Q: Solve the equation $$8x^2 - 5x$$ = $$9x^2 - 36x + 4$ for x$.

$$x = -4$$ \, \text{or} \, x = 40$

Question 1

Given the function $$f(x) = \frac{2x^3$ - 6}{3x + x^2$}$$, evaluate $$f(-1)$$ and simplify your answer.

Accepted Answer

$$-2$$

Question 2

Based on the graph showing the percent of students in the College of Engineering at Stale University, does the graph represent a function?

Accepted Answer

Yes, because each year corresponds to exactly one percentage.

Question 3

Refer to the graph of percent of students in College of Engineering. If $$f$$ represents the function, what is $$f(1995)$$?

Accepted Answer

$$20\%$$

Question 4

If $$f(x) = 12\%$$, what year is represented by $$x$$ according to the graph?

Accepted Answer

1975

Question 5

Find and simplify the difference quotient for $$f(x) = 7x - 4.$$

Accepted Answer

$$7$$

Question 6

Write the equation of the line in point-slope form passing through $$(3, 5)$$ and $$(-5, 6).$$

Accepted Answer

$$y - 5 = -\frac{1}{8}(x - 3)$$

Question 7

A car's value depreciates from $$14,760 in 1991 to$$ $$4,440 in 1994. $$Let $$y be $$the value in year $$x$$, where $$x=0 is 1991. $$Write the linear equation modeling the value.

Accepted Answer

$$y = -4,106.67x + 14,760$$

Question 8

Find the average rate of change of $$f(x) = x^2$ from x = 2$ to x = 8$.

Accepted Answer

$$10$$

Question 9

Given $$f(x) = 2x^2$ + 2x - 2$$ and $$g(x) = 2x^2$ - 4x - 4$$, find $$(f \circ g)(-2).$$

Accepted Answer

$$14$$

Question 10

The function $$f(x) = 3x + 7 is $$one-to-one. Find the equation for $$f^{-1}(x$$)$$, the inverse function.

Accepted Answer

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

Question 11

Solve the equation $$8x^2 - 5x$$ = $$9x^2 - 36x + 4$ for x$.

Accepted Answer

$$x = -4$$ \, 	ext{or} \, x = 40$

Question 12

A ladder that is 10 feet long is 6 feet from the base of a wall. How far up the wall does the ladder reach?

Accepted Answer

$$8$$ feet

Question 13

You have $$600$$ feet of fencing to enclose a rectangular plot that borders a river (no fence along the river). What is the largest area that can be enclosed?

Accepted Answer

$$45,000$$ square feet

Question 14

Solve the quadratic equation $$x^2 + 7x - 34 = 5x$.

Accepted Answer

$$x = -17, x = 2$$

Question 15

Find the sum of the first $$100$$ natural numbers.

Accepted Answer

$$5,050$$

Question 16

Write a formula for the general (nth) term of the arithmetic sequence $$2, 7, 12, 17, \ldots$$ and find $$a_{20}.$$

Accepted Answer

$$a_n = 2 + 5(n-1); a_{20} = 97$$

Question 17

Find the sum of the infinite geometric series $$\frac{2}{3} + \frac{2}{9} + \frac{2}{27} + \ldots.$$

Accepted Answer

$$1$$

Question 18

A city is growing at the rate of $$0.8\%$$ annually. If there were $$3,980,000$$ residents in 1995, how many are living in that city in 2000? Use $$y = 3,980,000(2.7$$)^{0.008t}$$, where t$ is the time since 1995.

Accepted Answer

$$4,140,000$$

Question 19

Evaluate the expression $$\ln(e^2$) + 4\ln(e) - \ln(e).$$

Accepted Answer

$$5$$

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