Coburn J.W., Herdlick J.D. College Algebra: Graphs and Models
Подождите немного. Документ загружается.
20. 21.
parabola, circle note the open circle showing noninclusion
at ; circle, parabola
22. 23.
24.
25. Maximum of 270 occurs at both (0, 6) and (3, 4)
on the line and all points on this
line in between these endpoints.
26. 50 cows, 425 chickens
Practice Test, pp. 632–633
1. (2, 3) 2. 3. 4.
5. 6.
7. 21.59 cm by 35.56 cm 8. Tahiti, 402 mi
2
; Tonga, 290 mi
2
9. Corn 25¢, Beans 20¢, Peas 29¢ 10. $15,000 at 7%, $8000 at 5%,
$7000 at 9%
11. 12. Maximum of P 400 at (8, 0)
13. 30 plain; 20 deluxe
14.
15.
16. 15 ft, 20 ft
113, 12, 113, 12, 1i121, 52, 1i121, 52
11 27, 1 17 2, 11 17, 1 17 2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
a 5, b 251x, y, z2|x 2z 1, y 5z 6, z 僆 ⺢6
12, 1, 4213, 22
1
2
5
,
4
5
2
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
x 4y 10
3x 2y 12
(2, 3)
y
2
3
x 6,
x
y
108642
6
4
2
2
4
6
4
6
8
10
2
(3, 4)
10 10
9.3
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
10, 32
564321
4
3
2
1
1
2
3
4
5
6
2
3
4
5
6
1
x
y
5
6564321
4
3
2
1
1
2
3
4
5
6
2
3
4
5
6
1
x
y
5
6
17.
18. a.
b. equilibrium is achieved when approx 150,000 plugs are sold at a price
near $1.18
19. 20. Answers may vary.
Possible solution:
Strengthening Core Skills, pp. 634–635
Exercise 1.
Cumulative Review Chapters R–6, pp. 635–636
1. 3. 5.
7. a. b. c.
d. n/a e. f.
g.
9. 11. 13. 1
15.
17. 19.
21. 23. 80 arrows, 25 balls, 15 bats
25. x 5, y ⬇ 4.7
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
y 1
x 2 x 2
(3, 0)
(0, 2.25)
(3, 0)
⬇9.7 yrx 僆 1q,
11
2
4 ´ 13, q2
1x 221x 221x 3 322
21x 3 3222
3x
2
5x 9, i12
¢y
¢x
7
4
f 1x26 0: x 僆 1q, 42 ´ 12, q2
f 1x27 0: x 僆 14, 22max: 11, 42f 1x2T: x 僆 11, q2
f 1x2c: x 僆 1q, 12R: y 僆 1q, 44D: x 僆 1q, q2
x
y
108642
10
8
6
4
2
9
18
27
36
45
18
27
36
45
9
(3, 0)
(4, 0)
(1, 0)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
(3, 1)
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
(0, 2)
(3, 0)
11, 42, elimination
•
x
2
y
2
7 1
x
2
y
2
6 4
x 7 0, y 6 0
x
y
54321
5
4
3
2
1
1
2
3
4
5
2
3
4
5
1
4.7 4.7
3.1
3.1
SA-36 Student Answer Appendix
cob19545_saa_018-038.qxd 11/29/10 2:02 PM Page SA-36
49. 51. 53. verified
55. verified 57.
59. a.
b. 3900 more by Minsk
c. d.
61. ; Total Profit N: $22,000, S: $19,000,
E: $23,500, W: $14,000
63. a. $108.20 b. $101
c.
65. a. 10 b. 20
c. p
13
gives the approximate number of females expected to join the
writing club
67. 69. 71.
Mid-Chapter Check, pp. 662–663
1. 2. 3. 4.
5.
6. a. b. c.
7. a. b. c.
8. a. b. c.
d. 9. used: $80, new: $125
10. p
11
: total rebates paid to individuals, p
21
: total rebates
paid to business, p
12
: free AAA years given to individuals, p
22
: free AAA
years given to business
Reinforcing Basic Concepts, p. 663
Exercise 1: p
32
Exercise 2:
1st row of A with 3rd column of B
2nd row of A with 2nd column of B
Exercise 3:
Exercise 4: only
Exercises 7.3, pp. 673–678
1. diagonal; zeroes 3. AB; BA; I; A
1
5. Answers will vary.
7. verified 9. verified 11. verified 13. verified 15. c
1
9
2
9
1
9
5
18
d
FE P
3A4S 3 n; 3B4S n 3; n 僆 ⺞
3A4S 3 3; 3B4S 3 3
3A4S 3 2; 3B4S 2 3
3A4S 3 1; 3B4S 1 3
c
4375 110
2400 59
d,
c
4 33
229
d
£
24 4
0 5
16 39
§c
26 18 24
2 10 4
dc
17 32 13
505
d
£
100
010
001
§£
3 1.5 6
1.5 0 3
6 1.5 6
§£
0.8 0.5 2.2
0.1 0.8 1
2.1 0.3 1.9
§
c
55
515
dc
46
12 2
dc
13 17
35 9
d
1p 3, 2p 8, p2
12, 0, 5212, 322 4, 03 3, 0.9
⬇4.3911, 1, 22£
2
n1
02
n1
2
n
112
n
1
2
n1
02
n1
§
c
32.4 10.3 21.3
29.9 9.6 19.5
d
c
100 101 119
108.2 107 129.5
d
322,000 19,000 23,500 14,0004
£
8361.6 5116.8
5636.8 4659.2
3307.2 1809.6
§
A 27.7269 cm
2
P 21.448 cm;
c
4284
8173
dc
1.75 2.5
7.5 13
d
Student Answer Appendix SA-37
27. a. b.
verified
29.
CHAPTER 7
Exercises 7.1, pp. 646–650
1. square 3. 2; 3; 1 5. Multiply R1 by 2 and add that result to R2.
This sum will be the new R2. 7. 3 2, 5.8 9. 4 3, 1
11. diagonal entries 1, 0, 1
13. 15.
17. 19.
21. 23.
25. 27.
29. (20, 10) 31. (1, 6, 9) 33. (1, 1, 2) 35. (1, 1, 1) 37. (2, 1, 3)
39. (10, 6, 8) 41. 43.
