Answers EAP-Algebra Functions and Data Analysis A CRSolving Linear Systems by Substitution

Solving Linear Systems by Substitution — Cumulative exam Answers

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A local car wash is inviting customers to join the Concierge Club, in which you can have your car washed as many times as you wish for a fixed monthly fee. Amy creates the graph below to compare the cost per wash versus the cost for the Concierge Club. Which conclusion is supported by the graph?

The Concierge Club costs $6 per month.

The Concierge Club is the better deal for three washes per month.

The pay-per-wash option is the better deal for eight washes per month.

The pay-per-wash rate is $5.00 per wash.

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An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.

5 years

7 years

19 years

22 years

What is the quotient?

StartFraction 1 Over 2 y EnDfraction

StartFraction 3 y + 2 Over 6 y squared EndFraction

StartFraction 1 Over y EndFraction

StartFraction 2 (3 y + 2) Over 3 EndFraction

Which graph represents the solution to the system of inequalities?

On a coordinate plane, a curve approaches the x-axis in quadrant 2 and increase through (0, 1) and (2, 9). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 8), (negative 4, 0), and (0, 8). Everything inside of the ellipse and below the curve is shaded.

On a coordinate plane, a curve approaches the x-axis in quadrant 2 and increase through (0, 1) and (2, 9). An ellipse has center (0, 0) and goes through (8, 0), (0, negative 4), (negative 8, 0) and (0, 4). Everything inside of the ellipse and below the curve is shaded.

Option

Brandi is downloading music for her MP3 player. Albums cost $10 each, and singles cost $1 each. She wants to purchase at least 5 singles but wants to spend no more than $25 total. If Brandi purchases x albums and y singles, which of the following is a possible combination of albums and singles that Brandi could purchase and stay within her guidelines?

5 albums and 2 singles

2 albums and 5 singles

2 albums and 10 singles

10 albums and 2 singles

A certain company has a fixed cost of $200 per day. It costs the company $3.10 per unit to make its products. The company is tracking its average cost to make x units using . Which statement is true?

The horizontal asymptote of y = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.

The horizontal asymptote of y = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.

The vertical asymptote of x = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.

The vertical asymptote of x = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.

What is the product?

StartFraction k + 1 Over k squared EndFraction

StartFraction k minus 1 Over k squared EndFraction

StartFraction negative 1 Over k EndFraction

StartFraction 1 Over k EndFraction

A scientist has 100 milligrams of a radioactive element. The amount of radioactive element remaining after t days can be determined using the equation . After three days, the scientist receives a second shipment of 100 milligrams of the same element. The equation used to represent the amount of shipment 2 remaining after t days is . After any time, t, the mass of the element remaining in shipment 1 is what percentage of the mass of the element remaining in shipment 2?

78.1%

81.2%

123.1%

128.0%

A store owner puts in an order for product X and product Y for a total of 4,000 units. It costs $0.10 per item to ship of product X and $0.04 per item to ship product Y. If the total shipping cost is $352, which system of equations can be used to determine how much of product X and product Y the store owner bought?

StartLayout Enlarged Left-Brace 1st Row x + y = 4,000 2nd Row 10 x + 4 y = 352 EndLayout

StartLayout Enlarged Left-Brace 1st Row 10 x + 4 y = 4,000 2nd Row x + y = 352 EndLayout

StartLayout Enlarged Left-Brace 1st Row x + y = 4,000 2ndRow 0.1 x + 0.04 y = 352 EndLayout

StartLayout Enlarged Left-Brace 1st Row 0.1 x + 0.04 y = 4,000 2nd Row x + y = 352 EndLayout

For what values of x does ?

x = –3, x = 1

x = –1, x = 3

x = negative three-halves, x = 2

x = negative 2, x = three-halves

Review the graph.

y ≤ x2 – 8 and x > y2 + 1

y ≥ x2 – 8 and x < y2 + 1

y ≤ x2 + 1 and x > y2 – 8

y ≥ x2 + 1 and x < y2 – 8

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?

The high school option costs less per class for six classes.

The gym option costs less per class for six classes.

The high school option costs less per class for seven classes.

The gym option costs less per class for seven classes.

Which system of equations is consistent and dependent?

mc014-1.jpg

mc014-2.jpg

mc014-3.jpg

mc014-4.jpg

The equation shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If planet Y is k times the mean distance from the sun as planet X, by what factor is the orbital period increased?

k Superscript one-third

k Superscript one-half

k Superscript two-thirds

k Superscript three-halves

What are the vertical and horizontal asymptotes for the function ?

vertical asymptote: x = 1horizontal asymptote: none

vertical asymptote: x = 1horizontal asymptote: y = 0

vertical asymptote: x = –2, x = 3horizontal asymptote: y = 0

vertical asymptote: x = –2, x = –3horizontal asymptote: none

Jerome solved the equation below by graphing.Which of the following shows the correct system of equations and solution?

; x = 3

; x = 4

; x = 33

; x = 44

Organizers of the town fair make a total of $706 from selling 164 hot dogs and 74 hamburgers at one of their concession stands. At their other concession stand, they make $884 by selling 256 hot dogs and 61 hamburgers. If the prices are the same at both concession stands, what is the price of a hot dog?

$0.40

$2.50

$3.75

$4.00

Sharon is jumping from an 18-foot diving board with an initial upward velocity of 4 ft/s. When Sharon jumps, Megan throws a beach ball up to Sharon with an initial upward velocity of 16 ft/s from a height 5 feet off the ground. To the nearest hundredth of a second, how long after she jumps does the ball reach Sharon?

0.65 seconds

0.92 seconds

1.08 seconds

1.15 seconds

An equation for the depreciation of a car is given by y = A(1 – r)t, where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The current value of a car is $12,282.50. The car originally cost $20,000 and depreciates at a rate of 15% per year. How old is the car?

years