Question 1

Simplify the expression: $$\sqrt{196}$$

Accepted Answer

$$14$$

Question 2

Simplify the expression: $$\sqrt[3]{(-729)}$$

Accepted Answer

$$-9$$

Question 3

Which of the following is the simplified form of $$\dfrac{a^3$ b$$^{-2}$$}{a$$^{-1}$$ b^4$}$$?

Accepted Answer

$$a^4$$ $$b^{-6}$$

Question 4

Simplify: $$\sqrt[3]{64x^3$y^2$$}$

Accepted Answer

$$4xy\sqrt[3]{y}$$

Question 5

Which of the following is the result of $$\sqrt[3]{x^2$} \cdot \sqrt[3]{x^5$}$$?

Accepted Answer

$$x^{7/3}$$

Question 6

Simplify: $$\sqrt{96} - 2\sqrt{24} + 4\sqrt{36}$$

Accepted Answer

$$12$$

Question 7

Which of the following is the simplified form of $$\dfrac{5}{\sqrt{2}}$$?

Accepted Answer

$$\dfrac{5\sqrt{2}}{2}$$

Question 8

Simplify: $$(4 - 2i)(3 - i)$$

Accepted Answer

Question 9

Solve for $$x$$: $$3x + 2 = 3$$

Accepted Answer

$$x = \dfrac{1}{3}$$

Question 10

Solve for $$x$$: $$8 = 3(x + 5)$$

Accepted Answer

$$x = -1$$

Question 11

Solve the quadratic equation: $$3x^2 + 7x - 2 = 0$

Accepted Answer

$$x = \dfrac{-7 \pm \sqrt{49 + 24}}{6}$$

Question 12

Which interval represents the solution to $$2x - 6 \u003c 0$$?

Accepted Answer

$$(-\infty, 3)$$

Question 13

Given $$f(x) = x^2$ - 4$$ and $$g(x) = x + 3$$, find $$(f - g)(-2).$$

Accepted Answer

$$-11$$

Question 14

Given $$f(x) = x^2$ - 4$$ and $$g(x) = x + 3$$, find $$(fg)(3).$$

Accepted Answer

$$24$$

Question 15

What is the domain of $$\dfrac{f(x)}{g(x)}$$ where $$f(x) = x^2$ - 4$$ and $$g(x) = x + 3$$?

Accepted Answer

$$x 
eq -3$$

Question 16

Find the composition $$(f \circ g)(x)$$ for $$f(x) = x^2$ - 4$$ and $$g(x) = x + 3.$$

Accepted Answer

$$(x + 3)^2$ - 4$$

Question 17

Which of the following is the vertex of the parabola $$f(x) = (x + 1)^2$ - 3$$?

Accepted Answer

$$(-1, -3)$$

Question 18

Write $$\log_2$ 16 = y in $$exponential form.

Accepted Answer

$$2^y = 16$$

Question 19

How much money will be in an account at the end of 5 years if $$2,250 is deposited at 6.5\%$$ compounded annually? Use $$A = P(1 + \frac{r}{n}$$)^{nt}$$.

Accepted Answer

$$A = 2250(1 + 0.065)^5$

Intermediate Algebra Final Exam Review – Step-by-Step Guidance

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