AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024Rational Equations

Rational Equations — Unit test Answers

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Max can mow a lawn in 45 minutes. Jan takes twice as long to mow the same lawn. If they work together, the situation can be modeled by the following equation, where t is the number of minutes it would take to mow the lawn together.How long will it take Maxine and Jan to mow the lawn together?

Question illustration
A
30.0 minutes
B
45.0 minutes
C
67.5 minutes
D
135.0 minutes
2
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Blake simplified the expression to . Since this answer is incorrect, what was Blake’s mistake?

Question illustration
A
He added 5 to the exponent in the numerator instead of multiplying.
B
He subtracted the exponents in the parentheses instead of dividing.
C
He multiplied only the exponent in the numerator of the fraction by 5.
D
He divided the exponents in the parentheses instead of subtracting.
3

Which expression is equivalent to ?

Question illustration
A
StartFraction m minus 4 Over (m + 4) (m + 2) EndFraction
Option A
B
StartFraction (m + 4) (m + 2) Over m minus 4 EndFraction
Option B
C
StartFraction (m minus 4) (m + 2) Over m + 4 EndFraction
Option C
D
StartFraction m + 4 Over (m minus 4) (m + 2) EndFraction
Option D
4

Which expression is equivalent to ? Assume .

Question illustration
A
StartFraction 5 Over x Superscript 12 Baseline y Superscript 30 Baseline EndFraction
Option A
B
StartFraction 1 Over 5 x Superscript 8 Baseline y Superscript 13 Baseline EndFraction
Option B
C
StartFraction 5 Over x Superscript 4 Baseline y Superscript 7 Baseline EndFraction
Option C
D
StartFraction y Superscript 7 Baseline Over 5 x Superscript 4 Baseline EndFraction
Option D
5

What is the product?

Question illustration
A
StartFraction 4 n Over n + 1 EndFraction
Option A
B
StartFraction n Over n + 1 EndFraction
Option B
C
StartFraction 1 Over n + 1 EndFraction
Option C
D
StartFraction 4 Over n + 1 EndFraction
Option D
6

Which expression is equivalent to ? Assume .

Question illustration
A
StartFraction m Superscript 5 Baseline Over 162 n EndFraction
Option A
B
StartFraction 1 Over 2 m cubed n EndFraction
Option B
C
StartFraction 8 m Superscript 9 Baseline Over n Superscript 9 Baseline EndFraction
Option C
D
StartFraction 4 m Superscript 8 Baseline Over 3 n cubed EndFraction
Option D
7

Which expression is equivalent to ?

Question illustration
A
Negative StartFraction 1 Over 125 EndFraction
Option A
B
Negative one-fifth
Option B
C
StartFraction 1 Over 125 EndFraction
Option C
D
One-fifth
Option D
8

How can Ari simplify the following expression?

Question illustration
A
Write the numerator and denominator with a common denominator. Then divide the numerator by the denominator. To do this, multiply the numerator by the reciprocal of the denominator.
B
Write the numerator and denominator with a common denominator. Then divide the numerator by the denominator. To do this, multiply the numerators and multiply the denominators.
C
Divide the numerator and the denominator by a – 3. Then divide the numerator by the denominator.
D
Divide the numerator and the denominator by a – 3. Then simplify the numerator and simplify the denominator.
9

What is the difference?

Question illustration
A
StartFraction 2 (x + 6) Over (x + 4) (x minus 4) EndFraction
Option A
B
StartFraction negative 2 (x + 6) Over (x + 4) (x minus 4) EndFraction
Option B
C
StartFraction x minus 3 Over (x + 5) (x minus 4) EndFraction
Option C
D
StartFraction negative 2 (x minus 6) Over (x + 4) (x minus 4) EndFraction
Option D
10

How many extraneous solutions does the equation below have?

Question illustration
A
0
B
1
C
2
D
3
11

Which expression is equivalent to ?

Question illustration
A
StartFraction 1 Over 4 x EndFraction
Option A
B
StartFraction 4 Over x EndFraction
Option B
C
StartFraction 8 Over x EndFraction
Option C
D
StartFraction 128 Over x EndFraction
Option D
12

Using V = lwh, what is an expression for the volume of the following prism?

Question illustration
A
StartFraction 4 (d minus 2) Over 3 (d minus 3)(d minus 4) EndFraction
Option A
B
StartFraction 4 d minus 8 Over 3 (d minus 4) squared EndFraction
Option B
C
StartFraction 4 Over 3 d minus 12 EndFraction
Option C
D
StartFraction 1 Over 3 d minus 3 EndFraction
Option D
13

Which expression is equivalent to ? Assume .

Question illustration
A
StartFraction 8 m Superscript 7 Baseline n Superscript 6 Baseline Over 3 EndFraction
Option A
B
StartFraction 10 m Superscript 7 Baseline n Superscript 6 Baseline Over 3 EndFraction
Option B
C
StartFraction 8 m Superscript 16 Baseline n Superscript 12 Baseline Over 3 EndFraction
Option C
D
StartFraction m Superscript 4 Baseline n Superscript 6 Baseline Over 3 EndFraction
Option D
14

What is the solution to the equation ?

Question illustration
A
y = –4 and y = 4
B
y = 0
C
all real numbers
D
no solution
15

Ted can clear a football field of debris in 3 hours. Jacob can clear the same field in 2 hours. When they work together, the situation can be modeled by the equation, where t is the number of hours it would take to clear the field together.How long will it take Ted and Jacob to clear the field together?

Question illustration
A
12 minutes
B
50 minutes
C
1 hour 12 minutes
D
2 hours 30 minutes
16

What is the product of ?

Question illustration
A
StartFraction 1 Over 625 EndFraction
Option A
B
StartFraction 1 Over 25 EndFraction
Option B
C
25
D
125
17

Which expression is equivalent to the expression below?

Question illustration
A
StartFraction 1 Over (m + 4) (m + 3) EndFraction
Option A
B
StartFraction 1 Over (m minus 4) (m minus 3) EndFraction
Option B
C
StartFraction m minus 4 Over m minus 3 EndFraction
Option C
D
StartFraction m + 3 Over m + 4 EndFraction
Option D
18

Which expression is equivalent to the following complex fraction?

Question illustration
A
StartFraction negative 2 y + 5 x Over 3 x minus 2 y EndFraction
Option A
B
StartFraction 3 x minus 2 y Over negative 2 y + 5 x EndFraction
Option B
C
StartFraction x squared y squared Over (negative 2 y + 5 x) (3 x minus 2 y) EndFraction
Option C
D
StartFraction (negative 2 y + 5 x) (3 x minus 2 y) Over x squared y squared EndFraction
Option D
19

Mr. Knotts found the difference of the following expression. Which statement is true about Mr. Knotts’s work? Step 1: Step 2: Step 3: Step 4:

Question illustration
A
In step 1, he did not correctly factor the denominator.
B
In step 2, he did not use the correct common denominator.
C
In step 3, he did not distribute the negative sign when he subtracted.
D
In step 4, he did not correctly subtract the numerator.
20

Which expression is equivalent to ? Assume .

Question illustration
A
StartFraction x Superscript 10 Baseline y Superscript 14 Baseline Over 729 EndFraction
Option A
B
StartFraction x Superscript 22 Baseline Over 18 y Superscript 46 Baseline EndFraction
Option B
C
StartFraction 729 Over x Superscript 10 Baseline y Superscript 14 Baseline EndFraction
Option C
D
StartFraction 18 y Superscript 46 Baseline Over x Superscript 22 Baseline EndFraction
Option D

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