Q: A chemist mixes two solutions, one with a concentration of $$20\%$$ salt and another with $$50\%$$ salt, to obtain $$10$$ liters of a $$32\%$$ salt solution. If $$x is $$the number of liters of the $$20\%$$ solution used, which equation models this situation?

$$0.20x + 0.50(10 - x) = 0.32 \times 10$$

Question 1

Which of the following is the correct simplification of the expression $$2x^2 - 3x$$ + $$4x^2 + 5x - 7$?

Accepted Answer

$$6x^2 + 2x - 7$

Question 2

A chemist mixes two solutions, one with a concentration of $$20\%$$ salt and another with $$50\%$$ salt, to obtain $$10$$ liters of a $$32\%$$ salt solution. If $$x is $$the number of liters of the $$20\%$$ solution used, which equation models this situation?

Accepted Answer

$$0.20x + 0.50(10 - x) = 0.32 	imes 10$$

Question 3

Which of the following is the solution set for the inequality $$3x - 7 \u003c 2x + 5$$?

Accepted Answer

$$x \u003c 12$$

Question 4

Given the function $$f(x) = 2x^2$ - 5x + 3$$, what is the value of $$f(-2)$$?

Accepted Answer

$$23$$

Question 5

Which of the following is the correct domain of the function $$f(x) = \dfrac{1}{x-4}$$?

Accepted Answer

$$x 
eq 4$$

Question 6

A line passes through the points $$(2, 5)$$ and $$(6, 13). $$What is the slope of the line?

Accepted Answer

$$2$$

Question 7

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

Accepted Answer

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

Question 8

Simplify the expression $$\dfrac{2x^2$y}{4xy^2$}.$$

Accepted Answer

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

Question 9

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

Accepted Answer

Question 10

Which of the following is the solution to the quadratic equation $$x^2 - 4x - 5 = 0$?

Accepted Answer

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

Question 11

A ball is thrown upward from the ground with an initial velocity of $$32 ft/s. $$Its height $$h (in $$feet) after $$t$$ seconds is given by $$h(t) = -16t^2$ + 32t. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$1$$ second

Question 12

Which of the following is the correct simplification of $$\dfrac{3}{x} + \dfrac{2}{x+1}$$?

Accepted Answer

$$\dfrac{3(x+1) + 2x}{x(x+1)}$$

Question 13

Which of the following is the correct solution to the equation $$\sqrt{x+5} = 3$$?

Accepted Answer

$$x = 4$$

Question 14

Which of the following is the correct scientific notation for the number $$0.00056$$?

Accepted Answer

$$5.6 	imes 10$$^{-4}$$

Question 15

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f$$ \circ g)(3)$$?

Accepted Answer

$$19$$

Question 16

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

Accepted Answer

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

Question 17

Which of the following is the correct exponential form of the logarithmic equation $$\log_2$ x = 5$$?

Accepted Answer

$$x = 2^5$

Question 18

A medical researcher is studying the spread of a virus. The number of infected people after $$t$$ days is modeled by $$N(t) = 100 \cdot 2^t. $$How many people are infected after $$3$$ days?

Accepted Answer

$$800$$

Question 19

Which of the following is the correct simplification of $$\left( x$$^{1/2}$$ \$$right)^4$$?

Accepted Answer

$$x^2$$

Question 20

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

Accepted Answer

Intermediate Algebra with Support: Syllabus and Learning Outcomes Study Guide

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