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Math 012 4010 Final Exam, Fall 2015 ID: 2 ©A \2B0U1A5Z eKsuWtIar YSTonfdt[wFaMrTeT XLBLmCJ.c ^ tAblQls krIiMguhUtDsZ TrteYsaeNrVvieJdq.

-1-

Solve each equation.

1) 8x - 4(1 + 5x) = -(4 - 6x) 2) -

50

21 = -

5

7 v +

5

3 v

Solve each inequality, write its solution set in interval notation, and graph the solution set on a number line.

3) v - 4(6v - 4) > 5(v - 8) 4)

3

5 + 2x £

19

5

Solve each compound inequality, write its solution set in interval notation, and graph the solution set on a number line.

5) -46 £ 3 + 7n < 10 6) -

28

9 < -

7

3 p £

35

9

Write the standard form of the equation of the line described.

7) through: (-2, -3), perpendicular to y = - 2 5 x - 5

Rewrite the equation in slope-intercept form and then use the slope and y-intercept to sketch a graph of the line with the given equation.

8) 3x - 4y = 12

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-2-

Show all work as you solve the linear modeling problem below.

9) There were 5474 CVS stores in the US in 2005 and 7702 CVS stores in the US in 2013. Write a linear equation in slope-intercept form that models this growth. Let x stand for the number of years after 2005 and let y = the number of CVS stores in the US.

Simplify. Your answer should contain only positive exponents.

10) 5x5y3 × 4xy5 11)

4x0y-4 × -2y4

3x4

12) (-3m-4n-3)-3 13) (-x-3y5)5 × -2x3y-4

Perform the indicated operation and simplify.

14) (4x + 5x3 - 7x4) - (8x4 - 6x3 - x)

Multiply as indicated and simplify.

15) (4n - 6)(7n2 + 5n + 6)

Solve the equation by factoring.

16) 4p2 = -15 - 17p

Solve the equation by completing the square.

17) x2 + 8x - 54 = 7

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-3-

Solve the equation by use of the quadratic formula.

18) 5n2 + 2n = 5

State the excluded values for the following expression. Then simplify the expression.

19) 3n + 24

n2 + 5n - 24

Solve the equation and show the check of the potential answer(s). If any answers are excluded values, state this on your answer sheet.

20) 1

a -

4a - 12 a2 + 6a

= a2 - a - 6 a2 + 6a

Simplify the radical expressions.

21) 75m2p3q4 22) ( 3 + 5 5 )(- 3 - 3 5 )

Solve the equation and show the check of the potential answer(s). If any answers are extraneous solutions, state this on your answer sheet.

23) p = 1 + 2p + 13

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-4-

Show all work as you solve the following problems and write complete answers, including appropriate units.

24) A cruise ship left Hawaii and traveled north at an average speed of 10 km/h. A submarine left two hours later and traveled in the same direction but with an average speed of 14 km/h. How long did the cruise ship travel before the submarine caught up?

25) Rebecca put $24,000 in an education account on the day her daughter was born. If the account earned 6.35% interest compounded monthly, what was the total in the account when her daughter turned 18? Round the final answer to the nearest cent.