Q: A chemist needs to mix a solution that is 30% acid with a solution that is 10% acid to obtain 20 liters of a 20% acid solution. Which equation represents this scenario?

$$0.3x + 0.1(20-x) = 0.2 \times 20$$

Question 1

Which of the following is the correct result when multiplying the rational expressions $$\frac{2x}{x^2$-4}$$ and $$\frac{x+2}{3x}$$?

Accepted Answer

$$\frac{2(x+2)}{3(x-2)}$$

Question 2

Simplify the expression $$\frac{5}{x+3} + \frac{2}{x-3}$$ and choose the correct answer.

Accepted Answer

$$\frac{5(x-3)+2(x+3)}{(x+3)(x-3)}$$

Question 3

Which of the following is the correct solution to the equation $$\frac{3}{x} = \frac{6}{x+2}$$?

Accepted Answer

$$x = -1$$

Question 4

A chemist needs to mix a solution that is 30% acid with a solution that is 10% acid to obtain 20 liters of a 20% acid solution. Which equation represents this scenario?

Accepted Answer

$$0.3x + 0.1(20-x) = 0.2 	imes 20$$

Question 5

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

Accepted Answer

$$5\sqrt{2} + 4\sqrt{2} = 9\sqrt{2}$$

Question 6

Solve for $$x$$: $$x^2 - 6x + 9 = 0$

Accepted Answer

$$x = 3$$

Question 7

Which of the following is the correct graph for the function $$f(x) = x^2$ - 4$$?

Accepted Answer

A parabola opening upwards with vertex at $$(0, -4)$$

Question 8

If $$f(x) = 2x + 3$$ and $$g(x) = x - 1$$, what is $$f(g(4))$$?

Accepted Answer

$$f(g(4)) = 2(3) + 3 = 9$$

Question 9

Which of the following is the correct solution to $$\sqrt{x+5} = 4$$?

Accepted Answer

$$x = 11$$

Question 10

A quadratic equation $$ax^2 + bx + c = 0$ has real and equal roots if:

Accepted Answer

$$b^2 - 4ac = 0$

Question 11

Which of the following is the correct inverse function of $$f(x) = 3x - 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x+7}{3}$$

Question 12

Solve for $$x$$: $$\frac{2}{x} + \frac{3}{x} = 5$$

Accepted Answer

$$x = 1$$

Question 13

Which of the following is the correct simplification of $$\frac{x^2$-9}{x+3}$$?

Accepted Answer

$$x-3$$

Question 14

If $$f(x) = x^2$ and g(x) = x+2$, what is f(g(3$$))$$?

Accepted Answer

$$f(g(3)) = 25$$

Question 15

Which of the following is the correct solution to $$x^2 = 25$?

Accepted Answer

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

Question 16

A rectangle has a length that is 3 units more than twice its width. If the area is 22 square units, which equation represents this scenario?

Accepted Answer

$$(2w+3)w = 22$$

Question 17

Which of the following is the correct solution to $$\frac{x-2}{x+1} = 1$$?

Accepted Answer

$$x = 3$$

Question 18

Which of the following is the correct simplification of $$\frac{4x^2$ - 9}{2x + 3}$$?

Accepted Answer

$$2x-3$$

Question 19

Solve for $$x$$: $$\sqrt{x^2$} = 7$$

Accepted Answer

$$x = 7 or$$ $$x = -7$$

Question 20

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

Accepted Answer

$$x = -2$$

Intermediate Algebra Course Weekly Outline and Key Topics

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