AnswersAlgebra II - MA3111 A-CRMultiplying and Dividing Rational Expressions

Multiplying and Dividing Rational Expressions — Unit test Answers

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Haji rows his canoe 10 mph in still water. He noticed one day that he could row 4 miles upstream in the same amount of time he could row 6 miles downstream. What was the approximate speed of the current that day?

A
2.0 mph
B
3.3 mph
C
5.0 mph
D
10.0 mph
2
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What is the product?

Question illustration
A
StartFraction k + 1 Over k squared EndFraction
Option A
B
StartFraction k minus 1 Over k squared EndFraction
Option B
C
StartFraction negative 1 Over k EndFraction
Option C
D
StartFraction 1 Over k EndFraction
Option D
3

Which is the simplified form of ? Assume .

Question illustration
A
StartFraction b cubed Over 8 a Superscript 18 Baseline EndFraction
Option A
B
StartFraction b squared Over 8 a Superscript 45 Baseline EndFraction
Option B
C
StartFraction a Superscript 6 Baseline Over 4 b EndFraction
Option C
D
StartFraction 2 a Superscript 6 Baseline Over b Superscript 5 Baseline EndFraction
Option D
4

The table below shows how the number of hours needed to fill a pool depends on the flow rate of the hoses used to fill it.Flow rate, x(gal/hr)Time, y(hours)60300454003650030600How long will it take to fill the pool if two hoses are used, one that fills at a rate of 40 gallons per hour and one that fills at a rate of 60 gallons per hour?

A
100 hours
B
150 hours
C
180 hours
D
200 hours
5

Riley makes a mistake in step 2 while doing her homework. What was her mistake? Step 1: Step 2: Step 3: Step 4:

Question illustration
A
She added the two fractions incorrectly.
B
She used the wrong common denominator.
C
She did not distribute the negative correctly.
D
She did not multiply the first fraction by a factor.
6

Which expression is equivalent to the following complex fraction?

Question illustration
A
StartFraction y + x Over y minus x EndFraction
Option A
B
StartFraction (y minus x) (y + x) Over x squared y squared EndFraction
Option B
C
StartFraction x squared y squared Over (y + x) (y + x) EndFraction
Option C
D
StartFraction y minus x Over y + x EndFraction
Option D
7

Which expression is equivalent to ? Assume .

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
8

A basketball player’s free-throw percentage is the ratio of the number of successful shots made to the number of shots attempted. A basketball player has made 13 of the first 20 free throws she has attempted this season. Which rational expression can be used to find the free throw percentage for the season if she successfully makes her next x free-throw attempts?

A
mc017-1.jpg
Option A
B
mc017-2.jpg
Option B
C
mc017-3.jpg
Option C
D
mc017-4.jpg
Option D
9

A chemist has 500 mL of a 30% acid solution. She adds x milliliters of a 10% acid solution. Which statement is true about the graph of the function that represents the concentration of the final solution?

A
The horizontal asymptote y = 30 means that the final concentration will always be less than 30%.
B
The horizontal asymptote y = 10 means that the final concentration will always be greater than 10%.
C
The vertical asymptote x = 500 means that the volume of the solution will always be greater than 500 mL.
D
The vertical asymptote x = 0 means that the volume of the solution will always be greater than 0 mL.
10

Naomi wants to take yoga classes. She can take classes at the high school for a one-time fee of $20 plus $10 per class. She can join the local gym for $50 and take classes for $5 per class. Which statement is true about the average cost for the two options?

A
The high school option costs less per class for six classes.
B
The gym option costs less per class for six classes.
C
The high school option costs less per class for seven classes.
D
The gym option costs less per class for seven classes.
11

Which expression is equivalent to the following complex fraction?

Question illustration
A
StartFraction x minus 3 Over x EndFraction
Option A
B
StartFraction x + 3 Over 1 EndFraction
Option B
C
StartFraction x + 3 Over x EndFraction
Option C
D
StartFraction x Over x + 3 EndFraction
Option D
12

What is the quotient in simplest form? Assume .

Question illustration
A
Negative StartFraction m Superscript 12 Baseline n Superscript 6 Baseline Over 2 EndFraction
Option A
B
Negative StartFraction m Superscript 27 Baseline n Superscript 8 Baseline Over 2 EndFraction
Option B
C
6 m Superscript 12 Baseline n Superscript 6 Baseline
Option C
D
8 m Superscript 12 Baseline n Superscript 6 Baseline
Option D
13

What is the solution to the equation ?

Question illustration
m
m = –4
m
m = –2
m
m = 2
m
m = 4
14

Mrs. Cho wrote the following problem on the board.Problem: Step 1: Step 2: Step 3: What should Mrs. Cho do next?

Question illustration
A
Find a common denominator for the two fractions.
B
Divide the numerator and denominator of the first fraction by x2 and y.
C
Multiply the numerators, multiply the denominators, and then simplify.
D
Multiply the first fraction by the reciprocal of the second fraction.
15

What is the quotient in simplified form? Assume .

Question illustration
A
Negative StartFraction 4 a Superscript 12 Baseline b Superscript 8 Baseline Over 5 EndFraction
Option A
B
Negative StartFraction 4 a Superscript 32 Baseline b Superscript 5 Baseline Over 5 EndFraction
Option B
C
StartFraction a Superscript 12 Baseline b Superscript 8 Baseline Over 80 EndFraction
Option C
D
StartFraction a Superscript 32 Baseline b Superscript 5 Baseline Over 80 EndFraction
Option D

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