Answers NC-Math 2Solving Linear Systems by Substitution

Solving Linear Systems by Substitution — Cumulative exam Answers

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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

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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

What is the solution of ?

x = –10

x = 3

x = –10 or x = 3

no solution

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%

Haji rows his canoe 10 mph in still water. He noticed one day that he could row 4 miles upstream in the same amount of time he could row 6 miles downstream. What was the approximate speed of the current that day?

2.0 mph

3.3 mph

5.0 mph

10.0 mph

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

If , what is the value of x?

Five-eighths

Eight-fifths

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

What is the solution of Round your answer to the nearest hundredth.

mc017-2.jpg

mc017-3.jpg

mc017-4.jpg

mc017-5.jpg

What is the solution to

mc004-2.jpg

mc004-3.jpg

mc004-4.jpg

mc004-5.jpg

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