AnswersFL-1200330-Algebra 2 CRModeling with Rational Functions

Modeling with Rational Functions — Unit test Answers

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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.
2
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Dimitri is solving the equation x2 – 10x = 21. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?

A
0
B
4
C
25
D
100
3

The product of two consecutive integers is 272. Which quadratic equation can be used to find x, the smaller number?

A
x2 + 1 = 272
B
x2 − 1 = 272
C
x2 + x − 272 = 0
D
x2 + x + 272 = 0
4

For what values of m does the graph of y = mx2 – 5x – 2 have no x-intercepts?

A
m greater-than negative StartFraction 25 Over 8 EndFraction
Option A
B
m less-than negative StartFraction 25 Over 8 EndFraction
Option B
C
m less-than StartFraction 25 Over 8 EndFraction
Option C
D
m greater-than StartFraction 25 Over 8 EndFraction
Option D
5

Solve for in the equation .

Question illustration
A
x = negative 11 plus-or-minus StartFraction 25 Over 2 EndFraction
Option A
B
x = negative eleven-halves plus-or-minus StartFraction 25 Over 2 EndFraction
Option B
C
x = negative 11 plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
Option C
D
x = negative eleven-halves plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
Option D
6

For which value of m does the graph of y = 18x2 + mx + 2 have exactly one x-intercept?

A
0
B
9
C
12
D
16
7

Which point shows the location of 5 – 2i on the complex plane below?

Question illustration
A
point A
B
point B
C
point C
D
point D
8

What are the values of x in the equation x2 – 6x + 9 = 25?

A
x = –2 or x = 8
B
x = –1 or x = –11
C
x = 1 or x = 11
D
x = 2 or x = –8
9

If the discriminant of a quadratic equation is 4, which statement describes the roots?

A
There are two complex roots.
B
There are two real roots.
C
There is one real root.
D
There is one complex root.
10

Tamika builds a wooden skateboard ramp. The ramp measures 63 centimeters, and the length of its horizontal base is 60 centimeters, as shown.In centimeters, what is the approximate height of the ramp? Round the answer to the nearest tenth of a centimeter.

Question illustration
Answer not available
11

Using the quadratic formula to solve 11x2 – 4x = 1, what are the values of x?

A
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 15 EndRoot Over 11 EndFraction
Option A
B
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction 2 StartRoot 15 EndRoot Over 11 EndFraction
Option B
C
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot Over 11 EndFraction
Option C
D
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot i Over 11 EndFraction
Option D
13

Which statements are true about the unknown side length in this right triangle? Check all that apply.

Question illustration
A
The equation can be used to find the unknown length.
Option A
B
The equation can be used to find the unknown length.
Option B
C
The equation can be used to find the unknown length.
Option C
D
The length of the unknown leg is meters.
Option D
E
The length of the unknown leg is 7 meters.
14

Which rule can be used to describe the growth of the y-values of the function over each interval from to ?

Question illustration
A
add 12
B
multiply by 12
C
add 1, then 12, then 144
D
multiply by 1, then by 12, then by 144
15

An architect designs a diagonal path across a rectangular patio. The path is 29 meters long. The width of the patio is x meters, and the length of the path is 5 meters more than the width.

Question illustration
A
0.5(x)(x + 5) = 29
B
0.5(x)(x + 5) = 841
C
x2 + (x + 5)2 = 29
D
x2 + (x + 5)2 = 841
16

What is the value of i 20+1?

A
1
B
–1
C
–i
D
i
17

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
18

Two sandboxes with the same area are shown.The equation represents the area of Sandbox 2 in terms of its width.

Question illustration
A
2.72 meters
B
3.06 meters
C
9.16 meters
D
10.18 meters
19

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
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
20

Which pair of complex numbers has a real-number product?

A
(1 + 3i)(6i)
B
(1 + 3i)(2 – 3i)
C
(1 + 3i)(1 – 3i)
D
(1 + 3i)(3i)
21

The diagram shows two different nature trails in a state park. The solid line shows the Dogwood Trail. The dashed line shows the Elm Trail.Which of the following statements are true about the lengths of the trails? Check all that apply.

Question illustration
A
The total length of the Dogwood Trail is 16 kilometers.
B
The total length of the Dogwood Trail is 24 kilometers.
C
The Elm Trail is longer than the Dogwood Trail.
D
The difference between the lengths of the trails is 2 kilometers.
E
The difference between the lengths of the trails is 6 kilometers.

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