45. linear dependence (p 4, 2p 8, p) 47. coincident dependence
{(x, y, z)|3x 4y 2z 2} 49. inconsistent, no solution
51. linear dependence, 53. (2, 1, 1) 55. (3, 0, 2)
57. (1, 2, 3, 1) 59. 28 units
2
61. LA to STL, 1600 mi; STL to CIN,
310 mi; CIN to NY, 570 mi 63. Moe 90, Larry 45, Curly 30
65. 15 m, 36 m, 39 m 67. $2000 at 5%; $3000 at 7%; $5000 at 9%
69. 71.
73. C 30,000 in the year 2011
(t ⬇ 6.39)
Exercises 7.2, pp. 658–662
1. a
ij
; b
ij
3. scalar 5. Answers will vary. 7. 2 2, a
12
3,
a
21
5 9. 2 3, a
12
3, a
23
6, a
22
5 11. 3 3, a
12
1,
a
23
1, a
31
5 13. true 15. conditional,
17. 19. different orders, sum not possible
21. 23.
25. 27. 29.
31. 33. matrix mult. not possible 35.
37. 39. 41.
43. 45. 47. £
0
3
4
1
4
1
2
3
8
1
8
1
4
11
16
1
16
§c
3
19
4
57
1
19
5
57
d£
100
010
001
§
c
10
01
dc
42 18 60
12 42 36
dc
79 30
50 19
d
c
12 24 90
6 15 57
dc
10
01
d
£
1 20
0 12
436
§£
5
2
10
0
7
2
1
2
3
2
6
§c
20 15
25 10
d
£
1
2
13
8
1
4
1
4
5
2
21
8
31
8
9
4
7
2
§c
263
32
19
8
85
16
35
16
d
c
10 0
010
d
c 2, a 4, b 3
x
4
2x
3
8x 16; x
2
2x 4
x
3
x 10; x
3
x 6; x 84°; y 25°
1p,
1
3
p, 4
5
3
p2
11,
3
2
, 22a
1
2
, 1,
1
4
b
4R
1
R
3
S R
3
3R
1
R
3
S R
3
5R
1
R
2
S R
2
2R
1
R
2
S R
2
£
31 1 8
0 3 3 6
0 10 13 34
§£
1 33 2
02312 15
21 0 4
§
c
1 6 2
0 28 6
d•
x 3y 4z 29
y
3
2
z
21
2
z 3
S 14, 15, 32
•
x 2y z 0
y 2z 2
z 3
S 111, 4, 32e
x 4y 5
y
1
2
S 13,
1
2
2
£
1211
10 13
2 113
§;
x ⬇ 39.74
y 1
3
x 8,
15 15
10
10
V
S
D
P
£
3820 1960
2460 1240
1540 920
§
T S
M
S
D
P
£
4220 2960
2960 3240
1640 820
§
T S
M £
4388.8 3078.4
3078.4 3369.6
1705.6 852.8
§
V £
3972.8 2038.4
2558.4 1289.6
1601.6 956.8
§
First row, total cost for science from each
restaurant; second row, total cost for math
from each restaurant.
cob19545_saa_018-038.qxd 11/29/10 2:02 PM Page SA-37
17. 19. verified 21. verified 23.
25. 27.
29.
31. 33. (4, 5) 35. (12, 12)
37. 39. 41. (3, 2, 5) 43.
45. 1, yes 47. 0, no 49. 1 51. singular matrix 53. 55. 7
57. singular matrix 59. (1, 6, 9) 61.
63. verified 65. singular
67. 31 behemoth, 52 gargantuan, 78 mammoth, 30 jumbo
69. Jumpin’ Jack Flash: 3.75 min
Tumbling Dice: 3.75 min
You Can’t Always Get: 7.5 min
Wild Horses: 5.75 min
71. 30 of clock A; 20 of clock B; 40 of clock C; 12 of clock D
73.
75. 77.
79. $450 in the CD, $350 in the MM 81. $1500 in retirement fund, $1500
in mutual fund, $1800 in stock fund 83. 2 oz Food I, 1 oz Food II, 4 oz
Food III 85. Answers will vary. 87.
89.
Exercises 7.4, pp. 689–692
1. a
11
a
22
a
21
a
12
3. constant 5. Answers will vary.
7. 9.
11. 13. no solution
15. a.
b. , solutions possible
c. Cramer’s rule cannot be used: coefficients
17. (1, 2, 1) 19. 21.
23. 25.
27. 29.
31. 33.
35. 37.
39. 41.
43. 45.
47. 49. 320 32 ⬇ 420.5 in
2
3
x 1
2
x 3
1
1x 32
3
1
x
3x 2
1x
2
12
2
5
x 2
x 1
x
2
3
3
2 x
4
x
2
2x 4
1
x
4
x 1
5
1x 12
2
7
x
2
x 1
1
x 1
4
2x 5
3
x 3
4
x
5
x 1
A
x 1
Bx C
x
2
2
Dx E
1x
2
22
2
A
x
B
x
2
C
x 2
A
x
B
x 3
C
x 1
A
x 1
B
x 2
C
x 3
A
x 3
B
x 2
10, 1, 2, 32a
3
4
,
5
3
,
1
3
b
R
1
R
2
R
3
冟
D
冟
0,
冟
D
冟
22
D
z
†
4 1 5
328
1 5 3
†D
y
†
4 52
381
1 33
†
D
x
†
5 12
821
3 53
†D †
4 12
321
1 53
†
a
26
3
,
25
3
b
15, 92D
y
`
27
31
`
D
x
`
75
14
`
;D
`
25
34
`
;
x 僆 aq,
9
2
d´ c
1
2
, qb
x 6, x 3, x 2
y x
3
2x
2
9x 10y x
2
4x 5
p
1
72.25°, p
2
74.75°, p
3
80.25°, p
4
82.75°
A
1
c
1
13
5
13
2
13
3
13
d
det1A2 0det1A25;
34
11, 0.5, 1.5, 0.5211.5, 0.5, 1.521
1
5
,
1
3
2
≥
2145
2 513
3161
1451
¥≥
w
x
y
z
¥ ≥
3
4
1
9
¥
£
121
10 1
2 11
§£
x
y
z
§ £
1
3
3
§
c
2 3
57
dc
x
y
d c
9
8
d£
9
80
31
400
27
400
1
80
41
400
3
400
1
20
1
100
17
100
§
£
2
39
1
13
10
39
1
3
0
1
3
4
39
2
13
19
39
§c
5 1.5
2 0.5
d
51. 8 cm
2
53. 27 ft
2
55. 19 m
3
57. yes 59. no 61. yes, yes, yes
63. ; 6%, 8%
65. 67. a.
b. 10,000 ft c. 3600 ft d. 25 sec 69.
