Question 1

Which of the following is the correct factorization of the polynomial $$x^2 - 5x + 6$?

Accepted Answer

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

Question 2

A rectangular garden has an area of $$24$$ square meters and a length that is $$2$$ meters longer than its width. Which equation can be used to find the width $$w of $$the garden?

Accepted Answer

$$w(w + 2) = 24$$

Question 3

Simplify the expression $$\sqrt{50} + 2\sqrt{8}.$$

Accepted Answer

$$7\sqrt{2}$$

Question 4

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

Accepted Answer

$$x = -2$$

Question 5

What is the sum of the rational expressions $$\frac{2}{x} + \frac{3}{x}$$?

Accepted Answer

$$\frac{5}{x}$$

Question 6

Solve for $$x$$: $$\frac{1}{x} + \frac{1}{2} = 1$$

Accepted Answer

$$x = 2$$

Question 7

Which of the following is the simplified form of $$\frac{x^2$ - 9}{x + 3}$$?

Accepted Answer

$$x - 3$$

Question 8

If $$i is $$the imaginary unit, what is the value of $$i^2$$?

Accepted Answer

$$-1$$

Question 9

Which of the following is the correct solution to the equation $$\sqrt{x + 5} = 3$$?

Accepted Answer

$$x = 4$$

Question 10

A chemist mixes two solutions, one with a concentration of $$x$$ and another with a concentration of $$2x. If $$the total concentration after mixing is $$9$$, which equation represents this scenario?

Accepted Answer

$$x + 2x = 9$$

Question 11

Which of the following is the correct application of the quadratic formula to solve $$2x^2 - 4x - 6 = 0$?

Accepted Answer

$$x = \frac{4 \pm \sqrt{(-4)^2$ - 4 \cdot 2 \cdot (-6)}}{2 \cdot 2}$$

Question 12

Simplify the expression $$\frac{3x^2$y}{6xy^2$}.$$

Accepted Answer

$$\frac{x}{2y}$$

Question 13

Which of the following is the correct factorization of $$x^2 - 16$?

Accepted Answer

$$(x - 4)(x + 4)$$

Question 14

A medical researcher is analyzing the growth of bacteria, which doubles every hour. If the initial population is $$P_0$$, which expression represents the population after $$t$$ hours?

Accepted Answer

$$P_0$$ \cdot 2^t$$

Question 15

Which of the following is the correct simplification of $$\sqrt{18} - \sqrt{8}$$?

Accepted Answer

$$\sqrt{2}$$

Question 16

Solve for $$x$$: $$x^2 = 25$

Accepted Answer

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

Question 17

Which of the following is the correct simplification of $$\frac{2}{x} - \frac{1}{x}$$?

Accepted Answer

$$\frac{1}{x}$$

Question 18

Which of the following is the correct solution to the equation $$x^2 + 1 = 0$?

Accepted Answer

$$x = i or$$ $$x = -i$$

Question 19

A company’s profit $$P is $$given by $$P = 3x^2$ - 12x + 9$$, where $$x is $$the number of units sold. What is the minimum profit, and for how many units sold does it occur?

Accepted Answer

Minimum profit is $$P = 0 at$$ $$x = 2$$

MTH 95 – Intermediate Algebra: Course Syllabus and Study Guide

스터디 가이드 - 연습 문제

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