Question 1

A pharmaceutical company is testing a new drug and models the number of bacteria in a culture by the function $$N(t) = 500 \cdot 2$$^{0.3t}$$, where t$ is the number of hours after the drug is applied. After how many hours will the bacteria count reach 4000?

Accepted Answer

$$t = 10.0$$

Question 2

Solve for $$x$$: $$3(x - 2) + 4 = 2x + 7. $$What is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 3

A rectangular garden has a length that is 4 meters more than twice its width. If the perimeter is 44 meters, what is the width of the garden?

Accepted Answer

$$w = 8$$

Question 4

Which of the following is the solution set for the inequality $$2x - 5 \leq 9$$?

Accepted Answer

$$x \leq 7$$

Question 5

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 $$h(t) = -16t^2$ + 32t. $$After how many seconds does the ball hit the ground?

Accepted Answer

$$t = 2$$

Question 6

Which of the following is equivalent to $$(3 + 2i)(1 - 4i)$$?

Accepted Answer

$$11 - 10i$$

Question 7

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

Accepted Answer

$$f(-2) = 15$$

Question 8

Which of the following is the solution to the equation $$x^2 - 6x + 9 = 0$?

Accepted Answer

$$x = 3$$

Question 9

A circle has the equation $$x^2$$ + $$y^2 - 6x + 8y = 0$. What are the center and radius of the circle?

Accepted Answer

Center $$(3, -4)$$, radius $$5$$

Question 10

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

Accepted Answer

$$x = 11$$

Question 11

Which of the following is the solution to the quadratic equation $$2x^2 - 4x - 6 = 0$?

Accepted Answer

$$x = 3, x = -1$$

Question 12

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

Accepted Answer

$$10$$

Question 13

Which of the following is the sum of $$\dfrac{3}{4} + \dfrac{5}{6}$$?

Accepted Answer

$$\dfrac{19}{12}$$

Question 14

If $$f(x) = x^2$ - 4x + 7$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$3$$

Question 15

A car rental company charges a flat fee of $$\25$ plus $$\$$0.20$$ per mile driven. If a customer paid $$\45$, how many miles did they drive?

Accepted Answer

$$100$$

Question 16

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

Accepted Answer

$$(2, 3)$$

Question 17

Which of the following is the simplified form of $$\dfrac{2x^2$y}{4xy^2$}$$?

Accepted Answer

$$\dfrac{x}{2y}$$

Question 18

A population of bacteria triples every 4 hours. If there are initially 200 bacteria, how many will there be after 12 hours?

Accepted Answer

$$5400$$

Question 19

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

Accepted Answer

$$x = 7, x = -2$$

Question 20

A triangle has sides of length $$5$$, $$12$$, and $$13. Is $$this triangle a right triangle?

Accepted Answer

Yes, because $$5^2$$ + $$12^2$$ = $$13^2$$

Comprehensive Study Guide: College Algebra Concepts and Problem Solving

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