125)
7x + 4y – z =50
x – 2y + 6z =47
5x + y + z =40
A)
(5, -6, -9)
B)
(6, 9, 6)
C)
(6, 4, 9)
D)
(5, 6, 9)
126)
6x – 2y + 6z =58
-8x + 5y + 4z =28
-2x – 9y + 4z =-10
A)
(3, 4, 8)
B)
(3, -4, -8)
C)
(4, 2, 8)
D)
(4, 8, 4)
127)
-3a+ 6c =18
3a + 5b + 3c =23
-6a – 8b=-20
A)
(2, 1, 4)
B)
(3, –1, 4)
C)
(1, 4, 1)
D)
(2, -1, -4)
Solve using matrices.
128)
3x + 3y =3
3x + 7y =27
A)
(6, 5)
B)
(-5, 6)
C)
(6, -5)
D)
(-5, -6)
129)
5x + y = 21
6x + 3y = 18
A)
(5, -5)
B)
(5, -4)
C)
(-4, 5)
D)
(-4, -5)
130)
x + 8y =8
4x – 9y =-9
A)
(1, 0)
B)
(0, 0)
C)
(0, 1)
D)
(1, 1)
131)
5x – 2y = – 1
x + 4y = 35
A)
(2, 8)
B)
(2, 9)
C)
(3, 8)
D)
(3, 9)
132)
x + 7y = – 2
3x + y = 34
A)
(3, 7)
B)
(7, 12)
C)
(–2, 3)
D)
(12, –2)
133)
x – 5y = – 4
x + 8y = – 4
A)
(4, 0)
B)
(–4, 0)
C)
(0, 4)
D)
(0, –4)
134)
7x +3y =0
7x – y =14
A)
3
2, 7
2
B)
3
2, – 7
2
C)
0, 0
D)
– 3
2, 7
2
135)
x + y + z = 1
x – y + 2z =-8
2x + y + z =-4
A)
(1, 5, -5)
B)
(1, -5, 5)
C)
(5, 1, -5)
D)
(-5, 5, 1)
136)
x – y + 3z =-7
5x + z =-1
x + 3y + z =11
A)
(4, -1, 0)
B)
(-1, 4, 0)
C)
(0, 4, -1)
D)
(-1, 0, 4)
137)
2x – y – 2z =2
-8x – 8z =-80
7y + z =18
A)
(-6, 2, 12)
B)
(2, 4, 6)
C)
(6, 2, 4)
D)
(6, 4, 2)
138)
9x + 2y – z =81
x + 2y – 5z =-15
8x + y + z =81
A)
(3, 6, 9)
B)
(-9, 3, 18)
C)
(9, 6, 3)
D)
(9, 3, 6)
139)
3x – y + 9z =18
-2x + 9y – 3z =19
6x – 6y + z =-10
A)
(1, 2, 3)
B)
(-1, 3, 2)
C)
(1, 3, 2)
D)
(2, 3, -1)
140)
x + y =4
3x + y =14
y +2z =-5
A)
(5, -1, -2)
B)
(3, -1, -4)
C)
(15, -1, -4)
D)
(5, 1, -2)
141)
3x +6y =14
3x –9z =-7
8y – 3z =18
A)
1
2, – 5
3, 2
3
B)
– 1
2, 5
2, 2
3
C)
– 1
3, 5
2, 2
3
D)
1
3, 5
2, – 2
3
17
Solve.
142)
Let f(x) =8x +8 and g(x) =7x2+4. Find f(3) + g(3) .
A)
87
B)
99
C)
95
D)
91
143)
Let f(x) =-7x +4 and g(x) =8x2+9. Find f(9) + g(9) .
A)
594
B)
585
C)
589
D)
598
144)
Let f(x) =5x +7 and g(x) =5x2+9. Find f(7) – g(7) .
A)
-219
B)
-212
C)
-210
D)
-203
145)
Let f(x) =-4x +6 and g(x) =4x2+4. Find f(6) – g(6) .
A)
-172
B)
-162
C)
-168
D)
-166
146)
Let f(x) =7x +4 and g(x) =6x2+6. Find g(4) – f(4) .
A)
68
B)
70
C)
74
D)
64
147)
Let f(x) =-5x +7 and g(x) =2x2– 1. Find g(2) – f(2) .
A)
17
B)
10
C)
11
D)
18
148)
Let f(x) =2x +9 and g(x) =4x2+ 3. Find f(2) · g(2) .
A)
208
B)
64
C)
76
D)
247
149)
Let f(x) =-4x +2 and g(x) =3x2+ 5. Find f(9) · g(9) .
