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3 years ago

Which of the following is equivalent to (x+4)(3x^2+2x)?

Mathematics

1 answer:

Mrrafil [7]3 years ago

7 0

We can multiple this binomial and this trinomial to find an equivalent expression.

(x + 4)(3x^2 + 2x)

3x^3 + 2x^2 + 12x^2 + 8x

Combine like terms.

3x^3 + 14x^2 + 8x is the equivalent polynomial.

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Solve & Explain your Math thinking 12-7

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For this case we have the following subtraction:

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We can rewrite the subtraction in an easier way.

We have then:

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3 years ago

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A rectangular pyramid and a rectangular prism are shown below.

maxonik [38]

The volume of the rectangular prism is 36 ft³.

Step-by-step explanation:

Step 1:

The volume of a rectangular prism $= lwh$ ,

The area of the base is length multiplied by the width. So $Area = (l)(w).$

The volume of a rectangular prism = $(area)(h).$

The volume of a rectangular pyramid $= a^{2} \frac{h}{3} .$

Where a is the side length. If the base is a square, the area $= a^{2}$ .

So the volume of a rectangular pyramid $=\frac{1}{3} (area)(h)$ .

So if a rectangular pyramid and a rectangular prism have the same base and height, then

3 times the volume of the rectangular pyramid = The volume of the rectangular prism.

Step 2:

As it is given that the volume of the pyramid is 12 ft³, we can calculate the volume of the prism. As both the shapes have the same height and base,

The volume of the prism = $(12)(3) = 36.$

The volume of the rectangular prism is 36 ft³.

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