Q: A chemist needs to mix a 20% saline solution with a 50% saline solution to obtain 10 liters of a 30% saline solution. Let $$x be $$the amount (in liters) of the 20% solution used. Which equation models this situation?

$$0.2x + 0.5(10 - x) = 0.3 \times 10$$

Question 1

Which of the following is the correct solution set for the inequality $$2x - 5 \leq 9$$?

Accepted Answer

$$x \leq 7$$

Question 2

A chemist needs to mix a 20% saline solution with a 50% saline solution to obtain 10 liters of a 30% saline solution. Let $$x be $$the amount (in liters) of the 20% solution used. Which equation models this situation?

Accepted Answer

$$0.2x + 0.5(10 - x) = 0.3 	imes 10$$

Question 3

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

Accepted Answer

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

Question 4

Solve the system of equations: $$\begin{cases} 2x + 3y = 12 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 3,\ y = 2$$

Question 5

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

Accepted Answer

$$x^2$$

Question 6

A rectangle has a length that is 3 meters more than twice its width. If the perimeter is 36 meters, what is the width?

Accepted Answer

$$5$$ meters

Question 7

Which of the following is the solution to the absolute value equation $$|2x - 7| = 5$$?

Accepted Answer

$$x = 6 or$$ $$x = 1$$

Question 8

Simplify the following expression: $$\dfrac{3x^2$y}{6xy^2$}$$

Accepted Answer

$$\dfrac{x}{2y}$$

Question 9

Which of the following is the equation of the line passing through the points $$(2, 5)$$ and $$(4, 9)$$?

Accepted Answer

$$y = 2x + 1$$

Question 10

A medical laboratory needs to dilute a 40% acid solution to a 25% acid solution. How many liters of water must be added to 8 liters of the 40% solution to obtain a 25% solution?

Accepted Answer

$$4.8$$ liters

Question 11

Which of the following is the correct solution to the quadratic equation $$x^2 + 6x + 5 = 0$?

Accepted Answer

$$x = -1 or$$ $$x = -5$$

Question 12

Simplify the radical expression $$\sqrt{50} + 2\sqrt{8}.$$

Accepted Answer

$$9\sqrt{2}$$

Question 13

Which of the following is the correct solution to the rational equation $$\dfrac{2}{x} + 1 = 3$$?

Accepted Answer

$$x = 1$$

Question 14

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

Accepted Answer

$$15$$

Question 15

Which of the following is the correct simplification of $$\dfrac{x^2$ - 9}{x^2$ - 6x + 9}$$?

Accepted Answer

$$\dfrac{x + 3}{x - 3}$$

Question 16

A company’s profit $$P (in $$dollars) from selling $$x$$ units of a product is given by $$P = -2x^2$ + 400x - 5000. $$How many units must be sold to maximize the profit?

Accepted Answer

$$100$$

Question 17

Which of the following is the solution set for the compound inequality $$-3 \u003c 2x + 1 \leq 7$$?

Accepted Answer

$$-2 \u003c x \leq 3$$

Question 18

Which of the following is the result of rationalizing the denominator of $$\dfrac{5}{\sqrt{3}}$$?

Accepted Answer

$$\dfrac{5\sqrt{3}}{3}$$

Question 19

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

Accepted Answer

$$x = 11$$

Question 20

Which of the following is the correct result of dividing $$2x^3$$ - $$3x^2 + 4x - 5$ by x - 2$ using synthetic division?

Accepted Answer

$$2x^2 + x + 6$ remainder 7$

MAT1033 Intermediate Algebra Syllabus and Course Structure

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