Solve the equation.
248)
3x – 2 +11 + x = – 1
248)
A)
{5}
B)
{0}
C)
–5
2
D)
Solve the problem.
249)
The formula v =20L can be used to estimate the speed of a car, v, in miles per hour, based on the
length, L, in feet, of its skid marks upon sudden braking on a dry asphalt road. If a car is involved
in an accident and its skid marks measure 80 feet, at what estimated speed was the car traveling
when it applied its brakes just prior to the accident?
249)
A)
45 mph
B)
50 mph
C)
35 mph
D)
40 mph
Find the perimeter or area of the figure as indicated. Express your answer in simplified radical form.
250)
Find the perimeter of the rectangle.
252 cm
448 cm
250)
A)
28 14 cm
B)
14 7 cm
C)
28 7 cm
D)
196 cm
Find the square root if it is a real number, or state that the expression is not a real number.
251)
1
64
251)
A)
8
B)
64
C)
1
8
D)
1
4096
Rewrite the expression with a positive rational exponent. Simplify, if possible.
252)
125–1/3
252)
A)
1
5
B)
1
125
C)
–5
D)
–1
5
Simplify the expression. Assume that variables can represent any real number.
253)
3
108x5y7
253)
A)
3xy234xy
B)
3xy23
4x2y
C)
4xy233xy
D)
3x3y63
4x2y
Find the cube root.
254)
327
254)
A)
5
B)
3
C)
±3
D)
9
Divide and simplify to the form a +
bi.
255)
5– 4i
8+ 9i
255)
A)
4
145 –77
145i
B)
–4
17 +77
17 i
C)
–76
17 +77
17 i
D)
76
145 –13
145i
Find the indicated function value for the function.
256)
Evaluate m(x) = – 3125x – 1 for m(0)
256)
A)
1
B)
not a real number
C)
–4
D)
–1
Simplify by factoring. Assume that any variable in a radicand represents a positive real number.
257)
x13
257)
A)
x6x
B)
13 x
C)
11 x2
D)
x2x11
Rationalize numerator.
258)
x+ 4 y
5 x
258)
A)
x –16y
5x + 20 xy
B)
x +16y
5x + 20 xy
C)
x –16y
5x – 20 xy
D)
x –4y
5x – 20 xy
Find the perimeter or area of the figure as indicated. Express your answer in simplified radical form.
259)
Find the perimeter of the triangle.
27 m 75 m
180 m
259)
A)
(8 3 +6 5) m
B)
(45 +6 5) m
C)
14 15 m
D)
(27 +75 +180) m
A
Solve the formula for the specified variable.
260)
r =2A
for
260)
A)
=2A
r2
B)
=2a
R
2
C)
=r2
2A
D)
=2A
r
Rationalize numerator.
261)
2+5
2–5
261)
A)
9
–1– 4 5
B)
–1
9+ 4 5
C)
1
D)
–1
9– 4 5
Solve the equation.
262)
2x + 5 –x – 2 = 3
262)
A)
{2, 38}
B)
{2}
C)
{3, 8}
D)
{–2}
Multiply and simplify. Assume that all variables represent positive real numbers.
263)
(6 5 + 8)2
263)
A)
244 – 96 5
B)
116 + 96 5
C)
188 + 96 5
D)
244 + 96 5
Find the x–intercept(s) of the graph of the function without graphing the function.
264)
f(x) =2x +21 –2x –3
264)
A)
2
B)
16
C)
no x–intercepts
D)
4
64
Simplify by factoring. Assume that any variable in a radicand represents a positive real number.
265)
4243x11
265)
A)
3x 43x3
B)
3x243x
C)
3x243x3
D)
3x24x3
Divide and simplify to the form a +
bi.
266)
9– 6i
5+ 2i
266)
A)
11
7–16
7i
B)
19
7–16
7i
C)
33
29 –48
29 i
D)
57
29 +12
29 i
267)
1 + i
1 – i
267)
A)
i
B)
Undefined
C)
–2 + 2i
D)
2 + 2i
Write in terms of i.
268)
–36
268)
A)
i 6
B)
6i
C)
–6i
D)
±6
Find each product. Write the result in the form a +
bi.
