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Aleksandr-060686 [28]
3 years ago
11

What an equivalent expression for 48 + 18x

Mathematics
2 answers:
FromTheMoon [43]3 years ago
7 0

Answer:

6(8+3x)

Step-by-step explanation:

48+18x

We can factor out an 6 from each term in the expression

6(8+3x)

White raven [17]3 years ago
7 0

Answer:

  6(8 + 3x)

Step-by-step explanation:

There are an infinite number of equivalent expressions. We presume you have a list to choose from.

One of the more useful ones is the expression you get when you factor out the greatest common factor of the two terms. That factor is 6, so ...

  48 + 18x = 6(8 + 3x)

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You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the
Inga [223]

Answer:

20 by 20 by 20

Step-by-step explanation:

Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz ... 1

Given the volume V = xyz = 8000 ... 2

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x  + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.

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3 years ago
In order for the function to be linear, what must a be and why?​
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Step-by-step explanation:

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If x is an integer use that integer

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[ 3.6 ] is not an integer, hence

[ 3.6 ] = 3

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