
1
1x2
x
2
2
3
, D: x 0, R: y
2
3
y 0x
2
3
f
1
1x2 22
3
x 1f
1
1x2
x
3
1
2
f
1
1x2 2
3
x 3
f
1
1x2 2x 6f
1
1x2 2x 5f
1
1x2
x 5
3
1f ⴰ g21x2 x, 1g ⴰ f 21x2 x1f ⴰ g21x2 x, 1g ⴰ f 21x2 x
1f ⴰ g21x2 x, 1g ⴰ f 21x2 x1f ⴰ g21x2 x, 1g ⴰ f 21x2 x
p
1
1x2 1x 2 4, x 2, y 4x 4, y 2
v
1
1x2
A
8
x
3, x 7 0, y 7 3x 7 3, y 7 0
f
1
1x2 1x 5, x 0, y 5x 5, y 0
f
1
1x2
x
1 x
, x 1, y 1;x 1, y 1;
f
1
1x2
8
x
2, x 0, y 2;x 2, y 0;
f
1
1x2 2
3
x 1, x 僆 ⺢, y 僆 ⺢;x 僆 ⺢, y 僆 ⺢;
f
1
1x2 x
3
2, x 僆 ⺢, y 僆 ⺢;x 僆 ⺢, y 僆 ⺢;
t1x2 x
3
4
f
1
1x2
x 3
4
p
1
1x2
5
4
xf
1
1x2 x 5
v
1
1x2 513, 42, 12, 32, 11, 02, 10, 52, 11, 122, 12, 212, 13, 3226
f
1
1x2 511, 22, 14, 12, 15, 02, 19, 22, 115, 526
y 3
h1x26 3,
x 8x 6y 1
y 0
x 2x 0.5x 3
111, 22, 15, 02, 11, 22, 119, 42
0 i
27.63 14.59i
2
41
59
41
i349.36 131.38i
80.09
x
y
54321
5
4
3
2
1
2
4
6
8
10
4
6
8
10
2
SA-28 Student Answer Appendix
cob19545_saa_018-038.qxd 11/29/10 2:00 PM Page SA-28
83. D:, R:;
D:, R:
85. a. b. , (0, 1), and (1, 3) are on the graph of
f; , (1, 0), and (3, 1) are on the graph of c. verified
d.
87. a. b. (0, 0), , and are on the graph of h;
(0, 0), , and are on the graph of h
1
c. verified
d.
89. a. 31.5 cm b. The result is 80 cm. It gives the distance of the projector
from the screen. 91. a. b.
independent: temperature, dependent: altitude c. 22,000 ft
93. a. 144 ft b. , independent: distance fallen, dependent:
time fallen c. 7 sec
95. a. 28,260 ft
3
b. , independent: volume, dependent:
height c. 9 ft 97. Answers will vary.
99. a. b. c. d.
e. f. g. h.
i. 101. rate of change is greater in [1, 2]
due to shape of the graph.
Exercises 5.2, pp. 499–503
1. b
x
, b, b, x 3. a,1 5. False; for and , so
function is decreasing 7. 16, 2, 8, 11.036 9. 1, , , 64
11. 13.
15. ; up 2 17. ; left 3
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y
0
(
3, 1)
(
1, 9)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y
2
(1, 5)
(0, 3)
y 3
x
y 3
x
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y
0
(
2, 9)
(0, 1)
decreasin
g
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
(2, 9)
increasin
g
y
0
(0, 1)
1
4
1
64
x
2
7 x
1
, b
x
2
6 b
x
1
冟
b
冟
6 1
⬇0.472, ⬇0.365;a
2
b
2
c
2
V
4
3
r
3
A
1
2
1b
1
b
2
2hA
1
2
bhC 2r
V
1
3
r
2
hV r
2
hA r
2
P 2l 2w
f
1
1x2
B
3
3x
f
1
1x2
1x
4
f
1
1x2
2
7
1x 592;63.5°F
3.1
3.1
4.7
4.7
1
2
3
, 221
1
2
, 12
12,
2
3
211,
1
2
2h
1
1x2
x
1 x
5
5
7.6
7.6
f
1
15, 32
13, 52f
1
1x2
x 1
2
y 僆 1q, 44x 僆 1q, 44
y 僆 1q, 44x 僆 1q, 44
x
y
54321
5
4
3
2
1
1
2
3
4
5
2
3
4
5
1
19. ; reflect across y-axis 21. ; up 1
23. ; right 2 25. e 27. a 29. b
31. 2.718282 33. 7.389056 35. 4.113250
37. 39. 41.
