Answers SS4 PGCPS ALGEBRA 2 OC SUMMER 2027 - 793033Radical Equations and Extraneous Roots

Unit Test Answers

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The orbital period, P, of a planet and the planet’s distance from the sun, a, in astronomical units is related by the formula . If Saturn’s orbital period is 29.5 years, what is its distance from the sun?

9.5 AU

19.7 AU

44.3 AU

160.2 AU

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Which equation is the inverse of y = 9x2 – 4?

y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 9 EndFraction

y = plus-or-minus StartRoot StartFraction x Over 9 EndFraction + 4 EndRoot

y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 3 EndFraction

y = StartFraction plus-or-minus StartRoot x EndRoot Over 3 EndFraction + two-thirds

What is the simplified form of the following expression?

6 StartRoot 2 EndRoot

18 StartRoot 2 EndRoot

30 StartRoot 2 EndRoot

36 StartRoot 2 EndRoot

What is the solution to the equation ?

w = –8

w = –5

w = 5

w = 8

Which equation is the inverse of ?

y = one-sixth x squared minus four-thirds x + StartFraction 43 Over 9 EndFraction

y = 4 plus-or-minus StartRoot 6 x minus StartFraction 34 Over 3 EndFraction EndRoot

y = negative 4 plus-or-minus StartRoot 6 x minus StartFraction 34 Over 3 EndFraction EndRoot

negative (x minus 4) squared minus two-thirds = negative 6 y + 12

The speed that a tsunami can travel is modeled by the equation , where S is the speed in kilometers per hour and d is the average depth of the water in kilometers. What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour?

0.32 km

0.75 km

1.12 km

3.17 km

Which of the following describes the graph of compared to the parent cube root function?

stretched by a factor of 2 and translated 64 units right and 5 units down

stretched by a factor of 8 and translated 8 units right and 5 units down

stretched by a factor of 2 and translated 8 units right and 5 units down

stretched by a factor of 8 and translated 64 units right and 5 units down

What is the following simplified product? Assume

10 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot + x squared StartRoot 15 x EndRoot

11 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus x Superscript 4 Baseline StartRoot 75 EndRoot + x squared StartRoot 15 EndRoot

10 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot minus x squared StartRoot 15 EndRoot

11 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot minus x cubed StartRoot 15 x EndRoot

What is the following quotient?

StartFraction StartRoot 3 EndRoot Over 4 EndFraction

StartFraction 1 + StartRoot 3 EndRoot Over 4 EndFraction

StartFraction 1 minus StartRoot 3 EndRoot Over 4 EndFraction

StartFraction negative 1 + StartRoot 3 EndRoot Over 2 EndFraction

Which expression is equivalent to ?

8y10

8y50

32y10

32y50

Which function is undefined for x = 0?

y = RootIndex 3 StartRoot x minus 2 EndRoot

y = StartRoot x minus 2 EndRoot

y = RootIndex 3 StartRoot x + 2 EndRoot

y = StartRoot x + 2 EndRoot

Which expression is equivalent to ?

8|a3|

8a6

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mc008-3.jpg

Which equation results from isolating a radical term and squaring both sides of the equation for the equation ?

mc012-2.jpg

mc012-3.jpg

mc012-4.jpg

mc012-5.jpg

Mario invested $6,000 in an account that pays 5% annual interest compounded annually. Using the formula A = P(1 + r)t, what is the approximate value of the account after 2.5 years?

$6,075

$6,118

$6,456

$6,778

Which expression is equivalent to ?

StartFraction RootIndex 4 StartRoot 200 EndRoot Over 2 EndFraction

StartFraction RootIndex 4 StartRoot 20 EndRoot Over 2 EndFraction

StartFraction 2 StartRoot 5 EndRoot Over 5 EndFraction

StartFraction 100 Over 8 EndFraction

Which expression is equivalent to ?

c3d4

c6d9

c3d4

c6d9

What is the following product?

x squared (RootIndex 3 StartRoot 28 x squared EndRoot)

x Superscript 5 Baseline (RootIndex 3 StartRoot 28 x EndRoot)

4 x squared (RootIndex 3 StartRoot 3 x squared EndRoot)

4 x Superscript 5 Baseline (RootIndex 3 StartRoot 3 x EndRoot)

What is the following sum?

7 x (RootIndex 6 StartRoot x squared y EndRoot)

7 x squared (RootIndex 6 StartRoot x y squared EndRoot)

7 x squared (RootIndex 3 StartRoot x y squared EndRoot)

7 x (RootIndex 3 StartRoot x squared y EndRoot)

Kaylib’s eye-level height is 48 ft above sea level, and Addison’s eye-level height is ft above sea level. How much farther can Addison 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.