Question # 5 what is the sum?

Mathematics

1 answer:

Blizzard [7]3 years ago

8 0

Answer: C) d+13/d+4

Here’s why:

Step 1: Rewrite the factor
d^2 + 7d +4d +28 / (d+4)^2 + 6 / d+4

Step 2 : factor out d from the expression and factor out 4 from the expression
d × (d+7) + 4(d+7) / (d+4) ^2 + 6 / d+4

Step 3: Factor out d+7 from the expression
(d+7) × (d+4) / (d+4) ^2 + 6 / d+4

Step 4: simply the expression
d+7 / d+4 + 6/ d+4

Step 5: write all numerators above the common denominator
d+7+6 / d+4

Step 6: add the numbers and you get
d+13 / d+4

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Find the volume of the garden shed

Leno4ka [110]

Answer:

47.3 m³

Step-by-step explanation:

The garden shed is made up of a rectangular prism and a pyramid.

<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>

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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>

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