43. 3 45. 47. 49. 4 51. 53. 3 55. 2 57.
59. 2 61. 3 63. 65.
67. a. 1732, 3000, 5196, 9000 b. yes c. as
d.
69. a. $100,000 b. 3 yr 71. a. b. 3 yr
73. a. $40 million b. 7 yr 75. no, they will have to wait about 5 min
77. 32% transparent 79. 17% transparent 81.
83. a. 8 g b. 48 min 85. 87. 75 89. ; answers will vary
91. 5; ; ;
93. a. no solution b.
Exercises 5.3, pp. 512–516
1. log
b
x, b, b, greater 3. , 0 5. 5; answers will vary 7.
9. 11. 13. 15. 17.
19. 21. 23. 25.
27. 29. 31. 33.
35. 37. 39. 1 41. 2 43. 1 45. 47.
49. 51. 1.6990 53. 0.4700 55. 5.4161 57. 0.7841
59. shift up 3 61. shift right 2, up 3
63. shift left 1 65. shift left 1, reflect across x-axis
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
(0, 0)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
(0, 0)
x
y
(3, 3)
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
(1, 3)
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
2
2
1
2
log
4
1
8
3
2
log
4
8
3
2
log
1
100
2log 1000 3log
1
3
27 30 ln 1
log
3
1
9
2log
4
64 3e
4
⬇ 54.59810
2
100
7
2
492
1
28
1
3
29
0
17
1
1
7
2
3
811, 02
55, 66
2a
2
4ah 2h
2
3a 3h2a
2
3a
7
9
9.5 10
7
1
5
⬇$25,526
⬇ $86,806
P
t
days
45123
10,000
20,000
30,000
40,000
50,000
t Sq, P Sq
x ⬇ 3.2x ⬇ 2.8
23
1
3
3
2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
(2, 0)
(0, 6.4)
x
y
4321
6
5
4
3
2
1
1
2
3
4
5
6
1
2
3
4
(0, 1)
(2,
5.4)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
(
2.3, 0)
(
1, 5.4)
(
3,
1)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y
0
(2, 1)
(0, 9)
y 1
1
3
2
x
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y
1
(0, 2)
(
2, 10)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y
0
(0, 1)
(
2, 9)
y 1
1
3
2
x
y 3
x
Student Answer Appendix SA-29
cob19545_saa_018-038.qxd 11/29/10 2:00 PM Page SA-29
67. II 69. VI 71. V 73.
75. 77. 79. acid
81. a. b. 83. about 398 times 85. about 3.2 times
87. a. b. 89. a. 20 dB b. 120 dB
91. about 501 times 93. about 3162 times 95. 6194 m
97. a. about 5434 m b. 4000 m 99. a. 2225 items b. 2732 items
c. $117,000 101. a. about 58.6 cfm b. about 1605 ft
2
103. a. 95% b. 67% c. 39% 105. ; acid 107. Answers will vary.
a. 0 dB b. 90 dB c. 15 dB d. 120 dB e. 100 f. 140 dB
109. a. b. c.
111.
113.
Exercises 5.4, pp. 523–526
1. e 3. extraneous 5. Answers will vary; Yes,
7. 9. 11. 13.
15. , 17. ,
19. , 21. ,
23. , 25. ,
27. 29. 31. 33.
35. 37. 39. log
2
42 41.
43. 45. 47. 49. 4 log
5
3
51. 53. 55.
57. 59.
61. 63.
65.
67. ;
outputs increase by 1;
69. ;
outputs are multiples of 0.3155;
71. verified 73. a. b. people 75. no,
77. no, and the soil must be treated further 79. 600
601
81. zeroes at and ; HA: , VA ,
83. or
Mid-Chapter Check, p. 526
1. a. b. 2. a. b.
