Question is in pic! Plz show work!

Mathematics

1 answer:

kipiarov [429]3 years ago

4 0

Answer:

x = 10 and x = -2

Step-by-step explanation:

The equation has 2 solutions because we have a square. When things are squares, we get a positive and negative solution.

(x-4)^2 - 28 = 8

Add 28 to each side

(x-4)^2 - 28+28 = 8+28

(x-4)^2 = 36

Take the square root of each side

sqrt((x-4)^2) = ±sqrt(36)

x-4 = ±6

Add 4 to each side

x-4+4 = 4 ±6

x = 4 ±6

x = 4+6 and x = 4-6

x = 10 and x = -2

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Step-by-step explanation:

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<h3><u>Volume of a rectangular prism</u></h3>

$\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\&=4 \times 4 \times 2\\&=16 \times 2\\&=32\;\; \sf m^3\end{aligned}$

<h3><u>Volume of a pyramid</u></h3>

<u />

From inspection of the given diagram, the slant height of the pyramid is 3.5 m.

Calculate the perpendicular height of the pyramid using Pythagoras Theorem:

$\begin{aligned}\implies a^2+b^2&=c^2\\2^2+h^2&=3.5^2\\h^2&=8.25\\h&=\sqrt{8.25}\;\; \sf m\end{aligned}$

Therefore:

$\begin{aligned}\textsf{Volume of a pyramid}&=\dfrac{\sf length \times width \times height}{3}\\\\&=\dfrac{\sf 4 \times 4 \times \sqrt{8.25}}{3}\\\\& = 15.31883372\;\; \sf m^3\end{aligned}$

<h3><u>Volume of the garden shed</u></h3>

$\begin{aligned}\implies \textsf{Volume of shed}&=\textsf{Volume of rectangular prism}+\textsf{Volume of pyramid}\\&=32+15.31883372\\& = 47.3\;\; \sf m^3\;(nearest\;tenth)\end{aligned}$