Q: A standardized test has 125 questions worth a total of 1300 points. True/False questions are worth 8 points each, and Multiple Choice questions are worth 10 points each. If $$T is $$the number of True/False questions and $$M is $$the number of Multiple Choice questions, which system models the situation?

$$\begin{cases} T + M = 125 \\ 8T + 10M = 1300 \end{cases}$$

Q: If the solution to a system of equations is $$(x, y) = (2, 5)$$, which of the following systems could produce this solution?

$$\begin{cases} x + y = 7 \\ x - y = -3 \end{cases}$$

Q: Which of the following is the correct piecewise equation for the graph below, where the slope changes at $$x = 2$$?

$$f(x) = \begin{cases} 2x+4 & x \u003c 2 \\ 3x-2 & x \geq 2 \end{cases}$$

Question 1

Given the piecewise function $$f(x) = \begin{cases} 2x+4 & x \u003c 2 \ 3x-2 & x \geq 2 \end{cases}$$, what is the value of $$f(2)$$?

Accepted Answer

Question 2

A car rental agency charges $$40/day plus 0.18/$$mile$$ for one company and 50/$$day plus $$0.15/mile$$ for another. If you plan to rent for one day, how many miles must you drive for the cost to be the same?

Accepted Answer

$$333.33$$ miles

Question 3

Which of the following systems of equations has no solution?

Accepted Answer

$$y = 2x + 1$$ and $$y = 2x - 3$$

Question 4

If two lines in a system of equations are parallel but not the same, what can you conclude about the system?

Accepted Answer

There is no solution.

Question 5

Given the system $$\begin{cases} 2x + y = 6 \ x - y = 4 \end{cases}$$, what is the solution $$(x, y)$$?

Accepted Answer

$$(\boxed{4, 0})$$

Question 6

A standardized test has 125 questions worth a total of 1300 points. True/False questions are worth 8 points each, and Multiple Choice questions are worth 10 points each. If $$T is $$the number of True/False questions and $$M is $$the number of Multiple Choice questions, which system models the situation?

Accepted Answer

$$\begin{cases} T + M = 125 \ 8T + 10M = 1300 \end{cases}$$

Question 7

What is the break-even point for the revenue function $$R(x) = 0.85x$$ and the cost function $$C(x) = 1.1x + 35$$?

Accepted Answer

$$x = 140$$

Question 8

Which method is most efficient for solving a system of equations when one variable can be easily isolated?

Accepted Answer

Substitution

Question 9

If a system of equations has infinitely many solutions, what does this mean about the graphs of the equations?

Accepted Answer

The lines are the same.

Question 10

Given the system $$\begin{cases} 3x - y = 7 \ 2x + y = 8 \end{cases}$$, what is the value of $$x$$?

Accepted Answer

$$x = 4$$

Question 11

A rectangular metal sheet is 8 feet longer than it is wide. If the perimeter is 228 feet, what is the width?

Accepted Answer

$$58$$ feet

Question 12

Which of the following systems has infinitely many solutions?

Accepted Answer

$$y = 2x + 3$$ and $$2y = 4x + 6$$

Question 13

If you solve the system $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases} by $$elimination, what is the value of $$y$$?

Accepted Answer

$$y = 3$$

Question 14

Which of the following is NOT a valid method for solving a system of linear equations?

Accepted Answer

Factoring

Question 15

A system of equations is given by $$\begin{cases} 4x + 2y = 6 \ 2x + y = 3 \end{cases}. $$What is the relationship between the two equations?

Accepted Answer

They are the same line.

Question 16

If the solution to a system of equations is $$(x, y) = (2, 5)$$, which of the following systems could produce this solution?

Accepted Answer

$$\begin{cases} x + y = 7 \ x - y = -3 \end{cases}$$

Question 17

Which scenario best describes a system with exactly one solution?

Accepted Answer

Two lines that intersect at one point.

Question 18

If you graph the equations $$y = 2x + 3$$ and $$y = -x + 1$$, what is the solution to the system?

Accepted Answer

$$(x, y) = (-2/3, 5/3)$$

Question 19

Which of the following is the correct piecewise equation for the graph below, where the slope changes at $$x = 2$$?

Accepted Answer

$$f(x) = \begin{cases} 2x+4 & x \u003c 2 \ 3x-2 & x \geq 2 \end{cases}$$

B5

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