Q: If $$A = \begin{pmatrix} 2 & 1 \\ 0 & 3 \end{pmatrix}$$ and $$B = \begin{pmatrix} 1 & 0 \\ 4 & 2 \end{pmatrix}$$, what is $$A + B$$?

$$\begin{pmatrix} 3 & 1 \\ 4 & 5 \end{pmatrix}$$

Question 1

A company wants to build a rectangular fenced area along a river, using the river as one side of the rectangle. If they have 300 meters of fencing available for the other three sides, what is the maximum area they can enclose?

Accepted Answer

$$11250\ 	ext{m}^2$$

Question 2

Solve the following system of equations for $$x$$ and $$y$$:

$$\begin{cases} 2x + 3y = 12 \ 4x - y = 5 \end{cases}$$

Accepted Answer

$$x = 2,\ y = 2$$

Question 3

A biologist is studying a bacteria population that doubles every 4 hours. If the initial population is 500, what will the population be after 12 hours?

Accepted Answer

$$8000$$

Question 4

Which of the following is the solution set for the inequality $$2x - 5 \u003c 9$$?

Accepted Answer

$$x \u003c 7$$

Question 5

A quadratic function models the height $$h (in $$meters) of a ball thrown upward from the ground as $$h(t) = -5t^2$ + 20t$$, where $$t is $$time in seconds. What is the maximum height reached by the ball?

Accepted Answer

$$25\ 	ext{m}$$

Question 6

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

Accepted Answer

$$19$$

Question 7

A chemist mixes a 20% saline solution with a 50% saline solution to obtain 10 liters of a 30% saline solution. How many liters of the 20% solution are needed?

Accepted Answer

$$6.67$$ liters

Question 8

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x - 4)(x - 5)$$

Question 9

A car rental company charges a flat fee of $$\30$ plus $$\$$0.20$$ per mile driven. If a customer is charged $$\50$, how many miles did they drive?

Accepted Answer

$$100$$ miles

Question 10

Which of the following is the solution to the equation $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 11

A student invests $$\1000$ in an account that earns 6% annual interest compounded quarterly. What will the balance be after 2 years? (Round to the nearest dollar)

Accepted Answer

$$\1127$

Question 12

Which of the following is the domain of the function $$f(x) = \dfrac{1}{x-3}$$?

Accepted Answer

$$x 
eq 3$$

Question 13

If $$A = \begin{pmatrix} 2 & 1 \ 0 & 3 \end{pmatrix}$$ and $$B = \begin{pmatrix} 1 & 0 \ 4 & 2 \end{pmatrix}$$, what is $$A + B$$?

Accepted Answer

$$\begin{pmatrix} 3 & 1 \ 4 & 5 \end{pmatrix}$$

Question 14

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

Accepted Answer

$$10$$

Question 15

Which of the following is the solution to the equation $$2^{x+1} = 16$?

Accepted Answer

$$x = 3$$

Question 16

A medical researcher is testing a new drug. The probability that a randomly selected patient will experience side effects is $$0.15. If 10 $$patients are selected at random, what is the expected number of patients who will experience side effects?

Accepted Answer

$$1.5$$

Question 17

Which of the following is the solution set for $$|2x - 3| = 7$$?

Accepted Answer

$$x = 5,\ x = -2$$

Question 18

A population of rabbits grows according to the function $$P(t) = 200e$$^{0.03t}$$, where t$ is measured in months. What is the population after 24 months? (Round to the nearest whole number)

Accepted Answer

$$406$$

Question 19

Which of the following is the solution to the equation $$x^2 + 6x + 5 = 0$?

Accepted Answer

$$x = -1,\ x = -5$$

Question 20

A student scores 80, 85, 90, and 95 on four tests. What score must they get on the fifth test to have an average of 90?

Accepted Answer

$$100$$

Mastery Problem-Solving Project: College Algebra Study Guide

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