A)
-8748
B)
-8928
C)
-8432
D)
-8262
150)
Let f(x) =7x +5 and g(x) =8x2+8. Find g(5) / f(5) .
A)
26
5
B)
40
7
C)
5
D)
208
35
151)
Let f(x) =-2x +4 and g(x) =9x2+7. Find f(5) / g(5) .
A)
– 5
116
B)
– 2
45
C)
– 2
75
D)
– 3
116
For the pair of functions, find the indicated sum, difference, product, or quotient.
152)
Let f(x) =5x2+ 7 and g(x) = x – 1. Find (f – g)(4).
A)
-91
B)
92
C)
82
D)
84
18
153)
Let f(x) = x – 6 and g(x) = x – 3. Find (f + g)(4).
A)
11
B)
17
C)
5
D)
-1
154)
Let f(x) =5x – 7 and g(x) =5x2+ 14x + 3. Find (f/g)(-4)
A)
5
27
B)
5
13
C)
– 1
D)
5
27
155)
Let f(x) = x – 6 and g(x) =-4x2+ 10x + 6. Find (f · g)(4).
A)
-580
B)
36
C)
–124
D)
-180
156)
f(x) =5x – 4, g(x) =2x – 9
Find (f – g)(x).
A)
3x – 13
B)
–3x – 5
C)
3x + 5
D)
7x – 13
157)
f(x) =4– 4x, g(x) =-2x + 4
Find (f + g)(x).
A)
–6x + 8
B)
-2x + 8
C)
2x
D)
–2x + 4
158)
f(x) =5– 7x, g(x) =-9x2+ 7
Find (f + g)(x).
A)
-9x2– 7x + 12
B)
–16x + 12
C)
–16x2– 7x + 12
D)
–9x2+ 5
159)
f(x) =7x2– 8x, g(x) = x2– 4x – 32
Find (f/g)(x).
A)
7– x
32
B)
7x – 8
-4
C)
7x2– 8x
x2– 4x – 32
D)
7x
x + 1
160)
f(x) =4x + 4, g(x) =6x + 9
Find (f · g)(x).
A)
24x2+ 60x + 36
B)
10x2+ 60x + 13
C)
24x2+ 36
D)
24x2+ 33x + 36
161)
f(x) =x2+ 1, g(x) =4x + 6
Find (f · g)(x).
A)
4x2+4x + 6
B)
4x3+4x2+ 6x + 6
C)
4x3+ 6
D)
4x3+ 6x2+4x + 6
Find the distance between the pair of points. Where appropriate, give an approximation to three decimal places.
162)
(6, 6) and (6, 15)
A)
9
B)
10
C)
15
D)
8
163)
(1, 2) and (-3, -7)
A)
97 9.849
B)
-5
C)
36
D)
65 8.062
164)
(4, -7) and (6, -1)
A)
32
B)
4
C)
32 245.255
D)
210 6.325
D
165)
(-6, -6) and (3, 7)
A)
4
B)
510 15.811
C)
88 22 412.757
D)
88
B
166)
(-7, 3) and (5, -3)
A)
108
B)
18
C)
108 3187.061
D)
6 5 13.416
D
167)
5
9, 1
18 and 1
5, 7
18
A)
481
45 0.487
B)
481
45 10.689
C)
213
90.801
D)
7
90.778
A
168)
(–2.4, 4.5) and (5.6, 19.5)
A)
23
B)
289
C)
17
D)
23
C
169)
(6.1, -2.5) and (-4.8, 3.7)
A)
157.25 12.54
B)
3.13
C)
3.13 1.769
D)
0.25 0.5
A
170)
(67, 32) and (47, -24)
A)
13,060
B)
13,060 114.28
C)
3536 59.464
D)
12,932
C
171)
(y, 0) and (0, p)
A)
y2–p2
B)
y+p
C)
y2+p2
D)
y2+p2
C
172)
( 5, 2) and (–10, –6)
A)
23 –10 2–4 3 1.389
B)
23 +10 2–4 3 5.497
C)
23 +10 2+4 3 6.639
D)
23 –10 2+4 3 3.973
C
173)
(-375,1207) and (942, -463)
A)
4,523,389 2126.826
B)
2,288,025 1512.622
C)
875,025 935.428
D)
3,110,389 1763.629
A
Find the midpoint of the segment with the given endpoints.
