Answers717- Algebra II AModeling with Systems

Modeling with Systems — Cumulative exam Answers

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Given that (3, 2, –6) and (–2, 5, 1) are solutions of two equations in a system of three linear equations, which of the following is true about the system?

A
The system can only be consistent and independent.
B
The system can be either inconsistent and independent or consistent and dependent.
C
The system can be either inconsistent and dependent or consistent and independent.
D
The system can only be inconsistent and dependent.
42
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During a baseball game, a player hits a ball while a bird is flying across the field. Let t be the time in seconds since the ball is hit and h be the height in feet. The height of the baseball over time is modeled by the equation h = –16t2 + 65t and the height of a bird over time is modeled by the equation h = 8t + 20. What do the intersection points of the equations represent?

A
the height of the bird and the ball when the ball and the bird are the same distance from the player
B
the height of the bird and the ball when the player hits the ball
C
the time when the height of the ball and the bird are the same
D
the time when the ball and the bird hit the ground
43

If and , what is the degree of ?

Question illustration
A
2
B
3
C
5
D
6
44

Which expression is equivalent to ? Assume x 0.

Question illustration
A
StartFraction x cubed StartRoot 2 EndRoot Over 2 EndFraction
Option A
B
StartFraction 4 StartRoot 2 EndRoot Over x cubed EndFraction
Option B
C
StartFraction StartRoot 2 EndRoot Over 2 x cubed EndFraction
Option C
D
StartFraction 2 StartRoot 2 EndRoot Over x cubed EndFraction
Option D
45

One root of a third degree polynomial function f(x) is –5 + 2i. Which statement describes the number and nature of all roots for this function?

A
f(x) has two real roots and one imaginary root.
B
f(x) has two imaginary roots and one real root.
C
f(x) has three imaginary roots.
D
f(x) has three real roots.
46

What is the vertex of the graph of f(x) = |x + 3| + 7?

A
(3, 7)
B
(7, 3)
C
(–3, 7)
D
(7, –3)
47

A coach purchases 47 hats for his players and their families at a total cost of $302. The cost of a small hat is $5.50. A medium hat costs $6.00. A large hat costs $7.00. He purchases three times as many medium hats as small hats. Using matrices, how many large hats did the coach purchase?

A
6
B
11
C
18
D
23
48

Dylan uses the expressions (x2 – 2x + 8) and (2x2 + 5x – 7) to represent the length and width of his bedroom. Which expression represents the area (lw) of Dylan’s room?

A
mc026-1.jpg
Option A
B
mc026-2.jpg
Option B
C
mc026-3.jpg
Option C
D
mc026-4.jpg
Option D
49

The length of a rectangular field is represented by the expression . The width of the field is represented by the expression . How much greater is the length of the field than the width?

Question illustration
A
mc026-3.jpg
Option A
B
mc026-4.jpg
Option B
C
mc026-5.jpg
Option C
D
mc026-6.jpg
Option D
50

What is the remainder when (3x3 – 2x2 + 4x – 3) is divided by (x2 + 3x + 3)?

A
30
B
3x – 11
C
28x – 36
D
28x + 30
51

Consider the inverse function. Which conclusions can be drawn about f(x) = x2 + 2? Select three options.f(x) has a limited range.f(x) has a restricted domain.f(x) has an x-intercept of (2, 0).f(x) has a maximum at the point (0, 2).f(x) has a y-intercept at the point (0, 2).

Question illustration
A
f(x) has a limited range.
B
f(x) has a restricted domain.
C
f(x) has an x-intercept of (2, 0).
D
f(x) has a maximum at the point (0, 2).
E
f(x) has a y-intercept at the point (0, 2).
52

Susan plans to use 120 feet of fencing to enclose a rectangular area for a garden. Which equation best models the area, y, of the rectangular garden that she creates if one side is x feet long?A = lw

A
y = (60 – x)(x)
B
y = (120 – x)(120 + x)
C
y = (120 – x)(x)
D
y = (60 – x)(60 + x)
53

Subtract 15mn – 22m +2n from 14mn – 12m +7n.

A
–mn + 10m + 5n
B
–mn – 34m + 5n
C
–mn – 34m + 9n
D
29mn – 34m + 9n
54

Fuaad solved an absolute value inequality and expressed the solution as . What is another way to show Fuaad’s solution?

Question illustration
A
mc008-2.jpg
Option A
B
(–12, 7]
C
mc008-3.jpg
Option C
D
mc008-4.jpg
Option D
55

Which equation represents a graph with a vertex at (1, –6)?

A
y = 3x2 + 6x – 3
B
y = 3x2 – 6x – 3
C
y = 3x2 – 8x – 1
D
y = 3x2 – 3x – 6
56

On a coordinate plane, an absolute value graph has a vertex at (negative 4, negative 2).

Question illustration
A
g(x) = |x + 4| – 2
B
g(x) = |x – 4| – 2
C
g(x) = |x – 2| – 4
D
g(x) = |x – 2| + 4
57

A cell phone carrier offers two plans for text messaging. Plan A costs $20 per month plus $0.05 per text. Plan B costs $10 per month plus $0.10 per text. For how many text messages per month are the plans the same cost?

A
20
B
30
C
200
D
300
58

If f(–5) = 0, what are all the factors of the function ? Use the Remainder Theorem.

Question illustration
A
(x – 2)(x + 5)(x – 3)
B
(x + 2)(x – 5)(x + 3)
C
(x – 2)(x + 5)
D
(x + 2)(x – 5)
59

Consider the function.f(x) = x2 + 3Which answer pairs a possible domain restriction that if placed upon f(x) would impact f–1(x) as shown?

A
f(x) domain: x ≥ 3f–1(x) domain: x ≥ 3
B
f(x) domain: x ≥ 3f–1(x) range: y ≥ 3
C
f(x) domain: x ≥ 0f–1(x) domain: x ≥ 0
D
f(x) domain: x ≥ 0f–1(x) range: y ≥ 0
60

The price that a company charged for a computer accessory is given by the equation where x is the number of accessories that are produced, in millions. It costs the company $10 to make each accessory. The company currently produces 2 million accessories and makes a profit of 100 million dollars. What other number of accessories produced yields the same profit?

Question illustration
A
1.45 million
B
3.45 million
C
40 million
D
48 million

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