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

$$x = 8$$

Question 3

Solve for $$x$$: $$2(x^2 + 3x$$) = $$3(x^2 + 2x$$)$$

Accepted Answer

$$x = 0 or$$ $$x = -2$$

Question 4

If $$\dfrac{5}{3x-6} = \dfrac{2}{x-2}$$, what is the value of $$x$$?

Accepted Answer

$$x = 4$$

Question 5

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

Accepted Answer

$$-2 + 11i$$

Question 6

Simplify: $$\sqrt{8} (\sqrt{3} - \sqrt{7})$$

Accepted Answer

$$2\sqrt{6} - 2\sqrt{14}$$

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

Accepted Answer

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

Question 12

Solve the inequality and give the interval notation: $$-55 \u003c 3x + 13 \leq 34$$

Accepted Answer

$$(-6, 7]$$

Question 13

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

Accepted Answer

$$x = 9$$

Question 14

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 $$9x$$, what is the ratio of the first solution to the second?

Accepted Answer

$$1:8$$

Question 15

A projectile is launched from the ground and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t + 1. $$After how many seconds does it reach its maximum height?

Accepted Answer

$$t = 2.04$$

Question 16

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

Accepted Answer

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

Question 17

If $$f(x) = x^2$ - 4x + 7$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$f(2) = 3$$

Question 18

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

Accepted Answer

$$x = 0 or$$ $$x = \dfrac{3}{4}$$

Question 19

A patient is given a medication that decays exponentially according to $$A(t) = A_0$ e$$^{-0.2t}$$, where A_0$ is the initial amount. What is the amount left after 5 hours if A_0$ = 100 mg$$?

Accepted Answer

$$60.7 mg$$

Question 20

Which of the following is the solution to $$x^2 + 4x + 8 = 0$?

Accepted Answer

$$x = -2 \pm 2i$$

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

Guida di studio - Domande di pratica

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