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2 years ago

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Bonus: Mr. Rao is planning on making a shed in his backyard (see his plan in the image below). However, local laws require sheds

to be at least 15 feet from the property lines. Describe how Mr. Rao should move his shed to comply with the laws. Be specific about the number of feet and the direction (north, south, east, west) that he should move the shed.

1 answer:

Leviafan [203]2 years ago

6 0

Answer:

North 10 feet, and East 5 feet.

Step-by-step explanation:

So we know that North is ^ way. We also know that East is > way.

These are the two directions we must go, since the property line is both South and West of the shed.

The shed is 10ft East of the property line, and we must be 15ft in that direction. So we must go another 5ft East.

Now, the shed is 5ft North of the property line, and we must be 15ft in that direction. So we must go another 10 feet North.

Hope this helps!

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$\huge \boxed{\mathfrak{Question} \downarrow}$

Expand & simplify ⇨ $( \sqrt{10} - \sqrt{2} ) ^{2}$ . Give your answer in the form $b - c \: \sqrt{5}$ where b & c are integers.

$\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}$

$( \sqrt { 10 } - \sqrt { 2 } ) ^ { 2 }$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(\sqrt{10}-\sqrt{2}\right)^{2}$ .

$\left(\sqrt{10}\right)^{2}-2\sqrt{10}\sqrt{2}+\left(\sqrt{2}\right)^{2}$

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$10-2\sqrt{10}\sqrt{2}+\left(\sqrt{2}\right)^{2}$

Factor $10=2\times 5$ . Rewrite the square root of the product $\sqrt{2\times 5}$ as the product of square roots $\sqrt{2}\sqrt{5}$ .

$10-2\sqrt{2}\sqrt{5}\sqrt{2}+\left(\sqrt{2}\right)^{2}$

Multiply $\sqrt{2}$ and $\sqrt{2}$ to get 2.

$10-2\times 2\sqrt{5}+\left(\sqrt{2}\right)^{2}$

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$10-4\sqrt{5}+2$

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$\boxed{ \boxed{\bf\:12-4\sqrt{5} }}$

Here, b & c are integers where $\boxed{ \sf \: b = 12 \: and \: c = 4}$

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