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3 years ago

A rectangular prism with a volume of 3x²+7x²+2x.

Mathematics

1 answer:

Zepler [3.9K]3 years ago

7 0

Answer:

3x+1

Step-by-step explanation:

The easiest way to think about this problem is to understand that volume is area multiplied by height.

So if volume = l*w*h, and area = l*w, then if you divide volume by area you will be left with height.

Assuming the volume equation is 3x^3+7x^2+2x and the area is x^2+2x, this problem can be solved using polynomial long division.

I'll be using 1. , 2. , etc to show steps for this part.

1. Divide 3x^3 by x^2

(3x^3/x^2) = 3x

2. Multiply 3x from step 1 by the area equation

3x(x^2+2x)=3x^3+6x^2

3. Subtract 3x^3+6x^2 from the volume equation

3x^3+7x^2+2x - 3x^3+6x^2 = x^2+2x

NOTE: This is equal to the area equation

4. Divide x^2+2x (from step 3) by x^2 +2x (from area equation)

Please note that this skips steps but is allowed in this case because the result from step 3 was equal to the area equation.

(x^2+2x)/(x^2+2x) = 1

5. Combine the results from step 1. and step 4.

3x+1

This answer is the height of the prism.

You can check this by multiplying 3x+1 by the area equation:

(3x+1)*(x^2+2x) = 3x^3+6x^2+x^2+2x = 3x^3+7x^2+2x = volume

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Brilliant_brown [7]

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4 years ago

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2 years ago

10 + 2n = 8n - 2n + 10

galina1969 [7]

Answer:

n=0

Step-by-step explanation:

Rearrange

10+2=8−2+10

2+10=8−2+10

Combine like terms

2n+10=8n−2n+10

2+10=6+10

Subtract from both sides

2+10=6+10

2+10−10=6+10−10

Simplify

2n=6n

Subtract both sides from 6n of the equation

2=6

2−6=6−6

Solution

n=0

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3 years ago