71. 73.
Exercises 7.5, pp. 697–699
1. 214.5 ft
2
of skin, 231.0 ft
2
of wood veneer, 516 tension rods, and 498 ft of
hoop 3. 955 ft
2
of skin, 1021.5 ft
2
of wood veneer, 2180 tension rods, and
2129.5 ft of hoop 5. 92,250 gal gasoline, 595,000 lb corn, 227,500 oz
yeast, and 134,750 gal water 7. 5 Silver, 9 Gold, and 2 Platinum
9.
11. Answers will vary. 13. Answers will vary. 15. Answers will vary.
17. Answers will vary. 19. Answers will vary. 21. Answers will vary.
23. Answers will vary. 25. Answers will vary. 27. Answers will vary.
Making Connections, p. 699
1. G 3. D 5. A 7. B 9. CD 11. E 13. D 15. H
Summary and Concept Review, pp. 700–702
1. Answers will vary. 2. 3. (1, 6, 9)
4. 5. ( , 7, 1, 8)
6. 7. 8. not possible
9. 10. 11.
12. 13. not possible 14.
15. 16. D 17. It’s an identity matrix.
18. It’s the inverse of B. 19. E 20. It is the inverse of F.
21. Matrix multiplication is not generally commutative. 22.
23. 24. 25. 26.
27. 28.
29. Year 1: fir 2670 ft
2
, jequitba 2752 ft
2
, teak 1090 ft
2
;
Year 2: fir 3570 ft
2
, jequitba 3668 ft
2
, teak 1456 ft
2
;
Year 3: fir 4470 ft
2
, jequitba 4584 ft
2
, teak 1822 ft
2
;
Year 4: fir 5370 ft
2
, jequitba 5500 ft
2
, teak 2188 ft
2
;
Year 5: fir 6270 ft
2
, jequitba 6416 ft
2
, teak 2554 ft
2
;
Total: fir 22,350 ft
2
, jequitba 22,920 ft
2
, teak 9110 ft
2
30. PIE ARE SQUARE
Practice Test, pp. 702–703
1. 2. 3.
4. a. b. c. d. c
2 1
2.5 1.5
dc
31
3 5
dc
1.2 1.2
1.2 2
dc
6 5
89
d
a2, 1,
1
3
ba3p
16
3
, p, 2p 3ba3,
1
2
b
5
x 2
2x 1
x
2
3
91
2
units
2
a
37
19
,
36
19
,
31
19
b11, 1, 22a
19
35
,
25
14
b12, 0,32
18,62
£
15.5 6.4 17
9 17 2
18.5 20.8 13
§
£
8120
2 44
16 0.4 20
§£
3 6 4
4.5 3 1
2 3.1 3
§
£
104
5.5 1 1
10 2.9 7
§c
10
01
dc
2 6
1 7
d
c
6.75 6.75
1.125 1.125
dc
7.25 5.25
0.875 2.875
d
21
6
5
p 1,
2
5
p 1, p2
12, 42
one bundle of third class 2.75 measures of grain
one bundle of second class 4.25 measures of grain;
one bundle of first class 9.25 measures of grain;
3
2x1
3
42x
; x 1.25
x
y
54321
5
4
3
2
1
2
4
6
8
10
4
6
8
10
2
A 195 units
2
h 10,000 16t
2
⬇ 103.9 lb F
1
F
2
6013
e
15,000x 25,000y 2900
25,000x 15,000y 2700
SA-38 Student Answer Appendix
cob19545_saa_018-038.qxd 11/29/10 2:03 PM Page SA-38
CHAPTER 8
Exercises 8.1, pp. 712–714
1. geometry, algebra 3. perpendicular 5. point, intersecting
7. 9. 11.
13. 15.
17. 19. a.
b. Answers will vary. 21. Verified, 23. a. B, C, E
b. Answers will vary. 25. Verified 27.
29. 31. Verified, verified 33.
35. Verified 37. about 12 yr
39.
x
y
4321
4
3
2
1
8
16
8
16
f1x2 1x 221x 12
2
1x 32
3x
2
y
2
34x
2
3y
2
48
y
1
16
x
2
d
815
5
d 13; B, C, E, Gax
13
2
b
2
1y 92
2
a
25
2
b
2
1x 22
2
1y 22
2
5
2
1x 22
2
1y 22
2
5
2
1
13
2
, 92; verified12, 22; verified12, 22; verified
e. 5. a. b.
c. d. e.
6. ( , 0), (1, , 1), (3, 4, 2), answers vary as ( )
7. 8. 9. 10. (1, 6, 9)
11. 12. 13. ( , 4), (2, 1), (4, )
14. 5 mi
2
15. 16. Dr. Brown owes $31,000; Dr. Stamper
owes $124,000 17. 7.5 hr, 15.5 hr 18. 11 one-day, 6 two-day, 3 five-day
19. federal program: $200,000; municipal bonds: $1,300,000;
bank loan: $300,000 20.
Strengthening Core Skills, pp. 704–705
Exercise 1: (1, 4, 1)
Cumulative Review Chapters R–7, pp. 705–706
1. a. b. c. d. i 3. 5.
7. 9. a. b. 1 c. 7 d. is not in the domain
11. 13. 15.
17. ,,
constant: none 19. 21.