174)
(1, 7) and (9, 4)
A)
10, 11
B)
– 4, 3
2
C)
-8, 3
D)
5, 11
2
175)
(3, -9) and (0, 7)
A)
3, -2
B)
3
2, – 8
C)
3
2, – 1
D)
3, -16
C
176)
(-7, -8) and (0, 4)
A)
– 7
2, – 6
B)
-7, -4
C)
-7, -12
D)
– 7
2, – 2
D
177)
(3, 3) and (-4, -4)
A)
-1, –1
B)
7, 7
C)
– 1
2, –1
2
D)
7
2, 7
2
C
178)
11
2, – 9
2 and 3
2, – 7
2
A)
7
2, – 4
B)
196, 256
C)
2, – 1
2
D)
64, 4
A
179)
(-3.3, -7.9) and (-7.1, -1.9)
A)
-10.4, -9.8
B)
1.9, –3
C)
3.8, –6
D)
-5.2, -4.9
D
180)
(10, –6) and ( 7, 7)
A)
10 +7
2, – 13
2
B)
10 +7
2, 1
2
C)
– 13
2, 10 +7
2
D)
1
2, 10 +7
2
B
Find the center and the radius of the circle.
181)
x2+y2=16
A)
(0, 0), r =16
B)
(4, 4), r =16
C)
(0, 0), r =4
D)
(0, 4), r =16
C
182)
(x + 2)2+y2=64
A)
(2, 0), r =64
B)
(0, -2), r =64
C)
(-2, 0), r =8
D)
(0, 2), r =8
C
21
D
183)
x2+(y – 9)2=16
A)
(–9, 0), r =16
B)
(0, 9), r =4
C)
(0, –9), r =4
D)
(9, 0), r =16
184)
(x + 6)2+(y + 1)2=64
A)
(-6, -1), r =8
B)
(6, 1), r =64
C)
(1, 6), r =64
D)
(-1, -6), r =8
185)
x2– 4x + 4 +(y – 3)2=81
A)
(-3, –2), r =81
B)
(–2, -3), r =81
C)
(2, 3), r =9
D)
(3, 2), r =9
186)
x2+y2+ 4x – 16y + 64 = 0
A)
(-2, 8), r =2
B)
(-8, 2), r =4
C)
(8, -2), r =2
D)
(2, -8), r =4
187)
x2+y2+ 14x + 18y + 114 = 0
A)
(7, 9), r =16
B)
(-7, –9), r =4
C)
(–9, -7), r =4
D)
(9, 7), r =16
188)
x2+y2+ 8x – 14y – 16 = 0
A)
(–4, 7), r =9
B)
(7, –4), r =9
C)
(-7, 4), r =81
D)
(4, -7), r =81
Graph the circle.
189)
x2+ y2=64
22
A)
B)
C)
D)
190)
(x – 1)2+ (y – 2)2=36
23
A)
B)
C)
D)
191)
x2+ (y – 3)2=16
24
A)
B)
C)
D)
192)
(x – 5)2+y2=9
25
A)
B)
C)
D)
193)
x2+ y2– 8x – 2y – 8 = 0
26
A)
B)
C)
D)
194)
x2+ y2+ 10x + 12y + 45 = 0
27
A)
B)
C)
D)
Give the equation for a circle with the given center and radius.
195)
Center at (-3, 10), radius 6
A)
(x – 3)2+ (y + 10)2=36
B)
(x + 3)2+ (y – 10)2=36
C)
(x + 10)2+ (y – 3)2=6
D)
(x – 10)2+ (y + 3)2=6
196)
Center at (6, 0), radius 8
A)
(x – 6)2+ y2=64
B)
x2+ (y + 6)2=8
C)
x2+ (y – 6)2=8
D)
(x + 6)2+ y2=64
197)
Center at (0, 8), radius 7
A)
(x – 8)2+ y2=49
B)
x2+ (y + 8)2=7
C)
(x + 8)2+ y2=49
D)
x2+ (y – 8)2=49
198)
Center at (10, -5), radius 19
A)
(x – 10)2+ (y + 5)2=19
B)
(x + 10)2+ (y – 5)2=19
C)
(x – 5)2+ (y + 10)2=361
D)
(x + 5)2+ (y – 10)2=361
199)
Center at (0, 2), radius 11
A)
(x – 2)2+ y2=121
B)
x2+ (y + 2)2=11
C)
x2+ (y – 2)2=11
D)
(x + 2)2+ y2=121
200)
Center at (10, 0), radius 7
A)
x2+ (y + 10)2=49
B)
x2+ (y – 10)2=49
C)
(x – 10)2+ y2=7
D)
(x + 10)2+ y2=7