3. a. b. 4. a. b. 5. a. $71,191.41
b. 6 yr 6. 7. ,
D: ; R: ; verified 8. a. , verified
b. verified 9. a. , verified
b. , verified 10. times more intense⬇7.9e
1.4
⬇ 4.0552
27
2
3
94 ⬇ ln 54.598,
4 log
3
81y 僆 33, q2x 僆 31, q2
f
1
1x2 1x 12
2
3F1x2 4
#
5
x3
2
b 5x 3b
5
4
x 5
1296
0.25
68
5
3
32
5
4
log
81
243
2
3
log
27
9
x 9x 1
x 1x 1y 1x 2x 3
pH ⬇ 5.9
pH ⬇ 7.32⬇ 3500N AX
m
h12
4
2⬇ 410.31552⬇ 1.2619
h1x2
log1x2
log192
; h122⬇ 0.3155; h142⬇ 0.6309; h182⬇ 0.9464
f 13
3
#
52⬇ 4.4650
f 1x2
log1x2
log132
; f 152⬇ 1.4650; f 1152⬇ 2.4650; f 1452⬇ 3.4650
log 0.125
log 0.5
; 3
log 1.73205
log 3
; 0.499999576
ln 152
ln 5
; 3.121512475
ln 60
ln 7
; 2.104076884
1
2
3log1x 22 log x4
2 ln x ln yln x
1
4
ln y3 log a log b
1
2
log 2212x 12 ln 51x 22 log 8
log
5
1x 22ln1x 22lna
x 5
x
b
log a
x
x 1
blog
3
4log1x
2
12ln12x
2
14x2
x ⬇ 1.7541x
e
0.4
5
2
x ⬇ 12.7828x 5 10
1.25
x ⬇ 10.3919x e
8
3
4x ⬇ 1.1221x
ln 2.32
0.75
x ⬇ 3.1079x log1782 5x ⬇ 4.7881x ln
65
4
2
x ⬇ 1.260x ⬇ 2.200x ⬇ 1.778x ⬇ 29.964
1.5663025 1.5663025
x 僆 1q, 52; f 1x2 1x 521x 42
2
x
3
3x
2
24x 80
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
D: x 僆 ⺢, R: y 僆 ⺢
5
2
3
2
2
3
⬇4.3
⬇1.2⬇2.4
⬇7.9⬇4.7
pH ⬇ 4.1;x 僆 13, 32x 僆 1
3
2
, q2
x 僆 1q, 12 ´ 13, q2
Reinforcing Basic Concepts, p. 527
Exercise 1. Answers will vary. Exercise 2. a.
b. c.
Exercises 5.5, pp. 535–538
1. variable, constant 3. uniqueness, one, one 5. False; answers will vary.
7. 9. 11. is extraneous
13. is extraneous 15. 17. 19.
21. 23. 25.
27. is extraneous 29.
31. no solution 33. is extraneous
35. 37.
39. 41.
43. 45.
47. 49. about 3.2 cmHg
51. a. 30 fish b. about 37 months 53. about 50.2 min
55. $15,641 57. a. 6 hr b. 18.0% 59.
61. a. 26 planes b. 9 days 63.
65. a. b.
67. a.
b. for
69. a. d b. e c. b d. f e. a f. c
71. a. b.
73. 13.5 tons
Exercises 5.6, pp. 547–552
1. Compound 3. 5. Answers will vary. 7. $4896
9. 250% 11. $2152.47 13. 5.25 yr 15. 80% 17. 4 yr 19. 16 yr
21. $7561.33 23. about 5 yr 25. 7.5 yr 27. no 29. a. no
b. 9.12% 31. 7.9 yr 33. 7.5 yr 35. a. no b. 9.4%
37. a. no b. approx 13,609 euros 39. No; $234,612.02
41. about 7 yr 43. 22 yr 45. a. no b. $298.31
47. a. b. 49. a.
b. 51. a. b.
53. $709.74 55. a. 5.78% b. 91.67 hr 57. 0.65 g 59. about 816 yr
61. about 12.4% 63. $17,027,502.21 65. 7.2%
67. a.
b. c.
d.
