AnswersAZ-Common Core Algebra II ARational Inequalities

Graphing Exponential Functions Answers

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Which expression represents the correct form for the quotient and remainder, written as partial fractions, of ?

Question illustration
A
A + StartFraction B Over x + 3 EndFraction + StartFraction C Over 2 x minus 7 EndFraction
Option A
B
A + StartFraction B x + C Over x + 3 EndFraction + StartFraction D x + E Over 2 x minus 7 EndFraction
Option B
C
A x + B + StartFraction C Over x + 3 EndFraction + StartFraction D Over 2 x minus 7 EndFraction
Option C
D
A x + B + StartFraction C x + D Over x + 3 EndFraction + StartFraction E x + F Over 2 x minus 7 EndFraction
Option D
2
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What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

Question illustration
A
–6, 6
B
–4, 1, 3
C
–3, –1, 4
D
1, 3
3

Review the work showing the first few steps in writing a partial fraction decomposition.x3 + 8x – 3 = (Ax + B)(x2 + 5) + Cx + Dx3 + 8x – 3 = Ax3 + 5Ax + Bx2 + 5B + Cx + D

Question illustration
A
A = 0; B = 1; C = –3; D = 3
B
A = 0; B = 1; C = 3; D = –3
C
A = 1; B = 0; C = –3; D = 3
D
A = 1; B = 0; C = 3; D = –3
4

What is the solution to x 3 + 4x 2 > x + 4?

A
–4 < x < –1
B
–4 < x < 1
C
–4 1
D
x < –4 or –1 < x < 1
5

What is the solution of ?

Question illustration
A
or x > 4
Option A
B
or x > 4
Option B
C
mc008-4.jpg
Option C
D
mc008-5.jpg
Option D
6

Carlos graphed the system of equations that can be used to solve .What are the roots of the polynomial equation?

Question illustration
A
–3, –2, 3
B
–3, 2
C
18, 32
D
18, 32, 66
7

How many integers satisfy the inequality (x 2 – 4)(x 2 – 10) < 0?

A
none
B
two
C
four
D
an infinite number
8

What is the solution of ?

Question illustration
A
mc012-2.jpg
Option A
B
mc012-3.jpg
Option B
C
mc012-4.jpg
Option C
D
mc012-5.jpg
Option D
9

The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly’s reasoning is correct or incorrect?

A
She is incorrect because systems may have only complex solutions which are not visible on a graph.
B
She is incorrect because the solutions may have multiplicity greater than 1.
C
She is correct because all solutions are intersection points of the graphs.
D
She is correct because the solutions are irrational.
10

What is the solution set of ?

Question illustration
A
mc023-2.jpg
Option A
B
mc023-3.jpg
Option B
C
mc023-4.jpg
Option C
D
mc023-5.jpg
Option D
11

Mario makes 6 free throw shots out of his first 10 attempts. What is the least number of consecutive shots Mario must make to increase his overall percentage from 60% to at least 70%?

A
1 shot
B
4 shots
C
10 shots
D
14 shots
12

The square root of a number is greater than the square of the number. For what set of numbers is this true?

A
(0, 1)
B
[0, 1]
C
[1, ꝏ)
D
(1, ꝏ)
13

What is the correct form of the partial fraction decomposition for ?

Question illustration
A
StartFraction A Over x + 2 EndFraction + StartFraction B Over (x + 2) squared EndFraction
Option A
B
StartFraction A Over x + 2 EndFraction + StartFraction B x + C Over (x + 2) squared EndFraction
Option B
C
StartFraction A Over x EndFraction + StartFraction B Over x + 2 EndFraction + StartFraction C Over (x + 2) squared EndFraction
Option C
D
StartFraction A Over x EndFraction + StartFraction B Over x + 2 EndFraction + StartFraction C x + D Over (x + 2) squared EndFraction
Option D
14

What is the solution to (x – 3)3(x + 1)(x – 2) ≤ 0?

A
(–ꝏ, –1) U (2, 3)
B
(–ꝏ, –1] U [2, 3]
C
(–1, 2) U (3, ꝏ)
D
[–1, 2] U [3, ꝏ)
15

What is the partial fraction decomposition of ?

Question illustration
A
StartFraction 1 Over 3 x EndFraction + StartFraction x minus 2 Over 4 x squared + 9 EndFraction
Option A
B
StartFraction 1 Over 3 x EndFraction + StartFraction x + 2 Over 4 x squared + 9 EndFraction
Option B
C
StartFraction negative 2 Over 3 x EndFraction + StartFraction x minus 1 Over 4 x squared + 9 EndFraction
Option C
D
StartFraction negative 2 Over 3 x EndFraction + StartFraction x + 1 Over 4 x squared + 9 EndFraction
Option D
16

A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation can be used to find x. What was the side length of the original cube? Use a graphing calculator and a system of equations to find the answer.

Question illustration
A
4 inches
B
5 inches
C
9 inches
D
10 inches
17

What is the solution of ?

Question illustration
A
mc021-2.jpg
Option A
B
mc021-3.jpg
Option B
C
or
Option C
D
or
Option D
18

Review the work showing the first few steps in writing a partial fraction decomposition.4x + 40 = A(x + 6) + B(x + 2)4x + 40 = Ax + 6A + Bx + 2B

Question illustration
A
StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction negative 12 Over x + 2 EndFraction + StartFraction 16 Over x + 6 EndFraction
Option A
B
StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction negative 4 Over x + 2 EndFraction + StartFraction 8 Over x + 6 EndFraction
Option B
C
StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction 8 Over x + 2 EndFraction + StartFraction negative 4 Over x + 6 EndFraction
Option C
D
StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction 16 Over x + 2 EndFraction + StartFraction negative 12 Over x + 6 EndFraction
Option D
19

What is the quotient and remainder, written as partial fractions, of ?

Question illustration
A
5 + StartFraction 10 Over x minus 1 EndFraction + StartFraction 3 Over 3 x + 8 EndFraction
Option A
B
5 + StartFraction 10 Over x minus 1 EndFraction minus StartFraction 3 Over 3 x + 8 EndFraction
Option B
C
5 minus StartFraction 10 Over x minus 1 EndFraction + StartFraction 3 Over 3 x + 8 EndFraction
Option C
D
5 minus StartFraction 10 Over x minus 1 EndFraction minus StartFraction 3 Over 3 x + 8 EndFraction
Option D
20

What is the correct form of the partial fraction decomposition for the expression ?

Question illustration
A
StartFraction A Over x squared + StartFraction B Over 9 x EndFraction
Option A
B
StartFraction A Over x EndFraction + StartFraction B Over x + 9 EndFraction
Option B
C
StartFraction A x + B Over x squared EndFraction + StartFraction C Over 9 x EndFraction
Option C
D
StartFraction A x + B Over x EndFraction + StartFraction C Over x + 9 EndFraction
Option D

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