WILL GIVE BRAINLIEST HELP!!

Mathematics

1 answer:

Lera25 [3.4K]2 years ago

5 0

Answer is : $\sqrt[4]{5}$

Explanation:
$\frac{ \sqrt[4]{400}}{ \sqrt[4]{5}} = \frac{ \sqrt[4]{4*5*5*2*2} }{\sqrt[4]{5}}$

= $\frac{\sqrt[4]{5*5*2*2*4}}{\sqrt[4]{5}} = \sqrt[4]{5*2*2*4}$

= $\sqrt[4]{5*2*2*4} = \sqrt[4]{80}$
= $\sqrt[4]{2*2*2*2*5}$
= $\sqrt[4]{2^{4}} \sqrt[4]{5}$
= $\sqrt[4]{5}$

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Cynthia Besch wants to buy a rug for a room that is 24 ft wide and 33 ft long. She

qaws [65]

<h3>Answer: 16 ft by 25 ft</h3>

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Explanation:

Refer to the diagram below.

The outer dimensions 24 ft and 33 ft shrink down to 24-2x ft and 33-2x ft respectively. This subtraction of 2x is due to subtracting two copies of x per side.

The carpet has area of (24-2x)(33-2x)

Cynthia can afford to buy 400 sq ft of carpet

So we set 400 equal to that previous expression and solve for x

(24-2x)(33-2x) = 400

24(33-2x) - 2x(33-2x) = 400

792-48x - 66x + 4x^2 = 400

4x^2 - 114x + 792 = 400

4x^2 - 114x + 792-400 = 0

4x^2 - 114x + 392 = 0

From here, use the quadratic formula to isolate x.

Plug in a = 4, b = -114, c = 392

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-114)\pm\sqrt{(-114)^2-4(4)(392)}}{2(4)}\\\\x = \frac{114\pm\sqrt{6724}}{8}\\\\x = \frac{114\pm82}{8}\\\\x = \frac{114+82}{8} \ \text{ or } \ x = \frac{114-82}{8}\\\\x = \frac{196}{8} \ \text{ or } \ x = \frac{32}{8}\\\\x = 24.5 \ \text{ or } \ x = 4\\\\$