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Drupady [299]
3 years ago
7

Find the solution set to each inequality. Express the solution in set notation.

Mathematics
1 answer:
daser333 [38]3 years ago
3 0

The solution to the inequality 6m + 2 > -27 is  m > -4.33

The solution to the inequality 8(p-6)>4(p-4) is  p > 8

The given inequality is:

6m  +  2  >  - 27

Subtract 2 to both sides of the inequality

6m  +  2 - 2  >  -27  -  2

6m   >  -29

Divide both sides by 6

\frac{6m}{6}> \frac{-29}{6}  \\m  > \frac{-29}{6}\\m > -4.83

For the inequality  8(p-6)>4(p-4)

Expand the inequality using the distributive rule

8p  -  48   >  4p  -  16

Collect like terms

8p  -  4p  >  -16  +  48

4p    >  32

Divide both sides of the inequality 4

\frac{4p}{4} > \frac{32}{4}\\p > 8

The solution to the inequality 6m + 2 > -27 is m > -4.33

The solution to the inequality 8(p-6)>4(p-4) is p > 8

Learn more here: brainly.com/question/15816805

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Step-by-step explanation:

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(2x) (5) = 10x

(2x) (5) = 10x

5 (5) = 25

Combine like terms

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3 years ago
1.
Anna007 [38]

Answer:

1) The correct option is C. (2) The correct option is D. (3) The correct option is B. (4) The correct option is D. (5) The correct option is D.

Step-by-step explanation:

The slope formula is

m=\frac{y_2-y_1}{x_2-x_1}

(1)

Two points are (-2,5) and (1,4).

m=\frac{4-5}{1-(-2)}=\frac{-1}{3}tex]Therefore option C is correct.(2)Use the above mentioned formula for each pair of coordinates.[tex]m=\frac{10-13}{17-12}=\frac{-3}{5}

m=\frac{10-15}{13-16}=\frac{-5}{-3}=\frac{5}{3}

m=\frac{10-7}{3-0}=\frac{3}{3}=1

m=\frac{18-13}{8-11}=\frac{5}{-3}=\frac{-5}{3}

Therefore option D is correct.

(3)

The pair of points (6, y) and (10, -1). The slope is \frac{1}{4}.

\frac{1}{4}=\frac{-1-y}{10-6}

\frac{1}{4}=\frac{-1-y}{4}

1=-1-y

y=-2

Therefore option B is correct.

(4)

For vertical line the x coordinates always remains the same. Therefore when we subtract the same number we get zero in the denominator, therefore the value of slope is undefined for a vertical line.

Therefore option D is correct.

(5)

Two points from the table are (2,110) and (3,165).

m=\frac{165-110}{3-2}=\frac{55}{1}

Therefore option D is correct.

5 0
3 years ago
Read 2 more answers
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