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4 years ago

Apply the distributive property to factor out the greatest common factor. 56 + 32 =

Mathematics

1 answer:

valentina_108 [34]4 years ago

4 0

Answer:

8 * (7 + 4)

See process below

Step-by-step explanation:

We start by writing each number in PRIME factor form:

56 = 2 * 2 * 2 * 7

32 = 2 * 2 * 2 * 2 * 2

Notice that the factors that are common to BOTH numbers are 2 * 2 * 2 (the product of three factors of 2).Therefore we see that the greatest common factor for the given numbers is : 2 * 2 * 2 = 8

Using this, we can write the two numbers as the product of this common factor (8) times the factors that are left on each:

56 = 8 * 7

32 = 8 * 2 * 2 = 8 * 4

We can then use distributive property to "extract" that common factor (8) from the given addition as shown below:

56 + 32

8 * 7 + 8 * 4

8 * (7 + 4)

8 * (11)

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The volume of water and a rectangle swimming pool can be modeled by the function v(x)=x^3+13x-210. If the depth of the pool is g

S_A_V [24]

Answer:

Required,

$L=\frac{3+\sqrt{37}}{2}-\frac{144}{x-3}$

$W=\frac{3-\sqrt{37}}{2}-\frac{144}{x-3}$

Step-by-step explanation:

Given volume and depth respectively,

$V(x)=x^3+13x-210$ and $x-3$

To find length and width of the rectanglular swiming pool we know,

Volume=length $\times$ height $\times$ depth.

Let depth=D=x-3, length=L, width=W, then

$V=DLW$

$x^3+13x-210= LW(x-3)$

$LW=\frac{x^3+13x-210}{x-3}$

After divide we will get $x^2-3x-22$ with remainder -144.

Thus,

$x^3+13x-210=(x^2-3x-22)(x-3)-144=(x-3)LW$

Now to find root of,

$x^2-3x-144=\frac{3\pm\sqrt{9+88}}{2}=\frac{3\pm \sqrt{37}}{2}$

Thus,

$L=\frac{3+\sqrt{37}}{2}-\frac{144}{x-3}$

$W=\frac{3-\sqrt{37}}{2}-\frac{144}{x-3}$

5 0

3 years ago

Which of the following functions has an amplitude of 5 and passes through the point (0,0)?

dlinn [17]

Im gonna need to know what the choices are

5 0

3 years ago

What is 8(n-4)-4n =8-n equal to

Andru [333]

8(n-4)-4n=8-n

8n-32-4n=8-n

+32. +32

8n-4n=40-n

-4n

4n=40-n

+n +n

5n=40

__. __

5. 5

n=8

5 0

4 years ago

Read 2 more answers

Use Distributive Property to simplify<br><br> -7(3m - 4)<br><br> HEEEEEEEEEEEEEEEEELP!!!!!!

pishuonlain [190]

Answer:

-21m+28

Step-by-step explanation:

$-7(3m-4)\\\\-21m+28\\\\\left \{ {{-7*3m=-21m} \atop {-7*-4=28}} \right.$

Hope this helps.

3 0

3 years ago

Read 2 more answers

Plz help me with this

Zolol [24]

Answer : 4 & 5
Explanation :
4x-5/8 >-10 + 3x |multiply by 8
4x-5> -80 + 24x. | minus 4x , add 80
-5+80 > 24x -4x
75> 20x. |divide by 20
3.75 > x

So x is greater than 3.75 therefore 4 and 5 are the answers

7 0

3 years ago