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BaLLatris [955]
3 years ago
15

be rectangular prism and rectangular pyramid have the same volume. determine the value of x, the height of the pyramid.

Mathematics
1 answer:
Marina CMI [18]3 years ago
7 0
ANSWER

x= 9 \: in

EXPLANATION

The volume of a rectangular prism is given by the formula,

V = l \times b \times h
We substitute the dimensions to obtain,

V = 6 \times 3 \times 12 \: {in}^{3}

The volume of the rectangular pyramid is,

V = \frac{1}{3} \times 6 \times 12 \times x \: {in}^{3}

Equating the two volumes gives,

\frac{1}{3} \times 6 \times 12 \times x = 6 \times 3 \times 12

We divide through by 6×12 to get,

\frac{x}{3}=3

We solve for x to obtain,

x = 3 \times 3

x = 9 \: in
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<em><u>Solution:</u></em>

<em><u>Factorisation:</u></em>

Factorization is a method of writing numbers as the product of their factors or divisors.

In other words we can say, Finding what to multiply together to get an expression.

It is like "splitting" an expression into a multiplication of simpler expressions.

<em><u>Methods of factorisation:</u></em>

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<em><u>Factoring out the GCF:</u></em>

This methods means that factoring out common factors

For example:

12x^2 + 3x = 3x(4x + 1)

This can be used when each term in given expression shares a common factor

<em><u>The sum-product pattern</u></em>

A quadratic equation may be expressed as a product of two binomials

For example:

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This method can be used for quadratic equations of form ax^2 + bx + c = 0

<em><u>The grouping method</u></em>

If the polynomial is of the form  ax^2 + bx + c and there are factors of ac that add up to b , we can use this method

For example:

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<em><u>The perfect square trinomial pattern</u></em>

If the first and last terms are perfect squares and the middle term is twice the product of their square roots , we can use this method

For example:

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If the expression represents a difference of squares, we can use this method

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Answer:

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Step-by-step explanation:

Lets call measure of angle A is <em><u>X-10</u></em>

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Lets call measure of angle D is 2.5X+20

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