$$x = 2 + \\sqrt{3}$$ and $$x = 2 - \\sqrt{3}$$

$$\\frac{x^3$ y$$^{-2.5}$$}{2^5$ \\sqrt{y}}$$

$$x = \\frac{-b \\pm \\sqrt{b^2$ - 4ac}}{2a}$$

Question 1

Which of the following is the correct solution to the linear equation $$5x - 10 = 20$$?

Accepted Answer

$$x = 6$$

Question 2

Given the quadratic equation $$x^2 + 4x - 12 = 0$, which of the following is a correct factorization?

Accepted Answer

$$(x + 6)(x - 2)$$

Question 3

Solve for $$x$$ using the quadratic formula for $$x^2 - 4x + 1 = 0$.

Accepted Answer

$$x = 2 + \sqrt{3}$$ and $$x = 2 - \sqrt{3}$$

Question 4

Which value of $$x$$ makes the denominator zero in the equation $$\frac{2}{x-3} + \frac{3}{x} = \frac{6}{x(x-3)}$$?

Accepted Answer

$$x = 0$$ and $$x = 3$$

Question 5

Factor the expression $$x^2 - 9$.

Accepted Answer

$$(x + 3)(x - 3)$$

Question 6

What is the greatest common factor (GCF) of $$12x^3$$ - $$52x^2 - 40x$?

Accepted Answer

$$4x$$

Question 7

Simplify $$\sqrt{\frac{x^6$ y$$^{-4}$$}{2$$^{10}$$ y}}.$$

Accepted Answer

$$\frac{x^3$ y$$^{-2.5}$$}{2^5$ \sqrt{y}}$$

Question 8

Which of the following is the correct slope-intercept form for a line with slope $$m$$ and $$y-$$intercept $$b$$?

Accepted Answer

$$y = mx + b$$

Question 9

If two lines are perpendicular, what is the relationship between their slopes $$m_1$$ and $$m_2$$?

Accepted Answer

$$m_1$$ $$m_2 = -1$

Question 10

Find the domain of the function $$f(x) = \frac{x^2$ + 5x + 6}{x^2$ + 3x - 18}.$$

Accepted Answer

$$x \neq -6, x \neq 3$$

Question 11

Which of the following is the correct formula for the quadratic formula?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 12

Given $$g(x) = \log_3$(x+1)$$, what is the domain of $$g(x)$$?

Accepted Answer

$$x \u003e -1$$

Question 13

Which of the following is the correct simplification for $$\sqrt{x} = x$$^{1/2}$$?

Accepted Answer

$$x^{1/2}$$

Question 14

If $$f(x) = \sqrt{10 - x}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \leq 10$$

Question 15

Which of the following is the correct factorization for $$9x^4 - 121$?

Accepted Answer

$$(3x^2$$ + $$11)(3x^2 - 11$$)$$

Question 16

Which rule applies to the product of powers $$a^m \cdot a^n$$?

Accepted Answer

$$a^{m+n}$$

Question 17

Given the function $$f(x) = \frac{x^2$ + 5x + 6}{x^2$ + 3x - 18}$$, what type of discontinuity occurs at $$x = -2$$?

Accepted Answer

Removable discontinuity (hole)

Question 18

If a line passes through $$(6, 4)$$ and has a slope of $$1$$, what is its equation in point-slope form?

Accepted Answer

$$y - 4 = 1(x - 6)$$

Question 19

Which of the following is the correct simplification for $$\sqrt{x^3$} = x$$^{3/2}$$?

Accepted Answer

$$x^{3/2}$$

Foundations of Algebra for Business Calculus

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