23. 25. condominium: $400,000; delivery truck: $60,000;
business: $140,000 27. a. 144 b. 1148 29. 1q,
4
3
4 ´ 32, q2
a3,
5
2
b
x
3
4x
2
2x 202y
5
2
25
212y 12
f 1x2T: x 僆 1q, 02 ´ 12, 42f 1x2c: x 僆 10, 22 ´ 14, q2
1q, 12 ´ 15, q2
x
y
1
1
2
3
4
9
8
7
6
5
2
1
3
4
5
6
1
2
3
4
1
x
y
108642
10
8
6
4
2
2
4
6
8
10
4
6
8
10
2
318y
7
5
x
4
5
x
1
3
x
3
2
3 2i16 30i8 i
1
x 3
3x 2
x
2
3x 9
r 2, s 1
11B £
6
13
11
§x 1, y 1, z 2
a
97
34
,
18
17
b13, 2, 32a2,
2
3
b
2p 1, 5p 6, p11, 6
17
500
£
40
17
0
10
17
40
17
10
10
17
35
17
5
30
17
§£
0.31 0.13 0.08
0.01 0.05 0.02
0.39 0.52 0.02
§
£
0.3 0.06 0.12
0.06 0.06 0
0.18 0.24 0.48
§£
0 0.1 0
0.5 0.6 0
0.2 0.8 0.9
§2
Exercises 8.2, pp. 725–729
1. 3. 2a,2b 5. Answers will vary.
7.
(4.2, 5.6), (4.2, 5.6)
9.
11.
(5, 8), (5, 2)
13. 15.
center: (6, 5), center:
17. 19.
center: ( , 0),
21. 23.
x
y
10
10
10
10
x
y
10
10
10
10
x
y
10
10
10
10
r 艐 3.7
(3, 0)
r 114 3
x
y
10
10
10
10
1x 32
2
y
2
14
x
y
10
10
10
10
r 5
(2, 5)
x
y
10
10
10
10
r 3
(6, 5)
12, 52, r 5r 3
1x 22
2
1y 52
2
251x 62
2
1y 52
2
9
12.4
9.4
9.4
0
1x 12
2
1y 52
2
25
16, 12
2, 16, 122
3.1
0
9.4
3.1
1x 52
2
y
2
3
9.3
14.1
14.1
9.3
x
2
y
2
49
c
2
|
a
2
b
2
|
Student Answer Appendix SA-39
cob19545_saa_039-051.qxd 12/15/10 1:11 PM Page SA-39
25. a. , (0, 0),
b. ( , 0), (4, 0), (0, ), (0, 2) c.
d.
(2.4, 0.8), (2.4, 0.8), (2.4, 0.8), (2.4, 0.8)
27. a. , (0, 0),
b. (0, ), (0, 4), , (3, 0) c.
d.
(2.4, 0.8), (2.4, 0.8), (2.4, 0.8), (2.4, 0.8),
29. a. , (0, 0),
b. ( , 0), ( , 0), (0, ), (0, ) c.
31. ellipse 33. circle
35. ellipse 37.
39. 41.
R: y 僆 35 110
, 5 1104
D: x 僆 31,
54,D: x 僆 36, 24, R: y 僆 31, 34
x
y
10
10
10
10
(3, 5 √10)
(3, 5 √10)
(1, 5)
(3, 5)
(5, 5)
x
y
10
10
10
10
(2, 1)
(2, 1)
(2, 1)
(2, 3)
(6, 1)
1x 32
2
4
1y 52
2
10
1
1x 22
2
16
1y 12
2
4
1
D: x 僆 31,
14, R: y 僆 35, 14
(0, 1)
(0, 3)
(0, 5)
(1, 3)
(1, 3)
x
y
5
5
5
5
x
2
1y 32
2
4
1
x
y
10
10
10
10
x
y
10
10
10
10
r ≈ 3
x
y
10
10
10
10
x
y
5
5
5
5
12121515
a 15, b 12
x
2
5
y
2
2
1
3.1
4.7
4.7
3.1
x
y
10
10
10
10
13, 024
a 3, b 4
x
2
9
y
2
16
1
3.1
4.7
4.7
3.1
x
y
10
10
10
10
24
a 4, b 2
x
2
16
y
2
4
1 43.
45. k 20 47. k 20
49. a. (2, 1) b. ( , 1) and (7, 1) c. ( , 1) and ( , 1)
d. (2, 3) and (2, ) e.
51. a. (4, ) b. (4, 2) and (4, ) c. (4, 0) and (4, ) d. (0, )
and (8, ) e.
53. a. ()b. ( ) and (1, )
c. ( ) and ( ) d. ( ) and
()e.
55.
a.
b.
c. d. verified
57. a.
x
y
8
2
7
3
1x 32
2
9
1y 22
2
25
1
L 6.6
6.2
9.4
9.4
6.2
x
y
10
10
10
10
x
2
36
y
2
20
1
x
y
10
10
10
10
2, 2 16
2, 2 16 2 13, 22 13, 2
25, 22, 2
x
y
10
10
10
10
3
3683
x
y
10
10
10
10
1
2 121
2 1213
R: y 僆 32 110, 2 1104
D:
x 僆 32, 84,
x
y
10
10
10
10
(3, 2 √10)
(3, 2 √10)
(2, 2)
(8, 2
(3, 2)
1x 32
2
25
1y 22
2
10
1
SA-40 Student Answer Appendix
cob19545_saa_039-051.qxd 12/15/10 1:12 PM Page SA-40
b.
c. d. verified
59.
61.
63. 65. ,
67. 8.9 ft, 17.9 ft 69. 71.
73. 75. million miles, million
miles, orbit 77. about 66,697 mph 79. 90,000 yd
2
81. a. 45 ft b. 106 ft c. 25 ft 83. ellipse, since squared terms are
positive and the constant term
becomes zero; the graph is the single point
85.
87. a. b.
Mid-Chapter Check, pp. 729–730
1. 2. 3.
4. 5. 6.
7.
8. a.
b.
9. 10.
Reinforcing Basic Concepts, p. 730
Exercise 1:
Exercise 2:
Exercises 8.3, pp. 740–744
1. transverse 3. perpendicular, transverse, center 5 Answers will vary.
