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3 years ago

I need help finishing this.

Mathematics

1 answer:

tekilochka [14]3 years ago

3 0

Answer:

3x³

Step-by-step explanation:

(81x¹² / 3x³)^⅓

(27x⁹)^⅓

You got a good start. To finish, rewrite 27 as 3³, then multiply the exponents of each factor by ⅓.

(3³ x⁹)^⅓

3x³

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Your sister is considering two different shapes for her garden. One is a square with side lengths of 3.5 meters and the other is

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A)=14 meters because 3.5 times 4 is 14
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Which set of numbers could represent the lengths of the sides of a right triangle?

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Answer:

The first set: 8, 15, and 17.

Step-by-step explanation:

By the pythagorean theorem, a triangle is a right triangle if and only if

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$\text{longest side}^2 = 17^2 = 289$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 8^2 + 15^2\\ &=64 + 225 = 289 \end{aligned}$ .

In other words, indeed $\text{hypotenuse}^2 = \text{first leg}^2 + \text{second leg}^2$ . Hence, 8, 15, 17 does form a right triangle.

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Factor out the common factor $2$ to simplify the calculations.

$\text{longest side}^2 = 20^2 = 400$

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 10^2 + 15^2\\ &=100 + 225 = 325 \end{aligned}$ .

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$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

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<h3> $\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 7^2 + 9^2\\ &=49+ 81 = 130 \end{aligned}$ .</h3>

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Hence, by the pythagorean theorem, these three sides don't form a right triangle.

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4 years ago

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