Q: A chemist needs to mix a 10% saline solution with a 30% saline solution to obtain 20 liters of a 25% saline solution. Let $$ x be $$the amount (in liters) of the 10% solution used. Which equation models this scenario?

$$ 0.10x + 0.30(20-x) = 0.25 \times 20 $$

Question 1

Which of the following is the correct simplification of the expression $$ (2x^3$y^2$$) 	imes $$(3x^2y^4$) $$?

Accepted Answer

$$ 6x^5$y^6$$ $

Question 2

A quadratic equation models the height $$ h  (in $$meters) of a ball thrown upward from a bridge as $$ h(t) = -4.9t^2$ + 19.6t + 24 . $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$ t = 2 $$

Question 3

Which of the following is the correct factorization of $$ x^2$ - 9x + 20 $$?

Accepted Answer

$$ (x-4)(x-5) $$

Question 4

A chemist needs to mix a 10% saline solution with a 30% saline solution to obtain 20 liters of a 25% saline solution. Let $$ x  be $$the amount (in liters) of the 10% solution used. Which equation models this scenario?

Accepted Answer

$$ 0.10x + 0.30(20-x) = 0.25 	imes 20 $$

Question 5

Which of the following is equivalent to $$ \sqrt[3]{x^6$y^3$$} $?

Accepted Answer

$$ x^2$y $$

Question 6

Solve for $$ x  in $$the equation $$ 2x^2$ - 8 = 0 .$$

Accepted Answer

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

Question 7

Which of the following is the correct simplification of $$ \dfrac{2x^2$ - 8}{4x} $$?

Accepted Answer

$$ \dfrac{x^2$-4}{2x} $$

Question 8

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

Accepted Answer

$$ 15 $$

Question 9

Which of the following is the solution set for $$ |2x - 5| = 9 $$?

Accepted Answer

$$ x = 7  or$$ $$ x = -2 $$

Question 10

A company’s profit $$ P  (in $$thousands of dollars) is modeled by $$ P(x) = -2x^2$ + 12x - 16 $$, where $$ x  is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$ 16  at$$ $$ x = 3 $$

Question 11

Which of the following is the correct simplification of $$ (x^2$ - 9) \div (x + 3) $$?

Accepted Answer

$$ x - 3 $$

Question 12

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

Accepted Answer

$$ x = 2i  or$$ $$ x = -2i $$

Question 13

Which of the following is the correct simplification of $$ (3x^2$y^3)^2$ $$?

Accepted Answer

$$ 9x^4$y^6$$ $

Question 14

Which of the following is the correct solution to $$ \dfrac{5}{x} = 2 $$?

Accepted Answer

$$ x = 2.5 $$

Question 15

Which of the following is the correct simplification of $$ \dfrac{x^2$ - 16}{x - 4} $$?

Accepted Answer

$$ x + 4 $$

Question 16

Which of the following is the correct solution to $$ 3(x - 2) = 2x + 5 $$?

Accepted Answer

$$ x = 11 $$

Question 17

Which of the following is the correct simplification of $$ (x^2$ - 25) \div (x - 5) $$?

Accepted Answer

$$ x + 5 $$

Question 18

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

Accepted Answer

$$ x = 11 $$

Question 19

Which of the following is the correct simplification of $$ (2x^3$y^2$$) \div $$(x^2y$$) $?

Accepted Answer

$$ 2xy $$

Question 20

Which of the following is the correct solution to $$ x^2$ - 6x + 9 = 0 $$?

Accepted Answer

$$ x = 3 $$

Intermediate Algebra (Math 113) Syllabus and Course Structure – Wayne County Community College District

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