281x ⫺ 12
2
25
⫹
481y ⫹ 22
2
25
⫽ 1
251x ⫺ 22
2
2
⫹
91y ⫺ 32
2
4
⫽ 1
x
2
16
⫹
y
2
4
⫽ 1
x
2
25
⫹
y
2
194
⫽ 1
1x ⫺ 32
2
⫹ 1y ⫺ 22
2
⫽ 16; D: x 僆 3⫺1, 74, R: y 僆 3⫺2, 64
1x ⫹ 32
2
4
⫹
1y ⫺ 12
2
16
⫽ 1; D: x 僆 3⫺5, ⫺14, R: y 僆 3⫺3, 54
y ⫽
1
12
x
2
x
y
34567821
⫺
2
⫺
1
⫺
2
⫺
1
⫺
3
⫺
4
⫺
5
⫺
6
⫺
7
⫺
8
1
2
x
y
321
⫺
5
⫺
6
⫺
7
⫺
4
⫺
3
⫺
2
⫺
1
⫺
2
⫺
1
⫺
3
4
5
6
7
3
1
2
x
y
4321
⫺
6
⫺
5
⫺
4
⫺
3
⫺
2
⫺
1
⫺
1
⫺
2
5
6
7
8
4
2
3
1
x
y
7654321
⫺
3
⫺
2
⫺
1
⫺
1
⫺
2
⫺
3
⫺
4
⫺
5
2
3
4
5
1
x
y
12 1684
⫺
4
⫺
4
⫺
8
⫺
12
4
8
x
y
1284
⫺
4
⫺
4
⫺
8
⫺
12
4
0 6 x 6 6
x 7 0
or
x 6 6
x ⫺ 3 7 ⫺3
or
x ⫺ 3 6 3
0x ⫺ 306 3
⫺20x ⫺ 30⫹ 10 7 4
x
y
12
⫺
8
⫺
10
10
(6, 4)(0, 4)
x 僆 10, 62
log 20
log 3
⬇ 2.73
1⫺3, 42
A ⫽ B; 61x ⫹ 32
2
⫹ 31y ⫺ 42
2
⫽ 0,
time ⬇ 686 days
b ⬇ 141a ⬇ 142
x
2
36
2
⫹
y
2
135.252
2
⫽ 1
x
2
6.25
⫹
y
2
2.25
⫽ 1
x
2
15
2
⫹
y
2
8
2
⫽ 1; 6.4 ft
2.25 ft27 ⬇ 2.65 ftA ⫽ 12 units
2
1⫺3, ⫺1 ⫾ 2132
1x ⫹ 32
2
4
⫹
1y ⫹ 12
2
16
⫽ 1,
x
2
16
⫹
y
2
9
⫽ 1, 1⫾17, 02
L ⫽ 3.6
5
⫺6
12
⫺7
7. 9. 11.
13. 15. 17.
19. 21.
23.
25.
27. 29. 31.
33. 35. 37.
39. 41. 43.
45.
(0, ⫺10), (0, 6), (⫺10, ⫺10), (⫺10, 6)
47.
(2.8, 5.6), (2.8, 0.4), (⫺6.8, 0.4), (⫺6.8, 5.6)
14.4
⫺20.8
16.8
⫺10.4
x
y
(⫺2, 2)
(⫺2, 3)
(⫺2, 4)
6
⫺
14
⫺
6
14
1y ⫺ 32
2
1
⫺
1x ⫹ 22
2
4
⫽ 1
9.3
⫺18.8
9.4
⫺15.3
x
y
(⫺2, ⫺2)
(⫺5, ⫺2)
(⫺8, ⫺2)
10
⫺
10
⫺
10
10
1x ⫹ 52
2
9
⫺
1y ⫹ 22
2
36
⫽ 1
x
y
10
⫺
10
⫺
10
10
(0, 0)
(√6, 0)
(
⫺
√6, 0)
x
y
10
⫺
10
⫺
10
10
(0, ⫺2)
(0, 0)
(0, 2)
x
y
10
⫺
10
⫺
10
10
(⫺3, 0)
(0, 0)
(3, 0)
x
y
10
⫺
10
⫺
10
10
(4, 3)
冢4 ⫹兹5, 3冣
冢4 ⫺兹5, 3冣
x
y
10
⫺
10
⫺
14
6
(1, ⫺8)
(1, ⫺3)
(1, 2)
x
y
10
⫺
10
⫺
10
10
(⫺2, ⫺1)
(2, ⫺1)
(6, ⫺1)
x
y
(⫺5, ⫺1)
10
⫺
10
⫺
10
10
冢⫺5, ⫺1 ⫹兹7冣
冢⫺5, ⫺1 ⫺兹7冣
x
y
(⫺3, ⫺2)
(3, ⫺2)
(9, ⫺2)
10
⫺
10
10
x
y
(0, ⫺3)
(0, ⫺1)
(0, 1)
10
⫺
10
⫺
10
10
14, 12, 14, ⫺32, x ⫽ 4, 14, ⫺12, y ⫽⫺1
1⫺4, ⫺22, 12, ⫺22, y ⫽⫺2, 1⫺1, ⫺22, x ⫽⫺1
x
y
(0, 0)
(0, ⫺6)
(0, 6)
10
⫺
10
⫺
10
10
x
y
(0, 0)
10
⫺
10
⫺
10
10
(0, 3)
(0, ⫺3)
x
y
(0, 0)
10
⫺
10
⫺
10
10
(0, 2√3)
(0, ⫺2√3)
x
y
(0, 0)
(0, 3)
(0, ⫺3)
10
⫺
10
⫺
10
10
x
y
(0, 0)
(6, 0)
(⫺6, 0)
10
⫺
10
⫺
10
10
x
y
(0, 0)
(7, 0)
(⫺7, 0)
10
⫺
10
⫺
10
10
x
y
(0, 0)
(2, 0)
(⫺2, 0)
10
⫺
10
⫺
10
10
x
y
(0, 0)
(3, 0)
(⫺3, 0)
10
⫺
10
⫺
10
10
Student Answer Appendix SA-41
cob19545_saa_039-051.qxd 12/16/10 9:45 AM Page SA-41
49. circle; 51. circle; 53. hyperbola; A, B opposite signs
55. hyperbola; A, B opposite signs 57. circle; 59. ellipse;
61. 63.
65. a. (3, 4) b. (0, 4) and (6, 4)
c. and d. ,
e.
