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2 years ago

Find the volume of the trapezoidal prism

Mathematics

1 answer:

malfutka [58]2 years ago

4 0

Answer:

228 in³

Step-by-step explanation:

Volume of a trapezoidal prism

V = Area x height

Finding Base Area (on the side here)

A = 1/2 x (a + b) x h
A = 1/2 x (12 + 7) x 6
A = 3 x 19
A = 57 in²

Volume

V = A x h
V = 57 x 4
V = 228 in³

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Given:

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Explanation:

To find the value of x by using completing the square, first, we need to subtract 59 on both sides of the given equation:

So,

From the given equation:

$\begin{gathered} x^2+16x+59=0 \\ x^2+16x+59-59=0-59 \\ x^2+16x=-59 \end{gathered}$

Now,

Take half of the x term and square it:

So,

From the x term,

$\lbrack16\cdot\frac{1}{2}\rbrack^2=64$

Then,

Add 64 on both sides of the above equation.

So,

$\begin{gathered} x^2+16x=-59 \\ x^2+16x+64=-59+64 \\ x^2+16x+64=5 \\ (x+8)^2=5 \end{gathered}$

Hence, an option first is correct:

$(x+8)^2=5$

Now,

From the above square:

$\begin{gathered} (x+8)^2=5 \\ x+8=\pm\sqrt[]{5} \end{gathered}$

Then,

Subtract 8 from both sides of the equation;;

So,

$\begin{gathered} x+8=\pm\sqrt[]{5} \\ x+8-8=\pm\sqrt[]{5}-8 \\ x=\pm\sqrt[]{5}-8 \\ x=\sqrt[]{5}-8,\pm\sqrt[]{5}-8 \\ x=-5.7639,-10.236067 \end{gathered}$

Final answer:

Hence, the value of x is shown below:

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Step-by-step explanation:

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Answer:

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