69. P1x2 x
4
4x
3
6x
2
4x 15
f
1x2
1
x
, f
1x2
1
x
2
f 1x2 1
3
x
f 1x2 x, f 1x2 x
3
, f 1x2 1x, f 1x2
冟
x
冟
, f 1x2 x
2
, f 1x2
1
x
2
f 1x2 x
3
, f 1x2 x, f 1x2 1x, f 1x2 1
3
x, f 1x2
1
x
t
ln
a
Q1t2
Q
0
b
r
Q
0
Q1t2
e
rt
t
ln
a
A
p
b
n ln a1
r
n
b
r na
nt
B
A
p
1bp
A
1 rt
t
A p
pr
Q
0
e
rt
x 僆 1q, q2, y 僆 33, q2x 僆 3
3
2
, q2, y 僆 30, q2
r ln by b
x
, ln y x ln b, e
ln y
e
x ln b
, y e
xr
y 2
x
1 ln y x ln 2, e
ln y
e
x ln 2
1 y e
x ln 2
y e
x ln 2
e
ln 2
x
2
x
;
y e
x
2
3
ln x
ln 2
1 y
e
x
2
y 3
ln x
ln 2
y 1
x
2
ln1y 32 ln x 1y 12 ln 2
x 2 ln1y 32 x 2
y1
y 2 ln1x 32 y 2
x1
x 1.609438
M
f
52.76 tons
t
ln a
C
p
1
a
b
k
, t ⬇ 55.45
x ⬇ 46.210x ⬇ 2.013, x ⬇ 3.608
x ⬇ 4.815, x ⬇ 102.084x
ln 2
ln 3 ln 2
; x ⬇ 1.7095
x
ln 128,967
3 ln 5
; x ⬇ 2.4371x
ln 231
ln 7
; x ⬇ 2.7968
x 2 13
; 2 13
x 3e
3
1
2
; x ⬇ 59.7566x 2; 9
x
e
2
63
9
; x ⬇ 6.1790x
19
9
x
3
2
x
2
3
x
5
2
x 0x 2,
5
2
x 20, 5x 6.4x 32
log
x
x 3
ln1x
2
42
log1x
2
3x2
SA-30 Student Answer Appendix
cob19545_saa_018-038.qxd 11/29/10 2:01 PM Page SA-30
Exercises 5.7, pp. 557–565
1. scatterplot, context, situation 3. beyond 5. (1) clear out old data,
(2) enter new data, (3) display the data, (4) calculate the regression
equation, (5) display and use the results; Answers will vary.
7. e 9. a 11. d 13. linear 15. exponential
17. logistic 19. exponential
21. As time increases, the amount of radioactive
material decreases but will never truly reach 0 or
become negative. Exponential with and
is the best choice.
23. Sales will increase rapidly, then level off
as the market is saturated with ads and advertising
becomes less effective, possibly modeled by a loga-
rithmic function.
25. a. b. about 1750 c.
27. 4.95 29. 6.25 31. 5.75 33. 6.84
35. a. about 19 boards b. about 15 days
37. logarithmic,
a. 9.2 lb b. 29 days c. 34.8 lb
39. logarithmic,
a. 51,000 b. 1977 c. 29,900
41. exponential,
a. 155,100 b. 54,200 c. 2013
43. quadratic
a. 360 million b. about 513 million
c. from 1984 to 1990
45. linear,
a. 224.3 million b. 329.2 million c. 2010
Year (1990 S 0)
1
50
Debit cards (millions)
150
250
350
450
357911
x
y
y ⬇ 6.555x 165.308
2 6 10 14 18
320
Chicken production (millions)
360
400
440
480
Year (1980 S 0)
x
y
y ⬇ 0.576x
2
8.879x 394
Year (1980 S 0)
10 14 1826
50
Number of farms (1000s)
150
250
350
450
x
y
y ⬇ 346.7910.942
x
0
10
Offices (1000s)
30
50
70
90
4020 80 10060
x
y
Year (1900 S 0)
y ⬇ 78.8 10.3 ln x
Time (days)
50 70 9010 30
5
Weight (pounds)
15
25
35
45
x
y
y ⬇ 27.4 13.5 ln x
y ⬇
1719
1 10.2e
0.11x
Days after outbreak
50 70 9010 30
250
Cumulative cases
500
750
1000
1250
1750
1500
2000
x
y
y ⬇ 120.4938 217.2705 ln1x2
3551525
300
100
500
700
900
Cost
Sales
y ⬇ 11.04220.5626
x
k 7 0b 6 1
Grams
5602143
0.1
0.3
0.5
0.7
0.9
Time (hours)
47. linear,
49. exponential,
a. 220 b. The 22nd note, or F#
c. frequency doubles, yes
51. exponential,
$41.59/mo, $54.72/mo
53. quadratic,
month 8
55. logistic, ; about 55
million, about
184 million,
about 214
million; 2014
57. power regression,
a. , 9.5 AU;
b. 84.8 yr
59. a. power regression,
b. about 295 rodents c. about 17 predators
61. a. linear, , 32.5 lb, 35.3 in.
61. b. logarithmic,
about 49.3 cm, about 34 mo
C1a2⬇ 37.9694 3.4229 ln 1a2,
Age (months)
5
36
Circumference (cm)
40
44
48
52
10 15 20 25
a
C(a)
W ⬇ 1.24L 15.83
Length (in.)
