All categories

3 years ago

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

You might be interested in

Whoops i forgot to read the lesson :P 30 points

andriy [413]

Step-by-step explanation:

I'll do 2.

Alright,Alex let say we have factored a quadratic into two binomial, for example

$(5x + 3)(6x - 4)$

If we set both of those equal to zero

$(5x + 3)(6x + 4) = 0$

We can used the zero product property in this case to find the roots of the quadratic equation.

This means that

$if \: ab = 0 \: then \: a = 0 \: and \: b = 0$

This means we set each binomal equal to zero to find it root.

$5x + 3 = 0$

$5x = - 3$

$x = - \frac{3}{5}$

$6x + 4 = 0$

$6x = - 4$

$x = - \frac{2}{3}$

So our roots are negative 3/5 and negative 2/3 using zero product property

6 0

2 years ago

Bradley and Kelly are out flying kites at a park one afternoon. A model of Bradley and Kelly's kites are shown below on the coor

Alex787 [66]

The correct answer is:

C. They are similar because the corresponding sides of kites KELY and BRAD all have the relationship 2:1.

Using the distance formula,

$d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

the lengths of the sides of BRAD are:

$\text{BR}=\sqrt{(7-6)^2+(3-4)^2}=\sqrt{1^2+(-1)^2}=\sqrt{1+1}=\sqrt{2}\\\\\text{RA}=\sqrt{(6-3)^2+(4-3)^2}=\sqrt{3^2+1^2}=\sqrt{9+1}=\sqrt{10}\\\\\text{AD}=\sqrt{(3-6)^2+(3-2)^2}=\sqrt{(-3)^2+1^2}=\sqrt{9+1}=\sqrt{10}\\\\\text{DB}=\sqrt{(6-7)^2+(2-3)^2}=\sqrt{(-1)^2+(-1)^2}=\sqrt{1+1}=\sqrt{2}$

The lengths of the sides of KELY are:

$\text{KE}=\sqrt{(2-0)^2+(11-9)^2}=\sqrt{2^2+2^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\\\\\text{EL}=\sqrt{(0-2)^2+(9-3)^2}=\sqrt{(-2)^2+6^2}=\sqrt{40}=2\sqrt{10}\\\\\text{LY}=\sqrt{(2-4)^2+(3-9)^2}=\sqrt{(-2)^2+(-6)^2}=\sqrt{40}=2\sqrt{10}\\\\\text{YK}=\sqrt{(4-2)^2+(9-11)^2}=\sqrt{2^2+(-2)^2}=\sqrt{8}=2\sqrt{2}$

Each side of KELY is twice the length of the corresponding side on BRAD. This makes the ratio of the sides 2:1 and the figures are similar.

8 0

3 years ago

Read 2 more answers

Simplify the expression.<br> - (m<br> m + 3n - 13)

natulia [17]

Answer:

$= - {m}^{2} - 3n + 13$

Step-by-step explanation:

$- (m \times m + 3n - 13)$

$m \times m = {m}^{1} \times m$

${m}^{1} \times {m}^{1} = {m}^{1 + 1} = {m}^{2}$

$- ( {m}^{2} + 3n - 13)$

$= - {m}^{2} - 3n + 13$

7 0

3 years ago

A clown bought 6 bags of round balloons with 24 balloons in each bag.The clown also bought 3 bags of long balloons with 36 ballo

Ierofanga [76]

6 bags × 24 balloons = the amount of round balloons
6× 24 = 144
3 bags × 36 balloons = the amount of long balloons
3 ×36=108

108 long balloons - 144 round balloons = number of more long balloons that round ones
108-144=-36
He has -36 more long balloons that round ones
Or 36 more round balloons that long ones

7 0

3 years ago

What is the slope of this line?

Marysya12 [62]

Answer:

1/4

Step-by-step explanation:

rise: 1, run: 4

4 0

3 years ago