Question 1

Solve for $$x$$: $$3x - 4 = 2x + 5.$$

Accepted Answer

$$x = 9$$

Question 2

Which of the following is the solution set for the inequality $$5x - 3 \leq 2x + 6$$?

Accepted Answer

$$x \leq 3$$

Question 3

Add the complex numbers: $$(6 + 7i) + (8 - 10i).$$

Accepted Answer

$$14 - 3i$$

Question 4

Multiply and write the result in the form $$a + bi$$: $$(5 + 2i)(3 - 4i).$$

Accepted Answer

$$23 - 14i$$

Question 5

Solve for $$x$$: $$x^2 - 4x + 3 = 0$.

Accepted Answer

$$x = 1, 3$$

Question 6

Which of the following is the standard form of the equation of a circle with center $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 25$$

Question 7

Given the points $$A(1,2)$$ and $$B(4,6)$$, what is the distance between them?

Accepted Answer

$$5$$

Question 8

If $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$15$$

Question 9

Solve for $$x$$: $$\sqrt{x + 5} = 4.$$

Accepted Answer

$$x = 11$$

Question 10

Which of the following is the vertex of the parabola $$y = (x - 3)^2$ + 2$$?

Accepted Answer

$$(3, 2)$$

Question 11

A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, how many will there be after 9 hours?

Accepted Answer

$$4000$$

Question 12

Which of the following is equivalent to $$\log_{2} 8$$?

Accepted Answer

$$3$$

Question 13

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 14

Which of the following is the solution to $$2x^2 - 8 = 0$?

Accepted Answer

$$x = 2, -2$$

Question 15

A ball is thrown upward from the ground with an initial velocity of $$32 ft/s. $$Its height $$h (in $$feet) after $$t$$ seconds is given by $$h = -16t^2$ + 32t. $$When does the ball hit the ground?

Accepted Answer

$$t = 2$$

Question 16

Which of the following is the inverse of the function $$f(x) = 3x - 7$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x + 7}{3}$$

Question 17

Which of the following is the solution to the equation $$|2x - 5| = 9$$?

Accepted Answer

$$x = 7, -2$$

Question 18

If $$f(x) = \dfrac{1}{x}$$, what is the domain of $$f$$?

Accepted Answer

$$x 
eq 0$$

Question 19

Which of the following is the solution to $$2^{x} = 16$?

Accepted Answer

$$x = 4$$

Question 20

A right triangle has legs of length $$6$$ and $$8. $$What is the length of the hypotenuse?

Accepted Answer

$$10$$

Precalculus Review: Equations, Inequalities, Complex Numbers, and Circles

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