16
5
Weight (lb)
10
15
20
25
20 24 28 32
L
W
y ⬇ 58,555.89x
1.056
;
Rodents
Predators
5000
2000
1000
4000
3000
20 40 60 80 100
x
y
y ⬇ x
0.665
7.5
0
015
Year (1990 S 0)
Exponential
Logistic
10 14 1826
25
50
75
100
125
150
175
Subscriptions (millions)
x
y
y ⬇
222.133
1 32.280e
0.336x
27
21
15
9
3
3
6
1357911
x
y
Month
Profit
y ⬇ 1.18x
2
10.99x 4.60;
4
4
12
20
28
36
44
12 20 28 36
x
y
Year (1980 S 0)
Monthly charge
y ⬇ 8.02 11.05642
x
Note number
48106122
110
Frequency
130
150
170
190
210
x
y
y ⬇ 103.83 11.05952
x
2005: 40.4%, 2010: 43.0%, 2015: 45.5%
x
y
25 4035302015510
5
10
15
20
25
30
35
40
45
50
Year (1970 → 0)
Percent of U.S. Population
P1t2⬇ 0.51t 22.51,
Student Answer Appendix SA-31
logistic
cob19545_saa_018-038.qxd 11/29/10 2:01 PM Page SA-31
63.
65.
Making Connections, p. 565
1. a 3. e 5. c 7. e 9. b 11. g 13. c 15. d
Summary and Concept Review, pp. 566–570
1. no 2. no 3. yes 4. 5.
6.
7.
8.
9.
10. a. $3.05 b. , c. 12 days
11. 12. 13.
14. 2 15. 16. 17. 12.1 yr 18. 19.
20. 21. 22.
23. 24. 5 25. 26.
27. 28. 29.
30. 31. 32. a. 4.79 b. 10
7.3
I
0
33. a. b. c. d.
34. a. b.
c. d.
35. a. ln 42 b. log
9
30 c. d.
36. a. 2 log
5
9 b. 2 log
7
4 c. d.
37. a. b.
c.
d.
38. a. b. c.
d. 39.
40. 41.
42. 43. is extraneous
44. 45. a. 17.77% b. 23.98 days 46. 38.6 cmHg
47. 18.5% 48. Almost, she needs $42.15 more. 49. a. no b. $268.93
50. 55.0%
x 4.25
x 5; 2x e
2
1, x ⬇ 6.3891
2
1 ln 3
, x ⬇ 0.9530x
ln 5
ln 3
1, 0 ⬇ x .4650
x
ln 7
ln 2
, x ⬇ 2.8074
ln 0.42
ln 5
⬇ 0.539
ln 124
ln 2
⬇ 6.954
log 128
log 3
⬇ 4.417
log 45
log 6
⬇ 2.215
log 4
5
3
log p
4
3
log q
3
2
log p log q
5
3
log x
4
3
log y
5
2
log x
3
2
log y
1
3
ln p ln qln x
1
4
ln y
13x 22ln 1012x 12ln 5
log1x
2
x2ln 1
x 3
x 1
2
x e
2.75
, x ⬇ 0.0639x
10
3
3
, x ⬇ 333.3333
x
log 19
0.2
, x ⬇ 6.3938x
ln 4
0.5
, x ⬇ 2.7726
x
1
2
log 7x ln 9.8x 10
2.38
x e
32
x 僆 1q, 02 ´ 16, q2x 僆 1
3
2
, q2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x 1
x
y
x 3
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
1
2
1log
3
81 4
ln 0.7788 ⬇ 0.25log
5
25 2e
3.7612
⬇ 43
5
3
1
125
3
2
9
5
2
2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y 2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y 1
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y 3
f
1
13.052 7f
1
1t2
t 2
0.15
R: y 僆 10, q2; f
1
1x2: D: x 僆 10, q2, R: y 僆 1q, q2
f 1x2: D: x 僆 1q, q2,f
1
1x2: D: 1q, q2, R: y 僆 1q, q2
f 1x2: D: x 僆 1q, q2, R: y 僆 1q, q2;R: y 僆 34, q2
f 1x2: D: x 僆 34, q2, R: y 僆 30, q2; f
1
1x2: D: x 僆 30, q2,
f
1
1x2 x
2
1; x 0
f
1
1x2 1 x 2 f
1
1x2
x 2
3
f 1x2T: x 僆 1q, 3.52 ´ 10.4, 2.32
f 1x2c: x 僆 13.5, 0.42 ´ 12.3, q2
min: 13.5, 3.52, 12.3, 1.42
max: 10.4, 1.82
D: x 僆 1q, 22 ´ 12, 12 ´ 11, 52 ´ 15, q2,
1
x 2
51.
a. logarithmic, b. 16.9 mi/gal
c. the year 2011
52.
a. logistic, b. microns
c. ; 5.56 hr (about 5 hr 34 min)
Practice Test, p. 571
1. 2. 3.