67. a. (0, 3) b. (0, 7), (0, 1)
c. d.
e.
69. a. b. and
c. and d. ,
e.
71. 73.
75. 77. , 4 by
79. a. b.
c.
81. 40 yd 83. 12 microns
85. about (24.1, 60) or
87.
89. a. b.
91. yes, 3 93. 42 solid, 46 liquid
Exercises 8.4, pp. 751–754
1. horizontal, right, a 0 3. (p, 0), 5. Answers will vary.x p
1x 22
2
1y 42
2
1
5
0
1x 42
2
1
4
1y 22
2
0
y
B
b
2
a
2
x
2
b
2
, as x Sq, y S
B
b
2
a
2
x
2
b
a
x
124.1, 602
x
2
225
y
2
2275
1,
6.2
9.4
9.4
6.2
x 僆 1q, 34 ´ 33, q2y
2
3
2x
2
9
215
1y 12
2
4
1x 22
2
5
1
x
2
4
y
2
9
1, 1113, 02
y
2
9
1x 22
2
9
1
x
2
36
y
2
28
1
x
y
10
10
10
10
2b 413 2a 417, 2211, 22
15, 2211, 2213,22
1x 32
2
4
1y 22
2
12
1
x
y
10
10
6
14
y 2x 3, y 2x 3
2a 4, 2b 810,
3 2152, 10, 3 2152
1y 32
2
16
x
2
4
1
x
y
10
10
10
10
2b 42a 613 113, 4213 113, 42
1x 32
2
9
1y 42
2
4
1
12, 2a 16, 2b 128, 2a 8, 2b 6
A BA B
A BA B 7. 9.
11. 13.
15. 17.
19. 21.
23. 25.
27. 29.
31. 33.
35. 37.
39. 41. 43.
x
y
10
10
10
10
(1, 0)
x 1
(0, 0)
x
y
10
10
10
10
冢0, 冣
(0, 0)
3
2
y
3
2
x
y
20
20
10
10
(0, 6)
y 6
(0, 0)
x
y
20
20
10
10
(1, 3)
(19, 0)
x
y
10
10
10
10
(0, 2)
y 2
(0, 0)
x 僆 31, q2, y 僆 1q, q2
x
y
15
15
10
10
(2, 3)
(11, 0)
x
y
10
10
10
10
(2, 3)
(0, 7)
x 僆 32, q2, y 僆 1q, q2x 僆 1q, q2, y 僆 33, q2
x
y
15
15
15
15
(11, 2)
(3, 0)
2
0,
4 兹22
冢
冣
2
0,
4 兹22
冢
冣
x
y
25
25
15
15
(0, 5 兹21)
(21, 5)
(4, 0)
(0, 5 兹21)
x 僆 1q, 114, y 僆 1q, q2x 僆 321, q2, y 僆 1q, q2
x
y
10
10
10
10
(0, 2)
(6.25, 0.5)
(6, 0)
(0, 3)
x
y
10
10
10
10
(0, 1)
(1, 0)
x 僆 36.25, q2, y 僆 1q, q2x 僆 1q, 04, y 僆 1q, q2
x
y
10
10
10
10
(0, 2)
(4, 0)
(0, 2)
x
y
84
8
4
4
8
4
8
(0, 6)
(0, 0)
(9, 3)
x 僆 34, q2, y 僆 1q, q2x 僆 39, q2, y 僆 1q, q2
x
y
168
16
8
4
8
4
8
(0, 4)
(16, 0)
x
y
168
16
8
4
8
4
8
(0, 7)
(7, 0)
(16, 3)
(0, 1)
x 僆 1q, 04, y 僆 1q, q2x 僆 1q, 164, y 僆 1q, q2
(1, 0)
(0, 7)
(1.25, 10.125)
(3.5, 0)
x
y
126
12
6
6
12
6
12
x
y
84
8
4
4
8
4
8
(0, 3)
(4, 1)
(3, 0)
(0, 1)
y 僆 310.125, q2
x 僆 34, q2, y 僆 1q, q2x 僆 1q, q2,
x
y
7
3
20
20
(2, 18)
(1, 0) (5, 0)
(0, 10)
x
y
(3, 0)
(1, 4)
(0, 3)
(1, 0)
10
10
10
10
x 僆 1q, q2, y 僆 1q, 184x 僆 1q, q2, y 僆 34, q2
SA-42 Student Answer Appendix
y
2
3
2x
2
9
cob19545_saa_039-051.qxd 12/15/10 1:13 PM Page SA-42
45. 47. 49.
51. 53. 55.
57. 59.
61. 63. 65.
67. 69.
71. 73.
; vertex ( , 0); focus (1, 0)
75.
; directrix: ; endpoints
( , 6) and ( , )
77.
79.
81.
83. (4, 4), (6.187, 1.571) 85.
87. 16 units
2
11.863, 11.8082, 17.863, 1.8082
9.3
14.1
14.1
9.3
15, 52, 15, 52, 15, 52, 15, 52
6.2
9.4
9.4
6.2
13, 52, 13, 52, 10, 42
6.2
9.4
9.4
6.2
14, 32, 14, 32, 14, 32, 14, 32
244
x 01y 22
2
81x 22
1y
2
81x 121x 32
2
81y 22
1x 42
2
121y 721y 22
2
121x 22
x
2
20yy
2
16xx
2
8y
x
y
10
10
15
15
x 7
(6, 5)
(5, 5)
x
y
10
10
10
10
(1, 3)
(2, 3)
x 3
x
y
10
10
20
20
x 5
(0, 6)
(5, 6)
x
y
10
10
10
10
(4,
2)
(4,
3)
y 4
x
y
25
25
10
10
y 8
(7, 2)
(7, 4)
x
y
15
15
10
10
(4, 0)
(4, 2)
y 2
x
y
10
10
10
10
x
5
2
5
2
(0, 0)
冢
,
0冣
x
y
10
10
10
10
( , 0)
9
2
x
9
2
(0, 0)
89.
91. 6 in.; (13.5, 0) 93. ⬇14.97 ft, (0, 41.75)
95. or 1.25 cm 97.
