Q: Write the augmented matrix for the system: $$2x + y = 2$$, $$3x - 5y = 4$$, $$x - 3y = -4.$$

$$\begin{bmatrix}2 & 1 & 2 \\ 3 & -5 & 4 \\ 1 & -3 & -4\end{bmatrix}$$

Question 1

Simplify the expression $$\sqrt{25/3}.$$

Accepted Answer

$$5/\sqrt{3}$$

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

$$3x^2 + 14x + 4$

Question 4

Expand and simplify: $$(2x+5)^2.$$

Accepted Answer

$$4x^2 + 20x + 25$

Question 5

Simplify: $$\frac{15x^2$}{3x}.$$

Accepted Answer

$$5x$$

Question 6

Divide and simplify: $$\frac{2}{x(x+2)}.$$

Accepted Answer

$$\frac{2}{x(x+2)}$$

Question 7

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

Accepted Answer

$$(x-9)(x+6)$$

Question 8

Factor completely: $$x^3 + 8$.

Accepted Answer

$$(x+2)(x^2-2x+4$$)$$

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

$$x = -7$$

Question 11

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

Accepted Answer

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

Question 12

Write the augmented matrix for the system: $$2x + y = 2$$, $$3x - 5y = 4$$, $$x - 3y = -4.$$

Accepted Answer

$$\begin{bmatrix}2 & 1 & 2 \ 3 & -5 & 4 \ 1 & -3 & -4\end{bmatrix}$$

Question 13

Given the circle $$x^2 - 4x$$ + $$y^2 + 2y = 1$, find its center and radius.

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Find the equation of a line in standard form $$Ax + By = C$$ passing through $$(1, 2)$$ and $$(3, -4).$$

Accepted Answer

$$3x + y = 5$$

Question 16

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

Accepted Answer

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

Question 17

A person standing on the roof of a building 80 feet above the ground throws a ball directly upward. The ball rises, then falls to the ground. Its height $$s(t) in $$feet after $$t$$ seconds is given by $$s(t) = -16t^2$ + 32t + 80. $$What is the maximum height reached by the ball?

Accepted Answer

$$112$$ feet

Question 18

Given $$g(x) = \sqrt{x-4}$$, what is $$g(4)$$?

Accepted Answer

$$0$$

Question 19

If $$f(x) = \frac{x-3}{4}$$, what is $$f(7)$$?

Accepted Answer

$$1$$

Precalculus Exam Solutions and Study Guide

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