4. 5. 6. 7. 2.68 8.
9. 10.
11. a. 4.19 b. 12. f is a parabola (hence not one-to-one),
; vertex is at , so restricted domain could be
to create a one-to-one function;
.
13. 14. is extraneous
15. 16. a. b.
17. 19.1 months 18. a. no b. $54.09 19. a. 10.2 lb b. 34 weeks
20. logistic; 0.89 sec
Strengthening Core Skills, p. 573
Exercise 1. about 126 times hotter Exercise 2. about 4.2 hb
5
40
0
2
y
39.1156
1 314.6617e
5.9483x
;
P ⬇ 15.3 lb 1M 202P kM
␣
⬇5 yr
x 1, x 5x 1
ln 89
ln 3
, x ⬇ 5.0857
f
1
1x2 1x 3 2, x 僆 33, q2, y 僆 32, q2
x 僆 32, q2
12, 32x 僆 ⺢, y 僆 33, q2
0.81
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x 2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y 3
1.24x
5
3
x 10log
b
m1n
3
1p
5
2
log
b
x 3 log
b
y log
b
zlog
25
5
1
2
3
4
81
14 1.962 7.84
⬇ 6.8g1t2
8.0
1 1.0e
0.7t
0
10
0
8
y ⬇ 12.772 1.595 ln x
8
20
0
35
SA-32 Student Answer Appendix
cob19545_saa_018-038.qxd 11/29/10 2:01 PM Page SA-32
Cumulative Review Chapters R–5, p. 574
1. 3.
✓
5. ; ; Since they are inverse
functions. 7. a.
b. , triple births increase by 455 each year
c. sets of triplets, sets of triplets
9.
11. 13.
15. a. b. c.
17. is an extraneous root 19. a. about 88 hp for sport
wagon, about 81 hp for minivan b. rpm c. minivan, 208 hp
at 5800 rpm 21. 23. ,
25.
CHAPTER 6
Exercises 6.1, pp. 586–591
1. inconsistent 3. consistent, independent 5. Multiply the first
equation by 6 and the second equation by 10. 7.
9. 11.
13.
15. yes
17. yes
19.
10 10
10
10
Y
1
12 3X
2
, Y
2
X 9
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
(6, 3)
x 3y 3y x 2,
x 3y 3y x 2y
4
3
x 5
y
7
4
x 6,
x ⬇ 2.013, x ⬇ 3.608
x ⬇ 4.967x ⬇ 0.649x ⬇ 5.064
⬇3294
x 5, x 6
f
1
1
f 1x22 x
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
f
1
1x2
5x 3
2
2
2V
a
bx 3, x 2 1multiplicity 22; x 4
h1x2c: x 僆 12, 02 ´ 13, q2 h1x2T: x 僆 10, 32
D: x 僆 310, q2, R: y 僆 39, q2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
T1172 10,380T162 5375
¢T
¢t
455
1
T1t2 455t 2645 11991 S year 12
1f ⴰ g21x2 1g ⴰ f 21x2,g1f 1x22 xf 1g1x22 x
0 09 40i 32 40i 41 0
14 5i2
2
814 5i2 41 0
x 2 7i
21.
23. 25. 27. second equation, y,
29. second equation, x, 31. second equation, x,
33. 35. 37. 39. 41.
43. 45. 47. 49. (2, 8); consistent/
independent 51. ; inconsistent 53. consistent/
dependent 55. (4, 1); consistent/independent 57.
consistent/independent 59. consistent/independent 61. 1 mph,
4 mph 63. 2318 adult tickets; 1482 child tickets 65. premium: $3.97,
regular: $3.87 67. nursing student $6500; science major $3500
69. 150 quarters, 75 dimes 71. a. 3 mph b. 5 mph 73. a. 3.6 ft/sec
b. 4.4 ft/sec 75. a. 100 lawns/mo b. $11,500/mo 77. a. 1.6 billion
bu, 3 billion bu, yes b. 2.7 billion bu, 2.25 billion bu, yes c. $6.65,
2.43 billion bu 79. about 227 boards at $410 a piece
81. about 90,000,000 gal at $3.04 gal 83. 1776; 1865 85. Tahiti:
402 mi
2
, Tonga: 290 mi
2
87. 89. $50,000
91.