99. 101. symmetric to the y-axis,
symmetric to the origin,
Making Connections, p. 754
1. d 3. f 5. g 7. c 9. h 11. e 13. b 15. g
Summary and Concept Review, pp. 755–757
1. verified (segments are perpendicular and equal length)
2. 3. yes 4. verified
5. 6. 7.
8. 9.
10.
one possibility is (3, 2.4), (3, 2.4), (3, 2.4), (3, 2.4)
11. a. b.
12. 13.
14. 15. 16.
x
y
20124
20
12
4
4
12
20
12
20
4
(0, 1)
center: (0, 1)
vertices: (0, 2), (0, 4)
x
y
1593
15
9
3
3
9
15
9
15
3
center: (2, 1)
vertices: (5, 1), (1, 1)
x
y
20124
20
12
4
4
12
20
12
20
4
center: (2, 3)
vertices: (2, 1), (2, 7)
x
y
5674321
3
2
1
1
2
3
4
5
2
3
4
5
1
(2 兹21, 1) (2 兹21, 1)
(
3, 1)
(2, 1)
(7, 1)
x
y
8
center: (0, 0)
vertices: 0, 5)
4
8
4
4
8
4
8
1x 22
2
25
1y 12
2
4
1
x
2
144
y
2
400
1
x
2
169
y
2
25
1
6.2
9.4
9.4
6.2
x
2
25
y
2
9
1
x
y
10
10
10
10
x
y
5
5
5
5
x
y
10
10
10
10
x
y
10
10
10
10
x
y
10
10
10
10
x
2
1y 12
2
34
f
1x2f 1x2
f
1x2 f 1x2;y 2x
2
5x 6
1x 22
2
1
2
1y 82; p
1
8
; 12, 82x
2
5y,y
2
5x
x
y
54321
1
x
25
64
冢
,
0冣
25
64
(4, 2.5)
(4, 2.5)
Student Answer Appendix SA-43
cob19545_saa_039-051.qxd 12/15/10 1:14 PM Page SA-43
17.
18.
19. a. b.
20. 21.
22. 23.
24. 25. circle, parabola; (3, 2), (3, 2)
Practice Test, pp. 757–758
1. c 2. d 3. a 4. b
5. 6.
7. 8.
x
y
10
10
10
10
(5, 2)
r 5
x
y
10
10
10
10
(3, 4)
(0, 4)
(6, 4)
(3
兹
13, 4)
(3
兹
13, 4)
y 4
2
3
(x 3)
x
y
10
10
10
(2, 3)
(6, 3)
C (2, 3)
F
1
(2
兹
15, 3)
F
2
(2
兹
15, 3)
x
y
10
10
10
10
(4, 3)
r 3
x
y
15
15
10
10
(0, 2)
(4, 2)
(8, 2)
(4, 0)
y 2
x
y
10
10
10
10
(0, 0)
(0, 5)
(10, 5)
(10, 5)
y 5
x
y
10
10
10
10
(0, 2)
(0, 3)
(6, 0)
(6.25, 0.5)
x
y
14
6
10
10
y x
2
3
16
3
y x
2
3
4
3
(2, 2)
(5, 2)
(8, 2)
x
y
10
10
10
10
(0, 2)
(0, 2)
(4, 0)
1x 52
2
9
1y 22
2
4
1
y
2
16
x
2
9
1
x
2
225
y
2
64
1
15, 5.3
2, 15, 5.32, 15, 5.32, 15, 5.32,
6.2
9.4
9.4
6.2
x
2
9
y
2
16
1
y
25155
25
15
5
3
9
15
9
15
3
x
35
(6, 1)
center: (6, 1)
vertices: (2, 1), (10, 1)
9. 10.
11. 12.
13. a. b.
14. 15 ft, 20 ft 15.
16.
(2, 3), (2, 3), (2, 3), (2, 3)
17. 154.89 million miles; 128.41 million miles
18.
19.
20.
Strengthening Core Skills, p. 759
1. 2.
3.
4.
Cumulative Review Chapters R–8, p. 760
1. 3. is extraneous 5.
7. 9. is extraneousx 5; x 2x 2
ln 7
ln 3
x 3 2ix 7; x 4x 2, x 2i
x
y
1010
10
10
(3, 1)
(艐6, 1) (艐0, 1)
1x 32
2
1
415
3
2
2
1y 12
2
1
9
2
2
2
1; a
41
5
3
⬇ 3, b
9
2
x
y
1010
10
10
(0.5, 1)
(3, 0.2)
(6.5, 1)
(3, 2.2)
1x 32
2
1
7
2
2
2
1y 12
2
1
6
5
2
2
1; a
7
2
, b
6
5
a
527
14
, b
523
12
a
22
5
, b
2
3
1x 12
2
1
527
14
2
2
1y 22
2
1
523
12
2
2
1
1x 22
2
1
22
5
2
2
1y 32
2
1
2
3
2
2
1
foci: 13, 313
2, 13, 313 2
R: y 僆 36, 64;D: x 僆 36, 04,
1x 32
2
9
y
2
36
1;
R: y 僆 34, 64D: x 僆 34, 64,1x 12
2
1y 12
2
25;
focus: 11,
15
4
2
R: y 僆 34, q2;D: x 僆 1q, q2,y 1x 12
2
4;
6.2
9.4
9.4
6.2
x
2
16
y
2
12
1
1x 22
2
1y 52
2
8
12,
22, 12, 22, 12, 22, 12, 22a
10
3
,
16
3
b, 12, 02
x
y
15
15
15
15
x
5
(2, 3)
(1, 3)
x
y
10
10
10
4
10
x
9
(2, 3)
4
7
,
3
冢冣
x
y
10
10
10
10
(1
兹
13, 3) (1
兹
13, 3)
y 3
3
2
(x 1)
y 3
3
2
(x 1)
C (1, 3)
V
1
(3, 3)
V
2
(1, 3)
x
y
10
10
10
10
(1, 6)
(1, 0)
C (1, 3)
F
1
(1, 3
兹
5)
F
2
(1, 3
兹
5)
SA-44 Student Answer Appendix
cob19545_saa_039-051.qxd 12/15/10 1:15 PM Page SA-44
11. 13.
