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

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

Subject: Mathematics    / General Mathematics   
Question

Final exam

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Math 012 7986 Final Exam Fall 2016 ID: 33

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-1-

Solve each equation. 1) -8m + 6(1 + m) = -8(m – 6) 2) –

45

8 =

1

6

b +

4

3

b

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

number line. 3) 5 p – 8( p + 3) > -6( p + 8) + 3

4) –

1

2

k –

2

5

> –

31

40

Solve each compound inequality, write its solution set in interval notation, and graph the

solution set on a number line. 5) 6 £ 6 + 6n < 36

6) –

1

2

£ –

3

4

x <

21

20

Write the standard form of the equation of the line described. 7) through: (4, 2), perpendcular to y = –

5

6

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) 5x – 2y = 6

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-2-

Show all work as you solve the linear modeling problem below. 9) There were 246 Apple stores worldwide in 2008 and 317 Apple stores worldwide in 2010. 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 = the number of Apple stores worldwide. Simplify. Your answer should contain only positive exponents. 10) 2u

2

v

2

× 3u

5

11) –

2x

3

y

-4

4x

4

y

3

× -4yx

0

12) (3u

-1

v

3

)-1

13) -2ba

5

× ba

0

× (2a

-2

)-3

Perform the indicated operation and simplify. 14) (1 – 5b

4 – 8b

2

) – (5b

4 – 6b

2 – 7)

Multiply as indicated and simplify. 15) (5x – 6)(4x

2 + 4x – 5)

Solve the equation by factoring. 16) 5v

2 + 21v = -18

Solve the equation by completing the square. 17) r

2 + 2r – 41 = 6

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-3-

Solve the equation by use of the quadratic formula. 18) 3n

2 – 3 = 3n

State the excluded values for the following expression. Then simplify the expression. 19) p

2 – 2 p – 15

p

2 – 5 p – 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

x

2 – 8x + 15 –

x

x – 3 =

5

x

2 – 8x + 15

Simplify the radical expressions. 21) 125x

3yz

4 22) (-3 3 + 5)( 3 + 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) -v + 41 – v = 1

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-4-

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

appropriate units. 24) DeShawn left the mall and traveled toward

the ferry office. Shawna left two hours

later traveling 30 km/h faster in an effort

to catch up to him. After three hours

Shawna finally caught up. Find

DeShawn's average speed.

25) Jennifer put $17,000 in an education

account on the day her daughter was born. If the account earned 6.45% interest

compounded quarterly, what was the total

in the account when her daughter turned

18? Round the final answer to the nearest

cent.