93.
Exercises 6.2, pp. 599–602
1. triple 3. equivalent, systems 5. 7. Answers will vary.
9. Answers will vary. 11. yes, no; R2, R3 13. (5, 7, 4) 15. (2, 4, 3)
17. (4, 0, 3) 19. (5, 12, 13) 21. no solution, inconsistent
23. ,
other solutions possible
25. ; ,
other solutions possible
27. 29.
31. 33.
35. 37. (12, 6, 4) 39.
41. 43. 45. (5 cm, 3 cm, 4 cm)
47. $80,000 at 4%; $90,000 at 5%; $110,000 at 7% 49. World War II,
1945; Korean, 1953; Vietnam, 1973 51. Declaration of Independence,
1776; 13th Amendment, 1865; Civil Rights Act, 1964 53. 1 L 20%
solution; 3 L 30% solution; 6 L 45% solution 55. saturated: 1.2 g,
monounsaturated: 1.0 g, polyunsaturated: 0.6 g 57. h(t) 5t
2
30t 1;
a. 46 ft b. 17.2 ft 59. 2 61. 63.
Mid-Chapter Check, p. 603
1. (1, 1) consistent 2. (5, 3) consistent 3. 20 oz 4. No; R2, R3
5. 6. (1, 2, 3) 7. (1, 2, 3) 8.
9. Morphy: 13, Mozart: 8, Pascal: 16 10. prelude: 2.75 min, storm:
2.5 min, sunrise: 2.5 min, finale: 3.25 min
1p, p 5, p 422R1 R2
x 131,
3
2
4
a
1
5
,
1
2
, 2b11, 2, 32
11, 5, 621p 17, p 4, p2
a1,
3
2
, 2be1x, y, z2`x
1
2
y 2z 6f
1p 9, p 4, p21p, 2p, p 12
a
5
3
p
2
3
, p 2, pbe1x, y, z2
|
x
5
3
z
2
3
, y z 2, z 僆 ⺢ f
1p, 2 p, 2 p251x, y, z2
|
x 僆 ⺢, y 2 x, z 2 x6;
z 5
x
y
108642
10
8
6
4
2
5
10
15
20
25
10
15
20
25
5
x 僆 32, 84
1x 521x 221x 1213x 12
y 2x 3
1
1
2
,
4
3
2;
13, 42;
51x, y2
|
6x y 226;
16, 12213, 4212, 32
1
11
2
, 2212, 3213, 1212, 1212,
5
2
2
1
5
2
,
7
4
2110, 12
14, 3213, 5214, 12
10 10
10
10
Y
1
5 5X
2
, Y
2
16 X
3
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
(1, 5)
Student Answer Appendix SA-33
cob19545_saa_018-038.qxd 11/29/10 2:01 PM Page SA-33
Reinforcing Basic Concepts, pp. 603–604
Exercise 1. Premium: $4.17/gal,
Regular: $4.07/gal
Exercise 2. Verified
Exercises 6.3, pp. 612–615
1. region , solutions 3. Answers will vary.
5. a. 3 or 4 not possible
b. 3 or 4 not possible
c.
d.
e. 3 or 4 solutions not possible
f.
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
e
15.3R 35.7P 211.14
P R 0.10
7. parabola, line;
9.
circle, absolute value;
, (8, 6)
11. parabola, parabola;
, (2, 1)
13. 15. (2, 5), 17. , ,
(3, 4), 19. 21.
23.
25. 27.
29. 31. (0, 10), (ln 6, 45)
33. , (2, 1024) 35. , , (2, 4) 37. ,
(6, 4) 39. (3, 5), 41. (2, 1) 43. (0.72, 2.19),
(2, 3), (4, 3), (5.28, 2.19)
45. 47.
49. no solution 51.
53. 55. The company breaks even if
either 18,400 or 48,200 cars are sold.
57. ; approx. (12.4, 13) or (20, 5); The pool will likely
have the dimensions 20 ft by 20 ft by 5 ft.
59. 61. 5 km 9 km 63.
65. $1.83; $3, 90,000 gal 67. Answers will vary.
