Stewart J. College Algebra: Concepts and Contexts
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A34 Answers to Selected Exercises and Chapter Tests
25.
27.
3
_1
f
g
2
_2
f-g
f+g
t 0 1 2 3 4
f 1t 2
- 3 - 0.5
3 5 6
g1t 2
2 6 7
- 5 - 2
1fg21t2 - 6
- 3
21
- 25 - 12
1f>g21t 2 - 3>2 - 1>12 3>7
- 1 - 3
29. (a) , ;
, (b) 70;
31. (a) , ;
, (b) 0; undefined
33. (a) , ;
, (b) , 1
35. (a)
(b) 32 cameras
P1x 2=-0.4x
2
+ 300x - 9300
1
4
5x 0 x ⫽ 0, - 461f>g21x2=
x + 4
2x
5x
0 x ⫽ 0, - 461fg21x2=
8
x1x + 42
5x
0 x ⫽ 061f>g21x2=
x - 3
x
2
5x 0 - q 6 x 6 q61fg21x2= x
3
- 3x
2
10
7
5x 0 x ⫽ - 561f>g21x2=
3x + 4
x + 5
5x
0 - q 6 x 6 q61fg21x2= 3x
2
+ 19x + 20
0
20,000
40,000
60,000
80,000
100,000
120,000
200 400 600 800 1000
y
x
R
C
P
37. 39. (a) The monthly change
in value from 2007 to 2008 (b) The percentage change in value
from 2007 to 2008 (c) The percentage decrease in value levels
off in the last months of the year. 41. (a) The proportion of the
population that smokes (b) The proportion of smokers has
steadily decreased since 1970.
Algebra Checkpoint 6.2
■
page 500
1. (a) (b) (c) (d) 2. (a) 5, (b)
(c) (d) 1.65669 3. (a) 25 (b) 27 (c)
(d) 7.70385 4. (a) (b) (c)
(d) a
2
3
a
1
b
1>2.12
19w 2
5
;
3
223A
;
A
x
2
21
3
2
1
3
6
3
- 3- 5x
3>2
x
2
3
3
5
3
5
5
R1x 2= 0.15x - 0.000002x
2
6.2 Exercises
■
page 500
1. (a) (b) 2. ; ; ;
; 3. directly; fifth; 7 4.
5. (a) True (b) False
6.
y = 4x
3
y = x
5
y = x
3
y = x
6
y = x
2
y = x
4
x
3
x
2
y
0
x
1
y=x£
y
=x∞
y=x¢
y=x™
1
7. (a) (b)
y
0
x
1
2
y=x£
y=x£-8
_8
10
y
0
x
1
3
y=x£
y=27-x£
27
10
9. (a) (b)
y
0
x
1
y=x¡÷¢
y=x¡÷¢+2
2
1
y
0
x
1
y=x¡÷¢
y=x¡÷¢-8
_8
2
11. 13.
5
_5
y=x¶
y=x∞
y=x£
y=x
2
_2
5
1
2
_5
y=5x£
y=2x£
y=x£
y= x£
2
_2
As c increases, the graph of As c increases, the graph of
becomes steeper stretches vertically.
when .
15.
0
x 07 1
y = cx
3
y = x
c
As c decreases, the graph of
becomes less steep.y = x
c
1.5
_1
y=x¡÷£
y=x¡÷∞
y=x¡÷ª
y=x¡÷¶
1.5
_1
Answers to Section 6.3 A35
(c)
20
5
0
y=x∞
y=2˛
10¶
25
0
y=x∞
y=2˛
10•
50
0
y=x∞
y=2˛
17. (a) (b)
19. 21. 23. 25.
27.
8 29. (a) (b) (c) No
31. (a) (b) (c) 324 W 33. (a)
(b) No 35. (a) (b) 160,000
37. (a) (b) The speed of a car with
stopping distance D (c) 38.9 mi/h 39. (a) 15.3 lb
(b) 291.5 in.
