AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S1_2024Multiplying Radicals

Multiplying Radicals — Test Answers

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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
2
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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
3

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
4

What is the solution of ?

Question illustration
A
x = –10
B
x = 3
C
x = –10 or x = 3
D
no solution
5

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
6

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
7

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
8

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
9

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
10

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
11

Which graph represents ?

Question illustration
A
On a coordinate plane, a cubic function has an inflection point at (0, negative 2).
Option A
B
On a coordinate plane, a cubic function has an inflection point at (negative 2, 0)
Option B
C
On a coordinate plane, a cubic function has an inflection point at (0, 2).
Option C
D
On a coordinate plane, a cubic function has an inflection point at (2, 0).
Option D
12

What is the following quotient?

Question illustration
A
2 (RootIndex 3 StartRoot 3 EndRoot) minus RootIndex 3 StartRoot 18 EndRoot
Option A
B
2 (RootIndex 3 StartRoot 3 EndRoot) minus 3 (RootIndex 3 StartRoot 2 EndRoot)
Option B
C
3 (RootIndex 3 StartRoot 3 EndRoot) minus RootIndex 3 StartRoot 18 EndRoot
Option C
D
3 (RootIndex 3 StartRoot 3 EndRoot) minus 3 (RootIndex 3 StartRoot 2 EndRoot)
Option D
13

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
14

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
15

What is the following product? Assume

Question illustration
A
x StartRoot x EndRoot
Option A
B
RootIndex 12 StartRoot x Superscript 5 EndRoot
Option B
C
x (RootIndex 12 StartRoot x Superscript 5 EndRoot)
Option C
D
x6

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