1. Solve the given quadratic equations by extracting square roots. Provide an extra sheet for your solutions.

Mathematics

2 answers:

kondor19780726 [428]2 years ago

8 0

Answer:

1. m=-8 or m=8

2. x=-3 or x=3

3. equation has no roots

(thus if represented in graph format, the graph will not

intersect the x-axis)

4. s=-√12 or s=√12

5. x=0 or x=4

Step-by-step explanation:

for questions 1, 2 and 4, nite that when there is an even power of a variable in an equation, there will be an introduction of extra solutions thus you cannot just assume that the numbers attained will always be positive as the multiplication if negative numbers will also give you a positive answer especially when you square the number.

kirill [66]2 years ago

6 0

Step-by-step explanation:

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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>

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