269)
(9 – 6i)(7+ 4i)
269)
A)
–24i2– 6i + 63
B)
87 + 6i
C)
87 – 6i
D)
39 – 78i
65
C
Find the function value indicated for the function. If necessary, round to two decimal places. If the function value is not a
real number and does not exist, state so.
270)
Evaluate f(x) = – x +32 for f(–4)
270)
A)
6
B)
not a real number
C)
2.45
D)
5.29
Perform the indicated operation and, if possible, simplify. Assume that all variables represent positive real numbers.
271)
32x2·33y
271)
A)
23x2y
B)
3x 3y
C)
x36y
D)
36x2y
Find the square root if it is a real number, or state that the expression is not a real number.
272)
–0.09
272)
A)
not a real number
B)
–0.3
C)
0.03
D)
–0.03
Solve.
273)
Find the area of the square. Simplify the expression.
2 7 +11 ft
2 7 +11 ft
273)
A)
(905 +477 ) sq ft
B)
17 sq ft
C)
(39 +277) sq ft
D)
(39 +477) sq ft
A
Simplify the expression.
274)
4x8
274)
A)
2x8
B)
4x4
C)
2x
D)
2x4
Simplify by factoring. Assume that any variable in a radicand represents a positive real number.
275)
45x3
275)
A)
3 5x
B)
3x25x
C)
x45x
D)
3x 5x
Solve the problem.
276)
It has been found that the less income people have, the more likely they are to report that their
health is fair or poor. The function f(x) = – 4.4 x+ 38 models the percentage of Americans reporting
fair or poor health, f(x), in terms of annual income, x, in thousands of dollars. According to the
model, what annual income corresponds to 7% reporting fair or poor health? Round to the nearest
thousand dollars.
276)
A)
approximately $54 thousand
B)
approximately $26 thousand
C)
approximately $27 thousand
D)
approximately $50 thousand
Find each product. Write the result in the form a +
bi.
277)
3i(3– 5i)
277)
A)
9i – 15
B)
9i – 15i2
C)
9i + 15i2
D)
15 + 9i
Multiply and simplify. Assume that all variables represent positive real numbers.
278)
(12 + 5)( 12 – 5)
278)
A)
–13
B)
12 – 2 5
C)
37
D)
7
67
Add or subtract as indicated. You will need to simplify terms to identify like radicals.
279)
212x3+3x
279)
A)
(2x + 1) 3x
B)
5 x
C)
(4x + 1) 3x
D)
4x 6x
Multiply and simplify. Assume that all variables represent positive real numbers.
280)
(6 –x)(3–x)
280)
A)
18 –9 x – x
B)
18 –8x
C)
18 –9 x + x
D)
18 –8 x
Add or subtract as indicated.
281)
3 2 + 5 11 –2 2 – 8 11
281)
A)
2– 3 11
B)
5 2 – 3 11
C)
2– 13 11
D)
–213
Simplify by factoring.
282)
27x
282)
A)
3 3x
B)
9 x
C)
3x 3
D)
9x
Multiply and simplify. Assume that all variables represent positive real numbers.
283)
3x (3128x2–3x)
283)
A)
4x(x 32– 1)
B)
4x 32
C)
4x 32–
3x2
D)
64x –3x
Divide and, if possible, simplify.
284)
6xy3
2x
284)
A)
y23xy
B)
y23y
C)
y 3y
D)
y26y
Evaluate.
285)
i8
285)
A)
–1
B)
i
C)
–i
D)
1
Rewrite the expression with a positive rational exponent. Simplify, if possible.
286)
9–3/2
286)
A)
1
9
B)
–27
2
C)
1
27
D)
–1
27
Divide and, if possible, simplify.
287)
3270x4y4
310x2y
287)
A)
3xy 3x
B)
10y3x2
C)
93xy2
D)
3y 3x2
Solve the problem.
288)
The distance d in miles that can be seen on the surface of the ocean is given by d =1.4h1/2, where h
is the height in feet above the surface. How high would a platform have to be to see a distance of
20.5 miles? Round to the nearest foot.
288)
A)
146 ft
B)
420 ft
C)
214 ft
D)
588 ft
Divide and, if possible, simplify.