Algebra Checkpoint 6.3
■
page 512
1. (a) (b) (c)
(d) 2. (a)
(b) (c) (d)
3. (a) (b)
(c) (d)
4. (a) (b)
6.3 Exercises
■
page 512
1. (a) power (b) , , 4; ; 4 2. (a) factor; x
(b) 2, , 3; 2, , 3 3. positive, negative; test
4. (a) ii (b) iii (c) i (d) iv 5. No
7.
- 1- 1
3x
4
- 2x
3
3x
4
17z
3
+ 521z
2
- 221x
2
+ 121x + 32
1r
3
- 62
2
x
3
1x + 721x - 4 2
1w
2
+ 421w + 221w - 223t
3
1t + 221t - 2 2
13n + 221n - 1 21t + 721t - 4215m + 12
2
1x + 921x - 9 22y1y
2
- 3y + 22
t
2
1t
2
+ 42r1r - 32312x
2
+ 12
f
-1
1D 2=
A
D
0.033
E = kT
4
F =
100
9
s
2
3
250
P = ks
3
w = 2.1x
3
w = 2x
3
z =
1
4
1tA = 5x
3
z = k1yV = kx
3
20
_15
y=2x™
y=5
y=_x£+2x™+5
y=_x£
3
_3
9. (b) , 1 (c) Negative on and , positive
on 11, q 2
1- 1, 121- q, - 12- 1
y
0
x
1
1
11. 13.
15. 17.
19. (a) 21. (a)
(b) (b)
- x1x - 421x + 32x1x - 321x + 22
23. (a) 25. (a)
(b) (b)
1x
2
+ 121x - 221x + 22x
2
1x - 221x - 1 2
y
0
x
1
2
y
0
x
1
5
y
0
x
1
10
y
0
x
1
5
(d)
y
0
x
1
5
y
0
x
1
10
y
0
x
1
1
y
0
x
1
5
27. as , as 29. as
31. as , as
33. III 35. V 37. VI
x S - qy S - qx Sqy Sqx S;q
y Sqx S - qy S - qx Sqy Sq
A36 Answers to Selected Exercises and Chapter Tests
41. (a) (b) Local maximum:
local minimum:
(c) - 1P11.262= 1.24
P102= 6;
15
_15
4
_4
10
_5
3
_3
43. (a) 26 or 321 (b) No, $5279 45. (a) It began snowing.
(b) No (c) Just before midnight on Saturday night
47. (b) (0, 18) (c) 49. 10.5 in. by 10.5 in. by
107.8 in. or 35.1 in. by 35.1 in. by 9.7 in.
6.4 Exercises
■
page 522
1. (a) scatter (b) power 2. (a) exponential (b) power
5. (a) 7. (a)
(b)
(b)
29.0x + 10.2
y = 1.07x
3
- 10.7x
2
+y = 210.31x
1.2994
1728 in
3
1200
4
0
35
6
0
9. (a) Power
(b) y = 4.00x
3.50
1200
6
0
11. (a) (b) Semi-log
1.1
18
0
0.2
_1.2
18
0
0.2
_1.2
1.3
0
1.1
18
0
Log-log (c) Exponential
(d) y = 0.057711.20023 2
x
130
11
0
2.3
11
0
2.2
1.1
0
130
11
0
13. (a) (b) Semi-log
Log-log (c) Power
(d) y = 1.40x
1.9482
5
1.1
0
15. (a), (c)
(b)
(d) 44.79 m
17. (a)
d = 4.96t
2.0027
200
25
0
(b)
(c)
(d) Fourth-degree model
y =-0.00243x
4
+ 0.135x
3
- 2.014x
2
- 4.06x + 199
y = 30210.81972
x
39. (a) (b) Local maximum:
; local
minimum:
(c) , 2, 3- 2
P12.532=-1.13
P1- 0.532= 13.13
Answers to Section 6.5 A37
120
20
L=aw
b
L=ab
w
0
21. (a)
(b) (c) 43 (d) 2.0 s
y = 0.002x
3
- 0.105x
2
+ 1.97x + 1.46
22
30
0
19. (a) (b)
(c) The power model is better. (d) 138 in.
