Question 1

Solve for $$x$$: $$9x - 5 = 7 + 4x$$

Accepted Answer

$$x = \dfrac{12}{5}$$

Question 2

Which of the following is the solution to $$3(7x - 5) - 6(x - 9) = 5x + 12$$?

Accepted Answer

$$x = \dfrac{19}{8}$$

Question 3

Solve for $$x$$: $$\dfrac{2x}{3} + \dfrac{x}{2} = 2x - 4$$

Accepted Answer

$$x = -8$$

Question 4

Which value of $$x$$ satisfies $$\dfrac{5}{3x-6} = \dfrac{2}{x-2}$$?

Accepted Answer

$$x = 4$$

Question 5

Simplify: $$(6 + 5i) - (8 - 6i)$$

Accepted Answer

$$-2 + 11i$$

Question 6

Simplify: $$\sqrt{8} (3 - \sqrt{17})$$

Accepted Answer

$$6\sqrt{2} - 2\sqrt{34}$$

Question 7

Simplify: $$(-4 + 2i) + (4 + 8i)$$

Accepted Answer

$$0 + 10i$$

Question 8

Solve for $$x$$ using the square root property: $$6x^2 = 150$

Accepted Answer

$$x = \pm 5$$

Question 9

Solve for $$x by $$completing the square: $$x^2 + 7x + 4 = 0$

Accepted Answer

$$x = -\dfrac{7}{2} \pm \dfrac{\sqrt{33}}{2}$$

Question 10

Solve for $$x$$ using the quadratic formula: $$x^2 - 2x + 26 = 0$

Accepted Answer

$$x = 1 \pm 5i$$

Question 11

Solve for $$x$$: $$4x - 3x^2$ = 0$$

Accepted Answer

$$x = 0 or$$ $$x = 4$$

Question 12

Solve for $$x$$: $$(x + 35$$)^{3/2}$$ = 512$$

Accepted Answer

$$x = 29$$

Question 13

Solve the inequality and give the interval notation: $$6x - 5 \leq 8$$

Accepted Answer

$$(-\infty, \dfrac{13}{6}]$$

Question 14

Solve the compound inequality: $$-5 \u003c 3x + 13 \leq 34$$

Accepted Answer

$$(-6, 7]$$

Question 15

Solve the inequality: $$72 + 4x \u003c 18$$

Accepted Answer

$$(-\infty, -14)$$

Question 16

Solve the inequality: $$65 - 27 \u003c 3(x - 11)$$

Accepted Answer

$$(7, \infty)$$

Question 17

A chemist is mixing two solutions, one with a concentration of $$x$$ and another with a concentration of $$2x. If $$the total concentration after mixing is $$9$$, what is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 18

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

Accepted Answer

$$P = P_0$ \cdot 2^t$$

Question 19

A projectile is launched from the ground with an initial velocity of $$v_0 m/s. $$Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + v_0$ t. If it $$hits the ground after $$5$$ seconds, what is $$v_0$$?

Accepted Answer

$$v_0 = 24.5$ m/s

College Algebra: Solving Equations, Simplifying Expressions, and Solving Inequalities

Guida di studio - Domande di pratica

Study guide - Flashcard