Q: A chemist is mixing two solutions. The first solution contains $$x$$ liters of 10% acid, and the second contains $$y$$ liters of 30% acid. If the total mixture is 20 liters and contains 22% acid, which system of equations models this scenario?

$$\begin{cases} x + y = 20 \\ 0.10x + 0.30y = 4.4 \end{cases}$$

Question 1

Given the relation $$R = \{ (2, 5), (3, 7), (4, 5), (6, 8) \}$$, what is the domain of $$R$$?

Accepted Answer

$$\{ 2, 3, 4, 6 \}$$

Question 2

Which of the following graphs represents a function?

Accepted Answer

A graph where every vertical line crosses the curve at most once.

Question 3

Given the points $$A(1, 2)$$ and $$B(4, 8)$$, what is the slope of the line passing through them?

Accepted Answer

$$2$$

Question 4

Which of the following is the equation of a vertical line passing through the point $$(3, -2)$$?

Accepted Answer

$$x = 3$$

Question 5

Convert the equation $$2x - 3y = 6 to $$slope-intercept form.

Accepted Answer

Question 6

If a line has the equation $$y = -\frac{1}{2}x + 4$$, what is the slope of a line perpendicular to it?

Accepted Answer

$$2$$

Question 7

Which of the following inequalities represents the region above the line $$y = 3x - 1$$ with a solid boundary?

Accepted Answer

$$y \geq 3x - 1$$

Question 8

A chemist is mixing two solutions. The first solution contains $$x$$ liters of 10% acid, and the second contains $$y$$ liters of 30% acid. If the total mixture is 20 liters and contains 22% acid, which system of equations models this scenario?

Accepted Answer

$$\begin{cases} x + y = 20 \ 0.10x + 0.30y = 4.4 \end{cases}$$

Question 9

Solve the system using the addition (elimination) method: $$\begin{cases} 2x + 3y = 7 \ 4x - 3y = 5 \end{cases}$$

Accepted Answer

$$x = 2, y = 1$$

Question 10

Which of the following lines is parallel to $$y = -\frac{3}{4}x + 2$$?

Accepted Answer

$$y = -\frac{3}{4}x - 5$$

Question 11

Given the equation $$x - 2y = 8$$, what is the slope of the line?

Accepted Answer

$$-2$$

Question 12

A company charges a flat fee of $$\50$ plus $$\$$20$$ per hour for consulting. Which equation models the total cost $$C$$ for $$h$$ hours?

Accepted Answer

$$C = 20h + 50$$

Question 13

Which of the following is the range of the relation $$\{ (1, 4), (2, 5), (3, 4), (4, 6) \}$$?

Accepted Answer

$$\{ 4, 5, 6 \}$$

Question 14

If the equation of a line is $$y = mx$$, which point does it always pass through?

Accepted Answer

$$(0, 0)$$

Question 15

Which of the following inequalities would have a dotted boundary when graphed?

Accepted Answer

$$y \u003e 2x + 1$$

Question 16

Solve the system using substitution: $$\begin{cases} y = 2x + 1 \ 3x + y = 10 \end{cases}$$

Accepted Answer

$$x = 3, y = 7$$

Question 17

A vertical line passes through $$(5, -3). $$Which of the following is its equation?

Accepted Answer

$$x = 5$$

Question 18

If two lines are perpendicular and one has a slope of $$\frac{3}{5}$$, what is the slope of the other?

Accepted Answer

$$-\frac{5}{3}$$

Question 19

Given the equation $$4x + 2y = 8$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, 2)$$

Question 20

A medical researcher is tracking the relationship between dosage ($$x mg) $$and patient response ($$y$$ units). If the data fits the line $$y = 1.5x + 2$$, what is the expected response for a dosage of $$6 mg$$?

Accepted Answer

$$11$$

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