L = 22.911.12632
W
L = 30.6W
0.395
Algebra Checkpoint 6.5
■
page 532
1. (a) (b) 2 (c) 15,625 (d) 2. (a) (b)
(c) (d) 3. (a) (b) 2 (c) (d)
4. (a) (b) 6, (c) (d)
6.5 Exercises
■
page 533
1. ; 2. (a) inversely; fifth; 7 (b)
5. (a)
table 1 table 2
y = 4x
-3
y = x
-2
y = x
-1
1
25
1
8
- 6
1
5
a
2
1
a
2
1
8
1
b
2
-
1
b
3
8
y
6
1
x
4
25
1
8
(b) As , ; as ,
(c) As , ; as , f 1x 2S 0x S - qf 1x 2S 0x Sq
f 1x 2Sqx S 0
⫹
f 1x 2S - qx S 0
-
x
f 1x 2
- 0.1
- 10
3
- 0.01
- 10
6
- 0.001
- 10
9
- 0.00001
- 10
15
x
f 1x 2
0.1
10
3
0.01
10
6
0.001
10
9
0.00001
10
15
x
f 1x 2
10
1.0 * 10
-3
50
8.0 * 10
-6
100
1.0 * 10
-6
100,000
1.0 * 10
-15
x
f 1x 2
- 10
- 1.0 * 10
-3
- 50
- 8.0 * 10
-6
- 100
- 1.0 * 10
-6
- 100,000
- 1.0 * 10
-15
table 3 table 4
x
f 1x 2
- 0.1
10
4
- 0.01
10
8
- 0.001
10
12
- 0.00001
10
20
x
f 1x 2
0.1
10
4
0.01
10
8
0.001
10
12
0.00001
10
20
x
f 1x 2
10
1.0 * 10
-4
50
1.6 * 10
-7
100
1.0 * 10
-8
100,000
1.0 * 10
-20
x
f 1x 2
- 10
1.0 * 10
-4
- 50
1.6 * 10
-7
- 100
1.0 * 10
-8
- 100,000
1.0 * 10
-20
7. (a)
table 1 table 2
table 3 table 4
(b) As , ; as ,
(c) As , ; as ,
9. 11.
f 1x 2S 0x S - qf 1x 2S 0x Sq
f 1x 2Sqx S 0
⫹
f 1x 2Sqx S 0
-
3
_3
c=1
c=3
c=5
c=7
3
_3
3
_3
2
1
c=
c=1
c=2
c=5
3
_3
17. 19.
13. 15.
y
0
x
1
1
y
0
x
1
2
y
0
x
1
2
y
0
x
1
2
21. 23. 25.
27. 29.
