How many times larger than the number (1 − 8 /15 ) is the number (1.2 + 2/ 3 )?

What is the solution to this inequality? 4(2x + 2) + 12 > 100 please help!!

skad [1K]

Subtract 12 from both sides

4(2x + 2) > 100 - 12

Simplify 100 - 12 to 88

4(2x + 2) > 88

Divide both sides by 4

2x + 2 > 88/4

Simplify 88/4 to 22

2x + 2 > 22

Subtract 2 from both sides

2x > 22 - 2

Simplify 22 - 2 to 20

2x > 20

Divide both sides by 2

x > 20/2

Simplify 20/2 to 10

x > 10

7 0

3 years ago

What is the square root

shusha [124]

Answer:

Step-by-step explanation:

Trying to factor as a Difference of Squares :

1.1 Factoring: r2-96

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 96 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step 1 :

r2 - 96 = 0

Step 2 :

Solving a Single Variable Equation :

2.1 Solve : r2-96 = 0

Add 96 to both sides of the equation :

r2 = 96

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

r = ± √ 96

Can √ 96 be simplified ?

Yes! The prime factorization of 96 is

2•2•2•2•2•3

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 96 = √ 2•2•2•2•2•3 =2•2•√ 6 =

± 4 • √ 6

The equation has two real solutions

These solutions are r = 4 • ± √6 = ± 9.7980

Two solutions were found :

r = 4 • ± √6 = ± 9.7980

Processing ends successfully

4 0

3 years ago

Help me with this? ______________

Simora [160]

Answer:

Austin will have to buy 180 squares of carpeting.

Step-by-step explanation:

First find the dimension of the room. We do that by multiplying the width times the length and then subtracting the cut out region in the top right. And, in order to know how big that region we cut out is, we have to do a little subtraction.

We know the room is 18' long on the left side and 12' long on the right side. We subtract 12 from 18 to get 6, and we know that the cut out region is 6' long. We do the same thing with the width, 25' wide at the bottom minus 10' wide at the top and we see that the cut out is 15' wide.

18 x 25 = 450

6 x 15 = 90

450 - 90 = 360. The area of the room is 360 $ft^{2}$

Each piece of carpet is 2' by 1'. So for every 2' long, the piece of carpet is 1' wide. Each carpet piece will cover 2 $ft^{2}$ . Divide 360 by 2 and you get 180.

5 0

3 years ago

Find the area of the compound shape

andrey2020 [161]

This shape is separated into two trapezoids. The equation for the area of a trapezoid is .5(base1 + base2) multiplied by height. Therefore, each half of the compound shape would be equal to .5(12 + 8) * 6 or 10 * 6 = 60. So the area of the total would be 60+60 or 120.

7 0

3 years ago

Hola me podrían ayudar por favor. Convertir las fracciones a decimales y ubicar a los decimales en la recta numérica. a. 2/3 b.

NISA [10]

Answer:

Step-by-step explanation:

a decimal

2/3 = 0.7

8/5 = 1.6

-5/2 = -2.5

7/4 = 1.8

9/2 = 4.5

-11/3 = -3.7

13/5 = 2.6

-7/4 = -1.8

Esto es solo un bosquejo del número, usando un gráfico, use 0.1 para una unidad en la recta numérica.

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-5 -4 -3.7 -3 -2.5 -2 -1.8 -1 0 0.7 1 1.6 1.8 2 2.6 3 4 4.5 5

8 0

3 years ago