Q: Which of the following is the correct graph for $y = \frac{2}{3}x - 3$?

A line with slope $\frac{2}{3}$ and $y$-intercept $-3$

Question 1

A rideshare company charges a flat fee of $6 plus $0.75 per hour. Which equation models the total cost $C$ for $h$ hours, and what is the cost for a 4-hour ride?

Accepted Answer

$C = 6 + 0.75h;\ C = 9$

Question 2

Solve the inequality $-2x + 2 > -10$ and express the solution in interval notation.

Accepted Answer

$(6, \infty)$

Question 3

Which of the following lines is perpendicular to $y = -2x + 7$?

Accepted Answer

$y = \frac{1}{2}x - 4$

Question 4

A club sells regular tickets for $12 and VIP tickets for $20. If 250 tickets are sold for a total of $3940, how many regular tickets were sold?

Accepted Answer

$90$

Question 5

Solve for $x$: $|2x + 5| = 9$

Accepted Answer

$x = 2$ or $x = -7$

Question 6

Find the equation of the line passing through $(4, -1)$ and parallel to $y = -2x + 7$.

Accepted Answer

$y = -2x + 7$

Question 7

Given $f(x) = x^2 - 4x + 6$ and $g(x) = 5x - 2$, find $f(g(-1))$.

Accepted Answer

$f(g(-1)) = 16$

Question 8

A coffee shop sells small cups for $3 and large cups for $5. If 65 cups are sold for $233, how many large cups were sold?

Accepted Answer

$33$

Question 9

Which of the following is the solution to the system: $\begin{cases} 2x + 3y = 11 \ x - y = 2 \end{cases}$?

Accepted Answer

$(3, 1)$

Question 10

Solve the inequality $7x - 4 < 17$ and write the answer in set-builder notation.

Accepted Answer

$\{x | x < 3\}$

Question 11

Which of the following is the correct graph for $y = \frac{2}{3}x - 3$?

Accepted Answer

A line with slope $\frac{2}{3}$ and $y$-intercept $-3$

Question 12

If $|x - 4| = 8$, what are the possible values of $x$?

Accepted Answer

$x = 12$ or $x = -4$

Question 13

A bookstore sells notebooks for $2 and binders for $6. If 120 items are sold for $420, how many notebooks were sold?

Accepted Answer

$90$

Question 14

Which of the following is the solution to the system: $\begin{cases} x + 2y = 7 \ 4x - y = 5 \end{cases}$?

Accepted Answer

$(3, 2)$

Question 15

Which of the following lines is parallel to $y = \frac{3}{4}x - 1$ and passes through $(0, -2)$?

Accepted Answer

$y = \frac{3}{4}x - 2$

Question 16

Given $f(x) = 3x^2 + 2x + 1$ and $g(x) = x - 4$, find $f(g(2))$.

Accepted Answer

$f(g(2)) = 25$

Question 17

Solve for $x$: $3(x - 2) = 2(x - 7)$

Accepted Answer

$x = -8$

Question 18

Which of the following is the solution to the system: $\begin{cases} 2x + 3y = 7 \ 4x - y = 1 \end{cases}$?

Accepted Answer

$(2, 1)$

Question 19

A snack stand sells empanadas for $4 and patties for $7. If 50 items are sold for $353, how many empanadas were sold?

Accepted Answer

$29$

Question 20

Which of the following is the correct solution to $2x - 4 \leq 16$?

Accepted Answer

$x \leq 10$

College Algebra: Linear Equations, Inequalities, Graphs, and Systems – Study Guide

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