0.1875 31. (a)
(b) 28.57 kPa 33. (a) (b) 0.7 dBL =
7000
d
2
P =
26.169
V
s =
45
1t
z =
6
t
y =
k
1t
P =
k
T
35. y-intercept 2
vertical
horizontal y = 0
x = 3
y
x
0
3
10
A38 Answers to Selected Exercises and Chapter Tests
35. (a) (b) 72 lb 37. (a)
(b) 8 times the heat
Algebra Checkpoint 6.6
■
page 542
1. (a) (b) (c) (d)
2. (a) (b) (c)
(d) 3. (a) (b)
(c) (d) 4. (a)
(b)
6.6 Exercises
■
page 542
1. , 2. a 3. (a) factored (b) compound fraction
(c) standard 4. (a) , 2 (b) (c) , 3 (d) 1
7. (a)
table 1 table 2
- 2
1
3
- 1
- qq
x
2
- 3x + 1 -
1
x + 3
x - 2 -
16
x - 4
2 -
3
x - 1
8 +
21
x - 2
1 -
4
x + 1
3 -
1
x + 2
x + 2
x1x + 12
1
x
2
+ 3x + 2
31x + 22
x + 3
2x
x
2
- 1
x12x + 32
2x - 3
x + 2
x + 1
1
x + 2
5
x + 1
H =
k
d
3
S =
360
n
x
f 1x 2
1.5
- 3
1.9
- 19
1.99
- 199
1.999
- 1999
x
f 1x 2
2.5 5
2.1 21
2.01 201
2.001 2001
x
f 1x 2
10 1.25
50 1.04
100 1.02
1000 1.002
x
f 1x 2
- 10
0.833
- 50
0.962
- 100
0.980
- 1000
0.998
table 3 table 4
(b) As , ; as ,
(c) As ,
9. (a)
table 1 table 2
f 1x 2S 1x S;q
f 1x 2Sqx S 2
⫹
f 1x 2S - qx S 2
-
x
f 1x 2
1.5
- 22
1.9
- 430
1.99
- 40,300
1.999
- 4.003 * 10
6
x
f 1x 2
2.5
- 10
2.1
- 370
2.01
- 39,700
2.001
- 3.997 * 10
6
x
f 1x 2
10 0.313
50 0.0608
100 0.0302
1000 0.00300
x
f 1x 2
- 10 - 0.278
- 50 - 0.0592
- 100 - 0.0298
- 1000 - 0.00300
table 3 table 4
(b) As , ; as ,
(c) As , 11. 1; 13. , 2;
15. 3; 3; ; 17. , 1; ; , ;
19. ; 21. No vertical asymptote;
23. , ; 25. , ;
27. 29.
y =
5
3
x =-2x =
1
3
y = 3x =-1x =
1
2
y = 0y = 0x = 2
y = 1x = 2x =-2
1
4
- 1y = 2x = 2
1
3
- 1-
1
4
f 1x 2S 0x S;q
f 1x 2Sqx S 2
⫹
f 1x 2Sqx S 2
-
31.
33. x-intercept 1
y-intercept
vertical
horizontal y = 4
x =-2
- 2
y
0
x
1
1
y
0
x
1
1
y
0
x
1
1
y
x
0
2
4
Answers to Chapter 6 Review A39
y
x
0
1
5
y
x
0
6
6
_6
_6
37. x-intercept 2
y-intercept 2
vertical
horizontal y = 0
x =-1, x = 4
y
0
x
10
10
14000
5.0 ⫻ 10
7
0
43. (a)
(b)
The escape velocity from
the earth’s gravitational pull
4.01 * 10
7
m
39. x-intercepts
y-intercept 2
vertical
horizontal y = 2
x =-3, x = 2
- 6, 1
41. (a) (b) (c) y Sqy S 35y =
35x
x - 35
5
_2
f+g
f-g
f
g
6
_2
5
_5
f+g
f-g
f
g
5
_5
Chapter 6 Review Exercises
■
page 548
1. (a) , ; ,
; , ;
, (b) 8; 4; 12; 3
(c)
1- q, 1 2´ 11, q 21f>g21x2=
2x
x - 1
1- q, q 21fg21x 2= 2x
2
- 2x1- q, q 2
1f - g21x2= x + 11- q, q 21f + g21x2= 3x - 1
3. (a) , ;
, ; 31, q 21f - g21x2= 1x
- 1x - 1
31, q 21f + g21x2= 1x + 1x - 1
5. 7.
9. (a) (b) 11. (a) (b) 18
13. 4
15. 17.
