Question 1

Given the functions $$f(x) = 8 + 4(3x)$$ and $$g(x) = 3(x - 6) + 10$$, for which value of $$x do$$ $$f(x)$$ and $$g(x)$$ have the same value?

Accepted Answer

$$x = 30$$

Question 2

What is the zero of the function $$f(x) = 2[2x - (3x - 7)] - 6(x - 7)$$?

Accepted Answer

$$x = 7$$

Question 3

Solve the equation $$8x - 5x = 9x - 36.$$

Accepted Answer

$$x = 9$$

Question 4

For the rational equation $$\frac{2}{x-3} = \frac{9}{x+3} + \frac{7}{x-3}$$, which values of $$x$$ make the denominators zero?

Accepted Answer

$$x = 3$$ and $$x = -3$$

Question 5

Electrostuff manufactures Electrogadget IV. The average cost per unit is modeled by $$f(x) = \frac{24,000 + 280x}{x}. $$How many units must be produced for the average cost per unit to be $$440$$?

Accepted Answer

$$150$$ units

Question 6

When $$80\% of a $$number is added to the number, the result is $$144. $$What is the number?

Accepted Answer

$$80$$

Question 7

You inherit $$10,000$$ and must invest it in two stocks paying $$6\%$$ and $$11\%$$ annual interest. If the total interest earned for the year is $$900$$, how much should be invested at $$6\%$$?

Accepted Answer

$$4,000$$

Question 8

After a $$9\%$$ price reduction, a boat sold for $$28,210. $$What was the boat's price before the reduction?

Accepted Answer

$$31,000$$

Question 9

A rectangular room's length is $$7$$ feet longer than twice its width. If the perimeter is $$194$$ feet, what is the width?

Accepted Answer

$$30 ft.$$

Question 10

Perform the operation and write the expression in standard form $$a + bi$$: $$(3 - 7i) - (2 + 4i).$$

Accepted Answer

$$5 - 11i$$

Question 11

Solve the quadratic equation $$x^2 = 20x + x$.

Accepted Answer

$$x = -4$$ and $$x = 5$$

Question 12

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

Accepted Answer

$$8 ft.$$

Question 13

An open box is made from a square sheet of cardboard by cutting out $$4-$$inch squares from each corner and folding. If the box is to have a volume of $$400$$ cubic inches, what are the original dimensions of the sheet?

Accepted Answer

$$18 in. by$$ $$18 in.$$

Question 14

You have $$600$$ feet of fencing to enclose a rectangular plot that borders a river. If you do not fence the side along the river, what is the largest area that can be enclosed?

Accepted Answer

$$45,000$$ $$ft^2$

Question 15

Solve the linear inequality $$24 - 20x + 4(5x - 6) \leq -x - 4. $$Write your answer in interval notation.

Accepted Answer

$$(-\infty, 1]$$

Question 16

Use interval notation to represent all values of $$x$$ satisfying $$f(x) = 4x - 5$$, $$g(x) = 3x - 9$$, and $$f(x) \u003e g(x).$$

Accepted Answer

$$(-4, \infty)$$

Question 17

Solve the compound inequality $$5 \leq 14 - 9x \u003c 29. $$Write your answer in interval notation.

Accepted Answer

$$[3, 12)$$

Question 18

Greg estimates his cost function as $$C(x) = 9000 + 0.09x$$ and his revenue function as $$R(x) = 1.95x$$, where $$x is $$the number of cars washed in six months. Find the number of cars that must be washed for Greg to make a profit. Write your answer in interval notation.

Accepted Answer

$$[4839, \infty)$$

Unit 2 Exam Review – Applications and Problem Solving in College Algebra

Guida di studio - Domande di pratica

Study guide - Flashcard