69. 18 in. by 18 in. by 77 in. 71. a.
b. c. 73. a. , the copier depreciates by
$400 a year b. c. $1700 d. 9.5 yr
Exercises 6.4, pp. 625–629
1. half, planes 3. solution 5. The feasible region may be bordered by
three or more oblique lines, with two of them intersecting outside and away
from the feasible region. 7. No, No, No, No 9. No, Yes, Yes, No
y 400x 4500
m
400
1
x 2x 0, x 8
x
2 2110
3
e
10P
2
6D 144
8P
2
8P 4D 12
8 ft 8 ft 25 ft8.5 m 10 m
e
x
2
y 2000
x
2
4xy 800
h ⬇ 45.8 ft: h 40 ft: h 30 ft
x
y
54321
5
4
3
2
1
1
2
3
4
5
2
3
4
5
1
x
y
20161284
20
16
12
8
4
4
8
12
16
20
8
12
16
20
4
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
12.43, 2.812,13, 52
12, 4211, 1213, 21213, 12
13, ln 9 12, 14, ln 16 12
15, log 5 5218, 12, 17, 42
12 i, 2 i2, 12 i, 2 i212i16, 7212i16, 7214, 32
14, 32,14i, 16 24i2, 14i, 16 24i214, 32
14, 3213, 4214, 7214, 32, 13, 42
11, 22
x
y
54321
5
4
3
2
1
1
2
3
4
5
2
3
4
5
1
16, 82
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
11, 52, 12, 22
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
SA-34 Student Answer Appendix
cob19545_saa_018-038.qxd 11/29/10 2:02 PM Page SA-34
11. 13.
15. (0, 0) is in the
solution region, and
3(0) 2(0) 8 is
true.
17. (0, 0) is in the
solution region, and
4(0) 5(0) 20
is true.
19. No, No, No, Yes
21. 23. 25.
27. 29. 31.
33. 35. 37.
39. 41.
43.
(2, 4)
0 9.4
0
9.3
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
54321
5
4
3
2
1
1
2
3
4
5
2
3
4
5
1
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
10 10
10
10
10 10
10
10
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
45.
(3, 2)
47. 49.
51. (5, 3) 53. (12, 11) 55. 26 at (2, 2) 57. 264 at (4, 3)
59.
61.
63. 300 acres of corn; 200 acres of soybeans
65. 240 sheet metal screws; 480 wood screws
67. 65 traditionals, 30 Double-T’s
69. 3 buses from company X; 4 buses from company Y
71. a. the region is a square
b. Max is 35.1 at (3, 3)
c. optimal solutions occur at vertices
73. 75.
Making Connections, p. 629
1. c 3. g 5. d 7. a 9. g 11. e 13. f 15. b
Summary and Concept Review, pp. 630–632
1. 2.
3. 4. no solution; inconsistent
5. ; consistent 6. (7, 2); consistent 7. ; consistent
8. ; consistent 9. Willis Tower is 1450 ft; Hancock Building is
1127 ft. 10. $1.20 11. (0, 3, 2) 12. (1, 1, 1) 13. no solution,
inconsistent 14. 3 aces, 4 face cards, 5 numbered cards
15. 1530 quarters, 1180 dimes, 710 nickels 16. circle, line, (4, 3),
17. parabola, line, 18. parabola, circle,
19. circle, parabola,
11, 32, 11, 32, 1
i1
10
3
,
10
3
2, 1
i1
10
3
,
10
3
2
1i22
, 321i22, 22,123, 22,
123
, 22,13, 2213, 42
1
11
4
,
1
6
2
13, 1215, 12
x
y
54321
5
4
3
2
1
1
2
3
4
5
2
3
4
5
1
2x y 2
x
2y 4
(
U, T
)
x
y
54321
5
4
3
2
1
2
4
6
8
10
4
6
8
10
2
0.2x 0.5y
1.4
x 0.3y 1.4
(
q, 3
)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
3x 2y 4
x 3y 8
(4, 4)
324 x 5, i13
x
y
(3, 3)
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
J A 50,000
J 20,000
A 25,000
A (in thousands)
J (in thousands)
100806020 40
80
100
60
20
40
5 6 H 6 10
•
y x 1
x y 6 3
y 0
e
y x 1
x y 7 3
0 9.4
0
9.3
Student Answer Appendix SA-35
cob19545_saa_018-038.qxd 11/29/10 2:02 PM Page SA-35