L = k√
1>3
1
4
E = k√
2
19. 21.
y
0
x
f
g
1
2
y
0
x
1
fg
2
y
0
x
1
2
y
0
x
1
2
y
0
x
1
2
y
0
x
1
1
23. (a) (b) Local maximum:
; local minimum:
(c) , 0.762, 2.96- 2.22
P122=-10
P1- 12= 17
20
_15
4
_3
, ; ,
(b) 1; 1; 0; not defined
(c)
11, q 21f>g21x 2=
1x
1x - 1
31, q 21fg21x2= 1x 1x - 1
A40 Answers to Selected Exercises and Chapter Tests
27. (a) Semi-log Log-log
0
3
18
0
3
1.5
0
400
18
y
0
x
1
1
y
0
x
1
1
(b) Power model (c) y = 5.3x
1.5143
29. 31.
25. (a) ;
(b) (c) Cubic
y = 0.965x
3
- 11.5x
2
+ 42.3x + 1.79
y = 21.8 + 5.83x
0
Linear
Cubic
65
7
y
0
x
1
1
y
x
1
1
33. (a) (b) 300 35. 0.586
37. 39.
G =
k
r
3
y
0
x
1
2
y
0
x
1
2
41. (a) ; 43. (a) 0; 0
(b) ; (b) ; ,
(c) (c)
x =-1x = 2y = 0x = 1y = 2
- 2- 1
45. (a) (i) Exponential (ii) Linear (iii) Power
(b) (c) Linear; exponential; power
(d) ; ;
47. (a) Subtraction; $390 (b) Average revenue per pen;
average cost per pen
49. (a) (b) [0, 10]
(c) (d) 5.77 in.
S = 1380x - 13.8x
3
y = 2.00x
1.32
y = 0.80012.52
x
y =-1 + 3x
g1x 2= 4x
51. (a) No; yes, (b) as
(c)
t SqC1t 2S 0y = 0
The maximum
concentration was 2.5 mg/L
at .t = 1 h
Chapter 6 Test
■
page 553
1. , ; , ; ,
; , ; 1; 1; 0; undefined
2. (a) I: h; II: f ; III: (b) (0, 0); (1, 1)
3. (a) (b) 0.471 (c)
4. (a) (b)
58.9 cm
3
V = kx
3
g
30, 12´ 11, q 2
1x
x
2
- 1
30, q 2
1x
1x
2
- 1230, q 21x - x
2
+ 130, q 21x + x
2
- 1
6000
10
0
5
5
0
y
0
x
1
2
y
0
x
1
2
Answers to Section 7.3 A41
5. Local minima: , ; local
maximum:
6. (a) Semi-log Log-log
Q102=-4
Q11.222=-6.25Q1- 1.222=-6.25
3
82
0
3
2
0
(b) Power model;
(c)
y = 1.02x
1.49
7. (a) (b)
8. , none; , and x = 2x = 0y = 0- 1
710
82
0
y
0
x
1
1
y
0
x
1
4
y
0
x
1
2
Chapter 7
7.1 Exercises
■
page 576
1. system 2. x, y; equation 3. (2, 1) 4. substitution;
elimination 5. two, infinitely many (a) None
(b) Infinitely many 6. infinitely many; , (1, 0), ,
7. (a) (3, 4) 8. (a) and (4, 8) 9.
11. 12, - 22
1- 2, 321- 2, 2215, - 42
1- 3, 421 - t
y
x
0
1
1
(2, _2)
2x+y=2
x-y=4
13. No solution 15. Infinitely many solutions
y
x
0
5
5
_5
_5
17. (2, 2) 19. (2, 1) 21. 23. (2, 1) 25. (3, 5)
27. (1, 3) 29. No solution 31.