289)
24
6
289)
A)
2 6
B)
2
6
C)
6
D)
2
290)
x2+ 14x + 45
x + 5
290)
A)
x + 9
B)
x – 9
C)
x + 9
D)
x – 9
Use radical notation to rewrite the expression. Simplify, if possible.
291)
(–125)2/3
291)
A)
–25
B)
–1
5
C)
25
D)
–5
Simplify the expression.
292)
52
292)
A)
25
B)
10
C)
5
D)
5
2
Solve the equation.
293)
7x + 3 =4
293)
A)
1
7
B)
1
C)
19
7
D)
13
7
Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers.
294)
(10x3/4)4
x1/8
294)
A)
10,000x6
B)
1000x9/8
C)
10,000x23/8
D)
10x23/8
295)
(y–7/8)–1/5
295)
A)
y7/40
B)
1
y43/40
C)
y43/40
D)
1
y7/40
Add or subtract as indicated. You will need to simplify terms to identify like radicals.
296)
53x10y2– 3 3xy2
296)
A)
5x3– 3 3xy2
B)
( 5x – 3)3xy2
C)
( 2x3)3xy2
D)
( 5x3– 3)3xy2
Divide and simplify to the form a +
bi.
297)
6+ 2i
4– 2i
297)
A)
1
12 +1
12 i
B)
28 + 4i
C)
7
3+1
12 i
D)
1+ 1i
Find the indicated root, or state that the expression is not a real number.
298)
–4256
298)
A)
–4
B)
not a real number
C)
–16
D)
4
Use radical notation to rewrite the expression. Simplify, if possible.
299)
(4xy5)1/6
299)
A)
1
4xy5
B)
y64x
C)
64xy5
D)
1
64xy5
D
Solve.
300)
The function f(x) = 0.07x3/2 models the duration of a storm, f(x), in hours, in terms of the diameter
of the storm, x, in miles. Use a calculator to determine the duration of a storm with a diameter of 12
miles. Round to the nearest hundredth.
300)
A)
0.77 hr
B)
41.57 hr
C)
2.91 hr
D)
0.24 hr
Rewrite the expression with a rational exponent.
301)
362
301)
A)
1
3·62
B)
623
C)
621/3
D)
1
623
Simplify by factoring.
302)
54
302)
A)
18
B)
3 6
C)
7
D)
6 3
Rewrite the expression with a positive rational exponent. Simplify, if possible.
303)
(4xy)–4/5
303)
A)
–1
(4xy)4/5
B)
1
( 4xy)5/4
C)
1
(4xy)4/5
D)
1
4xy4/5
Find the indicated function value for the function.
304)
Evaluate g(x) = – 33x – 4 for g(4)
304)
A)
3
B)
2
C)
32
D)
–2
Solve the equation.
305)
(4x + 3)1/3 + 4 = – 6
305)
A)
–1003
4
B)
C)
–33
4
D)
97
4
Write in terms of i.
306)
– – 236
306)
A)
–259
B)
2i 59
C)
259
D)
–2i 59
Use rational exponents to simplify the radical. If rational exponents appear after simplifying, write the answer in radical
notation.
307)
6x4
307)
A)
x2
B)
x
C)
3x2
D)
3x
Solve the radical equation.
308)
2x + 3 –x + 1 = 1
308)
A)
{–3, –1}
B)
{3}
C)
{3, –1}
D)
Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers.
309)
x1/3
x5/6
309)
A)
x1/2
B)
x2/5
C)
x7/6
D)
1
x1/2
Rewrite the expression with a rational exponent.
310)
4x11
310)
A)
x7
B)
x11/4
C)
x4/11
D)
x11
4
Multiply and simplify. Assume that all variables represent positive real numbers.
311)
(3 +3)(4+4 3)
311)
A)
24 +16 3
B)
24 +8 3
C)
12 +20 3
D)
72
Add or subtract as indicated.
312)
6 5 +9 5 –13
312)
A)
–3 5 –13
B)
28 5
C)
2 5
D)
15 5–13
Find the function value indicated for the function. If necessary, round to two decimal places. If the function value is not a
real number and does not exist, state so.
313)
p(x) =(x +5)2 for p(2)
313)
A)
49
B)
29
C)
not a real number
D)
7
75
B