Question 1

Which of the following is the correct simplification of the expression $$\sqrt{50} + 2\sqrt{8}$$?

Accepted Answer

$$7\sqrt{2}$$

Question 2

A chemist mixes two solutions, one with a concentration of $$x$$ percent and another with a concentration of $$2x$$ percent, to obtain 10 liters of a solution with a concentration of $$1.5x$$ percent. If the chemist uses $$y$$ liters of the first solution, which equation models this scenario?

Accepted Answer

$$x y + 2x (10 - y) = 1.5x (10)$$

Question 3

Which of the following is the solution set for the inequality $$2x - 5 \u003e 9$$?

Accepted Answer

$$x \u003e 7$$

Question 4

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

Accepted Answer

$$(3, -4)$$

Question 5

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

Accepted Answer

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

Question 6

A patient’s medication dosage is modeled by the equation $$D = \frac{mg}{kg} 	imes w$$, where $$w is $$the patient’s weight in kilograms. If the prescribed dosage is $$5 \frac{mg}{kg}$$ and the patient weighs 70 kg, what is the total dosage?

Accepted Answer

$$350\ mg$$

Question 7

Solve the system of equations: $$\begin{cases} 2x + 3y = 12 \ x - y = 1 \end{cases}$$

Accepted Answer

$$(3, 2)$$

Question 8

Which of the following is the solution to the quadratic equation $$x^2 - 4x - 5 = 0$?

Accepted Answer

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

Question 9

A company’s profit $$P (in $$dollars) from selling $$x$$ units of a product is given by $$P = -2x^2$ + 40x - 100. $$What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$300 at$$ $$x = 10$$ units

Question 10

Which of the following is the correct simplification of the expression $$\frac{2x^2$ - 8}{4x}$$ for $$x 
eq 0$$?

Accepted Answer

$$\frac{x - 2}{x}$$

Question 11

Which of the following is the correct solution to the equation $$|3x - 7| = 5$$?

Accepted Answer

$$x = 4 or$$ $$x = \frac{2}{3}$$

Question 12

A line passes through the points $$(2, 5)$$ and $$(6, 13). $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = 2x + 1$$

Question 13

Which of the following is the correct solution set for the inequality $$x^2 - 4x + 3$$ \u003c 0$$?

Accepted Answer

$$1 \u003c x \u003c 3$$

Question 14

A quadratic equation models the height $$h (in $$meters) of a ball thrown upward from the ground as $$h = -4.9t^2$ + 19.6t$$, where $$t is $$time in seconds. After how many seconds does the ball reach its maximum height?

Accepted Answer

$$2$$ seconds

Question 15

Which of the following is the correct result of performing the operation $$(3 + 2i) + (5 - 7i)$$, where $$i is $$the imaginary unit?

Accepted Answer

$$8 - 5i$$

Question 16

A rectangular garden has a length that is 3 meters more than twice its width. If the area of the garden is $$99\ m^2$, what is the width of the garden?

Accepted Answer

$$6\ m$$

Question 17

Which of the following is the correct simplification of the expression $$\frac{5}{x} + \frac{2}{x+1}$$?

Accepted Answer

$$\frac{5(x+1) + 2x}{x(x+1)}$$

College Algebra Syllabus and Study Guide

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드