Q: A cab company charges $$F(m) as $$follows: $$5$$ dollars plus $$0.50$$ per mile for $$m \leq 25$$, and for $$m \u003e 25$$, an additional $$7$$ dollars plus $$0.75$$ per mile after the 25th mile. Which of the following is the correct piecewise function for the fare?

$$F(m) = \begin{cases} 5 + 0.5m & 0 \leq m \leq 25 \\ 5 + 0.5 \times 25 + 7 + 0.75(m-25) & m \u003e 25 \end{cases}$$

Question 1

Solve the quadratic equation $$x^2 - 8x - 20 = 0$ for x$.

Accepted Answer

$$x = 10 or$$ $$x = -2$$

Question 2

Which of the following best describes the graph of $$f(x) = -x^2$ + 8x + 25$$?

Accepted Answer

Concave down, vertex is a maximum

Question 3

Find the vertex of the parabola $$f(x) = x^2$ + 4x + 5.$$

Accepted Answer

$$(-2, 1)$$

Question 4

A ball is thrown upward from a 112 ft building at 128 ft/sec. Its height after $$t$$ seconds is $$S(t) = 112 + 128t - 8t^2$. What does the vertex of this parabola represent in the context of the problem?

Accepted Answer

The maximum height the ball reaches and the time it occurs

Question 5

Suppose $$P(x) = 22.4x - 0.1x^2$ - 408$$ models the profit from producing and selling $$x$$ units. How many units must be produced and sold to reach the maximum profit?

Accepted Answer

$$x = 112$$

Question 6

Given the piecewise function $$f(x) = \begin{cases} 3 & x  9 \end{cases}$$, what is $$f(6)$$?

Accepted Answer

$$5$$

Question 7

Suppose $$W$$ varies inversely as the square of $$x$$, and $$W = 4$$ when $$x = 4. $$What is $$W$$ when $$x = 2$$?

Accepted Answer

$$16$$

Question 8

If $$y$$ varies directly as the third power of $$x$$, and $$y = 54$$ when $$x = 3$$, what is $$y$$ when $$x = 5$$?

Accepted Answer

$$250$$

Question 9

Solve for $$x$$: $$4\sqrt{2x-3} = 36$$

Accepted Answer

$$x = 42$$

Question 10

A cab company charges $$F(m) as $$follows: $$5$$ dollars plus $$0.50$$ per mile for $$m \leq 25$$, and for $$m \u003e 25$$, an additional $$7$$ dollars plus $$0.75$$ per mile after the 25th mile. Which of the following is the correct piecewise function for the fare?

Accepted Answer

$$F(m) = \begin{cases} 5 + 0.5m & 0 \leq m \leq 25 \ 5 + 0.5 	imes 25 + 7 + 0.75(m-25) & m \u003e 25 \end{cases}$$

Question 11

For $$f(x) = -3x^2$ + 7x + 5$$, for which interval of $$x is$$ $$f(x) \geq 0$$? (Round to the nearest hundredth)

Accepted Answer

$$-0.60 \leq x \leq 2.77$$

Question 12

Solve for $$x$$: $$x^{2/3}$$ - \frac{3}{4} = -\frac{1}{2}$$

Accepted Answer

$$x = \frac{1}{8}$$

Question 13

If $$y$$ varies inversely as $$\sqrt{x}$$, and $$y = \frac{1}{3}$$ when $$x = 36$$, what is $$x$$ when $$y = \frac{1}{4}$$?

Accepted Answer

$$64$$

Question 14

Given $$f(x) = (x-5)^2$ - 2$$, what is the vertex of the parabola?

Accepted Answer

$$(5, -2)$$

Question 15

Solve for $$x$$: $$3(3x-2)^4 = 768$

Accepted Answer

$$x = 2$$

Question 16

Suppose $$y$$ varies directly as $$x$$ and $$y = 7$$ when $$x = 35. $$What is $$y$$ when $$x = 100$$?

Accepted Answer

$$y = 20$$

Question 17

Given the function $$f(x) = x^2$ - 7x + 12$$, what is the vertex of the parabola?

Accepted Answer

$$(3.5, -0.25)$$

Question 18

Solve for $$x$$: $$5\sqrt{x} = 10$$

Accepted Answer

$$x = 4$$

Question 19

Given the piecewise function $$f(x) = \begin{cases} 5 - \frac{1}{2}x & x \leq -3 \ \frac{1}{3}(x^2$ - 10) & x \u003e 4 \end{cases}$$, what is $$f(5)$$?

Accepted Answer

$$5$$

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