Algebra Final

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Math 012 7981 Final Exam Spring 2018 ID: 46 ©J G2R0R1t8E ]KhuetHar VSWoZfktDwiaLrTe^ KLYLlCM.U P tAClylW prXikgchStasd `rceasZe_rovMeTdm.

-1-

Solve each equation.

1) 8(1 + 3m) – 4 = -7(-2m + 2) – 2 2) –

3

8 =

4

3 r –

1

4 –

3

2 r

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

3) -2(n + 7) > -5(6n – 8) + n 4) -3

2

3 –

5

3 m > –

9

2

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

5) 2 < 5x – 3 £ 27 6) –

16

5 £ –

4

5 x £ 2

Write the equation of the line described in standard form, Ax + By = C, where A, B, and C are integers.

7) through: (4, 5), perpendicular to y = – 2 3 x + 5

 

 

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-2-

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) 5x – 2y = -6

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

9) There were 273 Whole Foods stores worldwide in 2008 and 399 Whole Foods stores worldwide in 2014. Write a linear equation in slope-intercept form that models this growth. Let x stand for the number of years after 2008 and let y stand for the number of Whole Foods stores worldwide.

Simplify. Your answer should contain only positive exponents.

10) 5a3b4 × 4a5b3 11)

3x4y2 × -4x

-2x2y-3

12) (-3vu-4)2 13) (2x3y3)-3 × -2x5y3

Perform the indicated operation and simplify.

14) (2p2 – 6p + 5) – (2p – 8 + 3p2)

Multiply as indicated and simplify.

15) (8x + 4)(x2 – 8x – 6)

 

 

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-3-

Solve the equation by factoring.

16) 3m2 + 6 = 19m

Solve the equation by completing the square.

17) a2 – 22a – 149 = -6

Solve the equation by use of the quadratic formula.

18) 3k2 = 2k + 6

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

19) m2 + 4m – 45 m2 – 3m – 10

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 + 1

n2 + n – 12 =

n2

n2 + n – 12

Simplify the radical expressions.

21) 27p3q2r4 22) ( 3 + 4 2 )(-3 3 + 2 )

 

 

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-4-

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) -1 + 4n + 81 = n

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

24) Nicole left the science museum and drove toward her friend’s house. Adam left one hour later driving 14 km/h faster in an effort to catch up to her. After four hours Adam finally caught up. What was Nicole’s average speed?

25) Rebecca put $35,000 in an education account on the day her daughter was born. If the account earned 7.85% interest compounded monthly, what was the total in the account when her daughter turned 18? Round the final answer to the nearest cent.

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