AnswersFL-1200700-Mathematics for College Algebra MISRadical Equations and Extraneous Roots

Radical Equations and Extraneous Roots — Unit test Answers

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1
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Which function has a domain of and a range of ?

Question illustration
A
y = StartRoot x minus 5 EndRoot + 3
Option A
B
y = StartRoot x + 5 EndRoot minus 3
Option B
C
y = negative StartRoot x minus 5 EndRoot + 3
Option C
D
y = negative StartRoot x + 5 EndRoot minus 3
Option D
2
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What values of c and d make the equation true? Assume and

Question illustration
A
c = 1, d = 3
B
c = 1, d = 9
C
c = 2, d = 8
D
c = 2, d = 9
3

Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, an absolute value curve curves up and to the right in quadrant 4 and starts at y = negative 1.
Option A
B
On a coordinate plane, an absolute value curve curves up and to the right in quadrant 4 and starts at y = 1.
Option B
C
On a coordinate plane, an absolute value curve opens down and to the left in quadrant 2 and starts at y = 1.
Option C
D
On a coordinate plane, an absolute value curve opens down and to the left in quadrant 2 and starts at y = negative 1.
Option D
5

The formula gives the length of the side, s, of a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 480 square meters than a cube with the surface area of 270 square meters?

Question illustration
A
m
Option A
B
m
Option B
C
m
Option C
D
m
Option D
6

What is the following simplified product? Assume

Question illustration
A
3 x StartRoot 6 x EndRoot + x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared + 8 x Superscript 5 Baseline StartRoot 10 x EndRoot
Option A
B
3 x StartRoot 6 x EndRoot + x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared StartRoot 2 EndRoot + 8 x Superscript 5 Baseline StartRoot 10 EndRoot
Option B
C
3 x StartRoot 6 x EndRoot minus x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared StartRoot 2 EndRoot minus 8 x Superscript 5 Baseline StartRoot 10 EndRoot
Option C
D
3 x StartRoot 6 x EndRoot minus x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared StartRoot 2 x EndRoot minus 8 x Superscript 5 Baseline StartRoot 10 x EndRoot
Option D
7

The formula relates the time, T, in seconds for a pendulum with the length, L, in feet, to make one full swing back and forth. What is the length of a pendulum that makes one full swing in 2.2 seconds? Use 3.14 for .

Question illustration
A
2 feet
B
4 feet
C
11 feet
D
19 feet
8

Which function represents the following graph?

Question illustration
A
y = StartRoot x minus 3 EndRoot + 3
Option A
B
y = StartRoot x + 3 EndRoot + 3
Option B
C
y = RootIndex 3 StartRoot x minus 3 EndRoot + 3
Option C
D
y = RootIndex 3 StartRoot x + 3 EndRoot + 3
Option D
9

Which expression is equivalent to ? Assume x 0.

Question illustration
A
StartFraction x cubed StartRoot 2 EndRoot Over 2 EndFraction
Option A
B
StartFraction 4 StartRoot 2 EndRoot Over x cubed EndFraction
Option B
C
StartFraction StartRoot 2 EndRoot Over 2 x cubed EndFraction
Option C
D
StartFraction 2 StartRoot 2 EndRoot Over x cubed EndFraction
Option D
10

Which expression is equivalent to ?

Question illustration
A
StartFraction x Superscript one-half baseline Over y z squared EndFraction
Option A
B
StartFraction x Superscript one-half baseline Over y Superscript one-fourth Baseline z squared EndFraction
Option B
C
StartFraction y Superscript one-half Baseline Over x z squared EndFraction
Option C
D
StartFraction x z squared Over y Superscript one-half EndFraction
Option D
11

If x is a positive integer, which expression is equivalent to ? Assume .

Question illustration
A
RootIndex 20 StartRoot x Superscript 7 EndRoot
Option A
B
x (RootIndex 20 StartRoot x cubed EndRoot)
Option B
C
StartFraction RootIndex 6 StartRoot x Superscript 5 Baseline EndRoot Over x squared EndFraction
Option C
D
x cubed (RootIndex 6 StartRoot x Superscript 5 Baseline EndRoot)
Option D
12

Doug bought a new car for $25,000. He estimates his car will depreciate, or lose value, at a rate of 20% per year. The value of his car is modeled by the equation V = P(1 – r)t, where V is the value of the car, P is the price he paid, r is the annual rate of depreciation, and t is the number of years he has owned the car. According to the model, what will be the approximate value of his car after years?

Question illustration
A
$2,500
B
$9,159
C
$22,827
D
$23,791
13

What is the simplified form of the following expression? Assume .

Question illustration
A
StartFraction RootIndex 5 StartRoot 10 x EndRoot Over 3 x EndFraction
Option A
B
StartFraction RootIndex 5 StartRoot 30 EndRoot Over 3 x EndFraction
Option B
C
StartFraction RootIndex 5 StartRoot 120 x cubed EndRoot Over 3 x EndFraction
Option C
D
StartFraction RootIndex 5 StartRoot 810 x cubed EndRoot Over 3 x EndFraction
Option D
14

The equation shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If planet Y is k times the mean distance from the sun as planet X, by what factor is the orbital period increased?

Question illustration
A
k Superscript one-third
Option A
B
k Superscript one-half
Option B
C
k Superscript two-thirds
Option C
D
k Superscript three-halves
Option D
15

Which expression is equivalent to ?

Question illustration
A
Negative 4 x Superscript 4 Baseline y Superscript 6
Option A
B
Negative 8 x Superscript 4 Baseline y Superscript 6
Option B
C
StartFraction 4 x Superscript 4 Baseline Over y Superscript 6 EndFraction
Option C
D
StartFraction 8 x Superscript 4 Baseline Over y Superscript 6 Baseline EndFraction
Option D
16

Pam’s eye-level height is 324 ft above sea level, and Adam’s eye-level height is 400 ft above sea level. How much farther can Adam see to the horizon? Use the formula , with d being the distance they can see in miles and h being their eye-level height in feet.

Question illustration
A
1 mi
B
mi
Option B
C
19 mi
D
mi
Option D
17

What is the simplified form of the following expression?

Question illustration
A
StartRoot 3 EndRoot
Option A
B
9 StartRoot 3 EndRoot
Option B
C
11 StartRoot 3 EndRoot
Option C
D
15 StartRoot 3 EndRoot
Option D
18

What is the following sum?

Question illustration
A
6 b squared (RootIndex 3 StartRoot 2 a EndRoot)
Option A
B
12 b squared (RootIndex 3 StartRoot 2 a EndRoot
Option B
C
6 b squared (RootIndex 6 StartRoot 2 a EndRoot)
Option C
D
12 b squared (RootIndex 6 StartRoot 2 a EndRoot)
Option D
19

Which expression is equivalent to ? Assume and .

Question illustration
A
StartFraction a cubed b (RootIndex 3 StartRoot 15 b squared EndRoot) Over 2 c cubed EndFraction
Option A
B
StartFraction b (RootIndex 3 StartRoot 15 b EndRoot) Over 2 a squared c cubed EndFraction
Option B
C
StartFraction a cubed b (RootIndex 3 StartRoot 15 b squared EndRoot) Over 6 c cubed EndFraction
Option C
D
StartFraction b (RootIndex 3 StartRoot 15 b EndRoot) Over 2 a c EndFraction
Option D

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