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

$$\displaystyle 5.6 \times 10$$^{-4}$$

Question 1

Which of the following is the correct simplification of the expression $$\displaystyle \frac{2x^2$ - 8}{4x}$$ for $$x 
eq 0$$?

Accepted Answer

$$\displaystyle \frac{x-2}{2}$$

Question 2

A chemist is mixing two solutions. The concentration of the first is $$\displaystyle \frac{3x}{x+2}$$ and the second is $$\displaystyle \frac{2x}{x-2}. $$What is the least common denominator (LCD) when adding these two rational expressions?

Accepted Answer

$$\displaystyle (x+2)(x-2)$$

Question 3

Which of the following values must be excluded from the domain of $$\displaystyle \frac{x^2$-9}{x^2$-4x+3}$$?

Accepted Answer

$$\displaystyle x=1$$ and $$x=3$$

Question 4

Simplify the following expression using the properties of exponents: $$\displaystyle (2x^3$y^2)^2$

Accepted Answer

$$\displaystyle 4x^6$y^4$

Question 5

Which property of real numbers justifies the following equation: $$\displaystyle 5 + (3 + 2) = (5 + 3) + 2$$?

Accepted Answer

Associative Property of Addition

Question 6

A biologist is measuring the distance between two points on a petri dish, located at $$a = 2.5 cm $$and $$b = 7.8 cm. $$What is the distance between the points?

Accepted Answer

$$\displaystyle 5.3 cm$$

Question 7

Simplify the following radical expression: $$\displaystyle \sqrt{50} + 2\sqrt{8}$$

Accepted Answer

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

Question 8

Which of the following is the correct factorization of $$\displaystyle x^2$ - 16$$?

Accepted Answer

$$\displaystyle (x-4)(x+4)$$

Question 9

A medical researcher is analyzing the growth of bacteria, which doubles every hour. If the initial population is $$P_0$$, which expression represents the population after $$t$$ hours?

Accepted Answer

$$\displaystyle P_0$ \cdot 2^t$$

Question 10

Simplify the following expression: $$\displaystyle \frac{3x^4$y^2$$}{$$6x^2y$$}$

Accepted Answer

$$\displaystyle \frac{x^2$y}{2}$$

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

$$\displaystyle x^8$y^{12}$

Question 13

A factory produces $$n$$ items per hour. The total number of items produced in $$t$$ hours is modeled by which algebraic expression?

Accepted Answer

$$\displaystyle n \cdot t$$

Question 14

Which of the following is the correct factorization of $$\displaystyle x^3$ + 8$$?

Accepted Answer

$$\displaystyle (x+2)(x^2$-2x+4)$$

Question 15

Simplify the complex rational expression: $$\displaystyle \frac{\frac{1}{x} + \frac{1}{y}}{\frac{1}{x}}$$ for $$x 
eq 0, y 
eq 0.$$

Accepted Answer

$$\displaystyle 1 + \frac{y}{x}$$

Question 16

Which of the following is the correct simplification of $$\displaystyle \sqrt{18} - \sqrt{8}$$?

Accepted Answer

$$\displaystyle 3\sqrt{2} - 2\sqrt{2} = \sqrt{2}$$

Question 17

Which of the following is the correct result of multiplying $$\displaystyle (x-3)(x+5)$$?

Accepted Answer

$$\displaystyle x^2$ + 2x - 15$$

Question 18

Which of the following is the correct simplification of $$\displaystyle \frac{2x^2$y^{-3}$$}{$$4x^{-1}y^2$}$$?

Accepted Answer

$$\displaystyle \frac{x^3$}{2y^5$}$$

Question 19

A student is asked to find the intersection of the sets $$A = \{1,2,3,4\}$$ and $$B = \{3,4,5,6\}. $$What is $$A \cap B$$?

Accepted Answer

$$\displaystyle \{3,4\}$$

Precalculus Fundamentals: Algebraic Expressions, Exponents, Radicals, Polynomials, and Rational Expressions

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