Q: Which of the following is the correct augmented matrix for the system: $$2x + y = 2$$, $$3x - y = 4$$?

$$\begin{bmatrix}2 & 1 & 2 \\ 3 & -1 & 4\end{bmatrix}$$

Question 1

Simplify the expression $$\sqrt{25/3}$$ and choose the correct answer.

Accepted Answer

$$\frac{5\sqrt{3}}{3}$$

Question 2

Rationalize the denominator and simplify: $$\frac{3}{\sqrt{5}}.$$

Accepted Answer

$$\frac{3\sqrt{5}}{5}$$

Question 3

Multiply and simplify: $$(3x^2 + 11x$$) \cdot (x + 4)$$.

Accepted Answer

$$3x^3$$ + $$23x^2 + 44x$

Question 4

Factor completely: $$x^2 - 9x + 6$.

Accepted Answer

$$(x-6)(x-1)$$

Question 5

Find the domain and range of $$f(x) = \sqrt{x-7}.$$

Accepted Answer

Domain: $$x \geq 7$$, Range: $$y \geq 0$$

Question 6

Write the equation of the vertical line passing through $$(-7, 10).$$

Accepted Answer

$$x = -7$$

Question 7

Find the midpoint of the segment with endpoints $$(2, 4)$$ and $$(−13, 14).$$

Accepted Answer

$$\left(\frac{2 + (-13)}{2}, \frac{4 + 14}{2}\right)$$

Question 8

Solve for $$x$$: $$2x^2 - 11x + 5 = 0$.

Accepted Answer

$$x = 5 or$$ $$x = \frac{1}{2}$$

Question 9

Find the center and radius of the circle with equation $$x^2 - 4x$$ + $$y^2 + 2y = 1$.

Accepted Answer

Center: $$(2, -1)$$, Radius: $$3$$

Question 10

Given $$g(x) = \sqrt{x-4}$$ for $$x \geq 4$$, find $$g(4).$$

Accepted Answer

$$0$$

Question 11

Find the equation of a line in standard form $$Ax + By = C$$ passing through $$(1, 2)$$ and $$(3, -3).$$

Accepted Answer

$$3x + y = 5$$

Question 12

Find the slope of the line perpendicular to $$3x - 4y = 7.$$

Accepted Answer

$$\frac{4}{3}$$

Question 13

Solve the system of equations: $$2x + 5y = 14$$ and $$5(x - y) = 11.$$

Accepted Answer

$$(3, 2)$$

Question 14

An architect is designing a rectangular floor space with area $$15$$ square units. The length is $$x$$ and the width is $$x-7. $$What are the possible values for $$x$$?

Accepted Answer

$$x = 5 or$$ $$x = -3$$

Question 15

A person standing on the roof of a building $$80 ft $$above the ground throws a ball directly upward. The ball misses the building on the way down and hits the ground. The function $$s(t) = -16t^2$ + 32t + 80$$ gives the height of the ball after $$t$$ seconds. What is the maximum height reached by the ball?

Accepted Answer

$$112 ft$$

Question 16

Given $$f(x) = \frac{x-3}{4}$$, find $$f(19).$$

Accepted Answer

$$4$$

Question 17

Factor completely: $$2x^2 - x - 7$.

Accepted Answer

$$(2x+7)(x-1)$$

Question 18

Given $$f(x) = x^2$ + 2x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(-1, 0)$$

Question 19

Which of the following is the correct augmented matrix for the system: $$2x + y = 2$$, $$3x - y = 4$$?

Accepted Answer

$$\begin{bmatrix}2 & 1 & 2 \ 3 & -1 & 4\end{bmatrix}$$

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