15. 17. 19.
21. a. b.
c. d. none e. max: ( , 4)
f. g.
23. (3, 4), (3, ), 25. 27.
29.
CHAPTER 9
Exercises 9.1, pp. 770–772
1. pattern, order 3. recursive 5. formula defining the sequence uses the
preceding term(s); answers will vary. 7. 1, 3, 5, 7;
9. 0, 9, 24, 45; 11. 2, 4;
13. 15.
17. 1,
19.
21. 4, 16;
23. a. 79 b. { , 2, 7, 14, 23} 25. a. b. {1, }
27. a. b. {2, 1, } 29. a. approx. 2.6 b. {2, }
31. a. b. {}33. 2, 7, 32, 157, 782
35. 4, 19, 364, 132,499 37. 64, 32, 16, 8, 4
39. 336 41. 36 43. 28 45. 47.
49. 1, 2, 51. 15 53. 64 55.
57. 59.
61.
63. 65.
67.
69. a. b. 71. a. b.
73. 75. 77. 79. 35 81. 100
83. 35, verified 85. $7.25, $7.75, $8.25, $8.75, $9.25; $17,760
87. ; 6000, 4800, 3840, 3072, 2457.60, 1966.08
89. 91. approaches 1
93.
95. or 0.25 97.
99.
Exercises 9.2, pp. 779–782
1. common, difference 3. , nth 5. Answers will vary.
7. arithmetic; 9. arithmetic; 11. not arithmetic; all prime
13. arithmetic; 15. not arithmetic; a
n
n
2
d
1
24
d 2.5d 3
n1a
1
a
n
2
2
115, 22, 115, 22, 1 15, 22, 115, 22
3
x
1
81
; x 4
1
4
c
兺
n
j1
a
j
c1a
1
a
2
a
3
p
a
n1
a
n
2
兺
n
j1
ca
j
ca
1
ca
2
ca
3
p
ca
n1
ca
n
⬇2690
a
n
600010.82
n1
兺
7
n3
n
2
n
兺
3
n1
n
2
3
兺
5
n1
1n 32
兺
q
k1
1
k
2
兺
q
k1
12k 12
兺
5
n1
5n
兺
5
n1
4n
1
3
1
8
a
1
15
b
1
24
a
1
35
b
1
48
27
112
6 8 10 12 14 500.5 2 4.5 8 15
1 2 132 4 152 6 1724
1 5 15 29 47 952 1 4 7 10
137
60
9
2
,
32
3
1
3
,
1
120
,
1
15,120
,
1
3,991,680
1
2
,
1
3
,
1
4
,
1
5
1,
1
3
,
1
10
,
1
21
,
1
36
,
1
55
1
36
9
4
,
64
27
,
625
256
,
7776
3125
1
2
,
1
4
,
1
8
1
32
1
2
,
1
3
,
1
4
,
1
5
1
5
1
a
8
256; a
12
40968,2,
1
2
,
1
6
,
1
12
,
1
20
; a
8
1
72
; a
12
1
156
1
2
,
1
3
,
1
4
; a
8
1
8
; a
12
1
12
1
2
,
1
4
,
1
8
,
1
16
; a
8
1
256
; a
12
1
4096
1
2
,
2
3
,
3
4
,
4
5
; a
8
8
9
; a
12
12
13
a
12
12a
8
8;3,1,a
12
429a
8
189;
a
12
23a
8
15;
x ⬇ 1.387 ax
2 ln 2 ln 3
ln 2 ln 3
or
ln 12
ln 6
b
x 6, x 23
1
3
L13, 42, 13, 424
f
1x26 0: x 僆 1q, 42 ´ 12, q2f 1x27 0: x 僆 14, 22
1f
1x2c: x 僆 1q, 12, f 1x2T: x 僆 11, q2
y 僆 1q, 44x 僆 1q, q2
x
y
1010
10
10
(5, 2)
r 3
x
y
1010
10
10
f(x)
(0, 0)
x 1
x
y
x 3
x 3
1010
10
10
h(x)
(2, 0)
(
0, fl
)
x
y
1010
10
10
(3, 1)
x
y
1010
10
10
(0, 5)
(2, 3)
17. arithmetic; 19. 2, 5, 8, 11 21. 7, 5, 3, 1
23. 0.3, 0.33, 0.36, 0.39 25. 2, 3 27.
29.
31.
33.
35.
37. 61 39. 1 41. 2.425 43. 9 45. 43 47. 21 49. 26
51. a. appears linear b. c.
53. a. appears nonlinear b. no common difference
55. 57. 59.
61. 1275
63. 601.25
65.
67. 82.5 69. 74.04 71. 73.
75. at 11
P
.
M
. 77. 5.5 in.; 54.25 in. 79. ; yes
81. a. linear function b. quadratic 83.
85. 1364
Exercises 9.3, pp. 791–795
1. multiplying 3. 5. Answers will vary. 7.
9. 11. not geometric; 13.
15. not geometric; ratio of terms decreases by 1 17.
19. 21. 23. not geometric;
25. 5, 10, 20, 40 27. 3, 29. 4, 413
, 12, 1213
3
2
,
3
4
6,
a
n
240
n!
r
4
x
r
1
2
r
2
5
r 0.1a
n
n
2
1r 2
r 2a
1
r
n1
f 1x2 49x 972;
t ⬇ 3.6
a
7
220; a
12
2520
S
6
21; S
75
285021022
534
d
115
126
, a
1
472
63
a
1
0.65d 0.375,d 3, a
1
1
7
0
7
2
a
n
0.75n 0.75d 0.75
a
6
21
4
, a
10
33
4
, a
12
39
4
a
1
3
2
, d
3
4
, a
n
3
4
n
3
4
,
a
10
6.45, a
12
6.75
a
n
0.15n 4.95, a
6
5.85,
a
1
5.10, d 0.15,
a
6
27, a
10
47, a
12
57a
1
2, d 5, a
n
5n 3,
2, 5, 8, 11
3
4
,
5
8
,
1
2
,
3
8
5
2
,
3
2
,
d
6
Student Answer Appendix SA-45
cob19545_saa_039-051.qxd 12/17/10 9:28 PM Page SA-45