Q: Which of the following is the correct application of the order of operations to evaluate the expression $$2 + 3 \times 4^2$?

$$2 + 3 \times 16 = 2 + 48 = 50$$

Question 1

Which of the following is the correct application of the order of operations to evaluate the expression $$2 + 3 	imes 4^2$?

Accepted Answer

$$2 + 3 	imes 16 = 2 + 48 = 50$$

Question 2

A quadratic equation models the height $$h (in $$meters) of a ball thrown upward from the ground as $$h(t) = -4.9t^2$ + 20t. At $$what time $$t$$ does the ball reach its maximum height?

Accepted Answer

$$t = 2.04$$ seconds

Question 3

Which of the following is the simplified form of $$\sqrt{50} + 2\sqrt{8}$$?

Accepted Answer

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

Question 4

A company’s profit $$P (in $$dollars) is modeled by the function $$P(x) = -2x^2$ + 40x - 100$$, where $$x is $$the number of units sold. What is the maximum profit the company can achieve?

Accepted Answer

$$P(10) = -2(10)^2$ + 40(10) - 100 = -200 + 400 - 100 = 100$$

Question 5

Which of the following is the correct factorization of $$x^2 - 5x + 6$?

Accepted Answer

$$(x - 2)(x - 3)$$

Question 6

Solve the equation $$\frac{2}{x} + 1 = 3$$ for $$x.$$

Accepted Answer

Question 7

Which of the following is the correct simplification of $$\frac{3x^2$y}{6xy^2$}$$?

Accepted Answer

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

Question 8

If $$f(x) = 2x^2$ - 3x + 1$$, what is the value of the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$4x + 2h - 3$$

Question 9

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

Accepted Answer

$$x \u003c 6$$

Question 10

A rectangular garden has a length that is 3 meters more than twice its width. If the area of the garden is $$35$$ square meters, what is the width of the garden?

Accepted Answer

$$5$$ meters

Question 11

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

Accepted Answer

$$4x^6y^4$

Question 12

If $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, what is $$(f \circ g)(x)$$?

Accepted Answer

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

Question 13

Which of the following is the correct solution to $$|2x - 3| = 7$$?

Accepted Answer

$$x = 5 or$$ $$x = -2$$

Question 14

Which of the following is the correct result of multiplying $$(x + 2)(x - 3)$$?

Accepted Answer

$$x^2 - x - 6$

Question 15

A car rental company charges a flat fee of $$\25$ plus $$\$$0.20$$ per mile driven. Which function models the total cost $$C$$ for driving $$x$$ miles?

Accepted Answer

$$C(x) = 25 + 0.2x$$

Question 16

Which of the following is the correct simplification of $$\frac{5}{\sqrt{2}}$$?

Accepted Answer

$$\frac{5\sqrt{2}}{2}$$

Question 17

If $$f(x) = 3x - 7$$, what is $$f^{-1}(x$$)$$, the inverse function?

Accepted Answer

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

Question 18

Which of the following is the correct solution to the equation $$x^2 + 2x - 8 = 0$?

Accepted Answer

$$x = 2 or$$ $$x = -4$$

Question 19

Which of the following is the correct result of dividing $$(6x^3$$ - $$9x^2$$)$$ by 3x$?

Accepted Answer

$$2x^2 - 3x$

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