33. 35. 37. (5, 10) 39. No solution
41. (3.87, 2.74) 43. (61, 20) 45. 12, 22 47. 5 dimes,
9 quarters 49. 200 gallons regular, 80 gallons premium
51. Plane’s speed: 120 mi/h, wind speed: 30 mi/h
53. 200 g Food A, 40 g Food B
55. First: 25%, second: 10%
7.2 Exercises
■
page 586
1. (a) 3 (b) 1 (c) 3, 1, 7 (d) 7, 1, 3 2. (a)
(b) ; 5. (1, 3, 2) 7. (4, 0, 3)
9. 11. c
2x - y + 3z = 2
x + 2y - z = 4
3y + 7z = 14
c
x - 2y - z = 4
- y - 4z = 4
2x + y + z = 0
4y - 5z =-4- 3
x + 3z = 1
1- 3, - 72Ax, 3 -
3
2
xB
Ax,
1
3
x -
5
3
B
13, - 12
y
x
0
2
2
13. 15. (1, 2, 1) 17. (5, 0, 1) 19. (0, 1, 2)
21. 23. No solution 25. No solution
27. 29.
31. Short: $30,000; intermediate: $30,000; long: $40,000
33. Corn: 250 acres; wheat: 500 acres; soybeans: 450 acres
35. No solution 37. Midnight Mango: 50; Tropical Torrent:
60; Pineapple Power: 30 39. A: 1500; B: 1200; C: 1000
7.3 Exercises
■
page 599
1. 2.
3. (a) x, y (b) Dependent (c) , ,
4. (a) , , (b) , ,
(c) No solution 5. (a) (b) 0 7. (a) (b) 35
9. (a) (b) 3 11. (1, 1, 2) 13. (1, 0, 1)
15. 17. 19.
21. 23. 25. Inconsistent
27. Dependent, 29. Dependent,
31. 33. No solution 35.
37. 39. 41. VitaMax: 2;
Vitron: 1; VitaPlus: 2 43. Running: 5 mi; swimming: 2 mi;
cycling: 30 mi 45. Impossible
1- 2, 1, 0, 3215 - t, - 3 + 5t, t2
1- 9, 2, 021- 2, 1, 3212 + 3t, t, 42
12 - 3t, 3 - 5t, t2
110, 3, - 221- 1, 5, 02
1- 1, 0, 12
10, 2, - 121- 1, 1, 22
3 * 1
2 * 13 * 2
z = ty = 1 - tx = 2 - tz = 3y = 1x = 2
z = ty = 5 - 2tx = 3 + t
c
x + y + 2z = 4
3x + z = 2
5x + 2y - z =-2
C
11- 11
10 2- 3
02- 13
S
A2 - 2t, -
2
3
+
4
3
t, tB13 - t, - 3 + 2t, t2
11 - 3t, 2t, t2
12, 1, - 32
A42 Answers to Selected Exercises and Chapter Tests
Chapter 7 Review Exercises
■
page 630
1. (2, 1) 3. No solution
9. 11. No inverse
13. 15. No inverse
17. 19. 21.
23. 25.
27. (a)
(b) (c) Standard: $125;
deluxe: $150; leather: $200
C
112
211
121
SC
x
y
z
S= C
675
600
625
S
c
x + y + 2z = 675
2x + y + z = 600
x + 2y + z = 625
1- 20, 10, 1621- 38, 9, 472
1126, - 502112, - 82C
-
9
2
- 14
31- 3
7
2
1 - 3
S
C
- 4 - 45
11- 1
54- 6
S
c
13 5
- 5 - 2
d
y
x
0
1
1
y
x
411
0
1
6x-8y=15
x=2y=_4_
3
2
7.4 Exercises
■
page 607
1. Numerical 2. Categorical 3. Categorical 4. Numerical
5. 7. (a) 1 (b) 16 (c) 23
(d) 50 9. (a) 3 (b) 15 (c) 12 (d) 50
11. (a) (b) The proportion of
macaroni that is sold on Monday; the proportion of macaroni
that is sold on Wednesday 13. (a) (b) 23
15. (a) (b) 0.28 17. (a)
(b) $42,000.00 (c) $118,000
7.5 Exercises
■
page 616
1. dimension 2. columns; rows 3. (b), (c)
4. 5. (a), (b) 6. A must be a square matrix.
