Q: Which of the following correctly applies the order of operations to simplify the expression $$3 + 6 \times 2^2$?

$$3 + 6 \times 2^2$ = 3 + 6 \times 4 = 3 + 24 = 27$$

Question 1

Which of the following correctly applies the order of operations to simplify the expression $$3 + 6 	imes 2^2$?

Accepted Answer

$$3 + 6 	imes 2^2$ = 3 + 6 	imes 4 = 3 + 24 = 27$$

Question 2

A chemist mixes two solutions. The first solution contains $$x$$ liters of acid and the second contains $$2x + 3$$ liters. If the total mixture is $$15$$ liters, which equation represents this scenario?

Accepted Answer

$$x + 2x + 3 = 15$$

Question 3

Which of the following is the correct solution to the equation $$5(x - 2) = 3x + 8$$?

Accepted Answer

$$x = 6$$

Question 4

A company’s profit $$P (in $$dollars) is given by $$P = 50x - 200$$, where $$x is $$the number of items sold. What is the minimum number of items the company must sell to make a profit?

Accepted Answer

$$x = 4$$

Question 5

Which of the following is the correct graph of the equation $$y = -2x + 3$$?

Accepted Answer

A line with slope $$-2$$ and $$y-$$intercept $$3$$

Question 6

Simplify the expression $$2x^2 - 3x$$ + $$4x^2 + x - 5$.

Accepted Answer

$$6x^2 - 2x - 5$

Question 7

Factor the polynomial $$x^2 - 5x + 6$.

Accepted Answer

$$(x - 2)(x - 3)$$

Question 8

Which of the following is a rational expression?

Accepted Answer

$$\frac{x^2$ + 1}{x - 3}$$

Question 9

Solve the system of equations: $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2, y = 3$$

Question 10

Which of the following is the solution to the inequality $$3x - 4 \u003e 8$$?

Accepted Answer

$$x \u003e 4$$

Question 11

Simplify $$\sqrt{50} + 2\sqrt{2}.$$

Accepted Answer

$$7\sqrt{2}$$

Question 12

Which of the following is the distance between the points $$(1, 2)$$ and $$(4, 6)$$?

Accepted Answer

$$5$$

Question 13

What is the sum of the complex numbers $$(3 + 2i)$$ and $$(1 - 5i)$$?

Accepted Answer

$$4 - 3i$$

Question 14

Solve the quadratic equation $$x^2 - 4x - 5 = 0$.

Accepted Answer

$$x = 5 or$$ $$x = -1$$

Question 15

Which of the following is the inverse of the function $$f(x) = 2x + 3$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 3}{2}$$

Question 16

Which of the following is the correct application of the properties of exponents: $$x^3$$ \cdot $$x^4$$?

Accepted Answer

$$x^7$$

Question 17

A population of bacteria triples every hour. If the initial population is $$100$$, what will the population be after $$4$$ hours?

Accepted Answer

$$100 	imes 3^4$ = 8100$$

Question 18

Which of the following is the correct logarithmic form of the equation $$2^5 = 32$?

Accepted Answer

$$\log_2$ 32 = 5$$

Question 19

A rectangular garden has a length that is $$3$$ meters more than twice its width. If the perimeter is $$36$$ meters, what is the width?

Accepted Answer

$$4$$ meters

Question 20

Which of the following is the midpoint of the segment joining $$(2, 5)$$ and $$(8, 9)$$?

Accepted Answer

$$(5, 7)$$

Introductory & Intermediate Algebra (MATH 096) – Course Syllabus and Study Guide

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