7. 9. 11. Impossible
13. 15. (a) (b) Impossible
17. (a) (b) Impossible 19. (a) Impossible
(b) 21. (a) (b)
23. (a) (b) 25. (a)
(b) 27. (a)
(b) $1690 (c) $19,590 29. (a)
(b) Total amount (in ounces) of tomato sauce produced; total
amount (in ounces) of tomato paste produced.
7.6 Exercises
■
page 625
1. (a) identity (b) A, A (c) inverse
2. (a) (b)
(c) (d) 7. c
35
- 2 - 3
d1- 1, 32c
2 - 3
- 35
dc
4
3
d= c
- 1
3
d
c
2 - 3
- 35
dc
53
32
dc
x
y
d= c
4
3
d
3105,000 58,0004
34690 1690 13,2104c
8 - 335
0 343
d
c
4 - 45
049
dC
- 1
8
- 1
SC
5 - 310
610
- 522
S
c
6 - 8
4 - 17
dc
- 47
14
- 7
d314 - 144
c
10 - 25
035
d
c
5 - 25
110
dc
52 1
710- 7
d
C
36
12 - 3
30
Sc
13
15
d
C
49- 7
7 - 70
4 - 5 - 5
S
C
32,000
42,000
44,000
SC
200 80 60
160 300 80
140 240 400
S
C
19 23 17
13 17 12
6512
S
C
0.40 0.13 0.11
0.32 0.48 0.15
0.28 0.39 0.74
S
C
520
2103
042
S
5. (2, 1) 7. ;
9. (1, 1, 2) 11. (0, 1, 2) 13.
15. No solution 17.
19. Impossible 21. 23. Impossible
25. 27.
29. 33.
35. 37. (65, 154) 39.
41. (a)–(d), (f) (8, 2) (e)
43. (a) (b) Kieran is 13; Siobhan is 9.
45. Haddock: 160 lb, sea bass: 340 lb, red snapper: 60 lb
e
x = y + 4
x + y = 22
c
108
012
d
A-
1
12
,
1
12
,
1
12
BC
0.5 0.5 - 0.5
0.5 - 0.5 0.5
- 0.5 0.5 0.5
S
c
3 - 2
- 11
dC
- 0.5 5.5
3.75 - 1.5
- 0.5 1
§
c
30 22 2
- 91- 4
dc
- 3.5 10
1 - 4.5
d
C
418
4 0
2 2
S
11, - 2, 32
14 - 2t, 2 - t, t2
y =-12 + 3xx = any number
Answers to Section A.1 A43
47. (a) (b)
(c)
; ; ten $20 bills and eight $50 bills
Chapter 7 Test
■
page 634
1. 2. Wind speed: 60 mph; airplane speed: 300 mph
3. (a) (b) Neither 4. (a) No solution
(b) Inconsistent 5. (a) (b) Dependent
6. Coffee: $1.50; juice: $1.75; doughnut: $0.75
7. (a) Impossible (b)
(c) (d) Impossible (e) Impossible
(f) 8. (a)
(b) ; (70, 90)
Algebra Toolkit A
A.1 Exercises
■
page T5
2. (a) ba; Commutative (b) ; Associative
(c) ; Distributive 3. (a) factor; factors (b) term;
terms 4. (a) Distributive Property; a;
(b) Distributive Property; 5. (a) 50
(b) (c)
(d) , 6. (a) 11, (b)
(c) 1.001, , 3.14, , (d) 7. 1
8. 5 9. 10. 11. Commutative Property
12. Commutative Property 13. Associative Property
14. Distributive Property 15. Distributive Property
16. Distributive Property 17. Commutative Property
18. Distributive Property 19. 2 20. 21. 2 22. 2
23. 36 24. 170 25. 26. 27.
28. 29. 30.
31. 32.
33. 34.
35. 36. 37.
38. 39. 40.
41. 42.
43. 44.
A.2 Exercises
■
page T12
2. a is to the left of b 3. (a) (b) (2, 7)
5. Absolute value; positive 6. distance 7. (a) (b) 76
5x
˛ 0 2 6 x 6 76
1
8
˛ab˛ 14x + 2y - z22s1qr - 3qt + 6rt2
- 30
˛z 1x + 3y2- 5b1a - 2c 2
2a1x + y2b1a - 62- 201x - 2y2
- 21a + b261y - 2231x + 32
- 6pqs + 4pqrs + 10prs8mnp + 12mnpq - 8mnq
- 18abc + 15bcd- 12ax + 8x
7x + 14y6a - 18c8a - 16
3
x + 21- 3- 30
- 1
- 301- 2
- p
15
3
1160.3, - 11, 11,
13
15
- 11, 11, 116,
15
3
116,
15
3
2
3
217
0, - 10, 50,
22
7
, 0.583, 1.23, -
1
3
0, - 10, 50
a; a; a
˛ 1b + c2
ab + ac
ab + ac
1a + b 2+ c
A
-1
= c
- 23
- 34
d
c
4 - 3
3 - 2
dc
x
y
d= c
10
30
dC
5
0
- 6
S
C
30 3
03 0
60- 6
S
C
5 - 1.5
- 1.5 0
3 - 1
S
A
1
7
+
1
7
t,
2
7
+
9
7
t, tB
12, 1, - 12
13, - 12
X = c
10
8
dA
-1
= c
5
3
-
1
30
-
2
3
1
30
d
c
11
20 50
dc
x
y
d= c
18
600
de
x + y = 18
20x + 50y = 600
(c) 8. (a) (b) (c) 9. False 10. True
11. True 12. False 13. False 14. True 15. False
16. True
17. 18.
=76=
10
0_4
19. 20.
21. 22. 23. 24.
25. (a) (b) (c) (d)
(e) 26. (a) (b) (c)
(d) (e)
27. (a) {1, 2, 3, 4, 5, 6, 7, 8} (b) {2, 4, 6}
28. (a) {2, 4, 6, 7, 8, 9, 10} (b) {8}
29. (a) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (b) {7}
30. (a) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (b) ⭋
31. (a) (b)
32. (a) (b)
33. (a) All numbers greater than and less than 0
(b) (c)5x
˛ 0 - 3 6 x 6 06
- 3
5x
˛ 0 - 1 6 x … 565x˛ 0 x Ú-26
5x
˛ 0 - 1 6 x 6 465x˛ 0 x … 56
0
y - 7 0Ú 20 6 w … 17
b Ú 8z 7 1y 6 00
p - 3 0… 5
- 5 6 x 6
1
3
a Ú-1t 6 4x 7 0
x Ú 5x 7-
3
2
x 6-2x … 1
0_3
0
0_3
34. (a) All numbers greater than 2 and less than or equal to 8
(b) (c)5x
˛ 02 6 x … 86
80 2
02 8
35. (a) All numbers greater than or equal to 2 and less than 8
(b) (c)
36. (a) All numbers greater than or equal to and less than or
equal to
(b) (c)
37. (a) All numbers greater than or equal to 2
(b) (c)
38. (a) All numbers less than 1
(b) (c)
39. (a) All numbers less than
(b) (c)
40. (a) All numbers greater than or equal to
(b) (c)
41. [1, 2] 42. (3, 5)
5x
˛ 0 x Ú-36
- 3
5x
˛ 0 x 6-26
- 2
5x˛ 0 x 6 16
5x
˛ 0 x Ú 26
5x
˛ 0 - 6 … x …-
1
2
6
-
1
2
- 6
5x
˛ 0 2 … x 6 86
0
1
2
_
_6
20
10
0_2
0_3
012 0 53