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2 years ago

13

A triangle has vertices at coordinates $(1, 2), (7, 10)$ and $(1, 12)$. What is the number of units in the length of the shortes

t side of the triangle?

1 answer:

const2013 [10]2 years ago

7 0

Answer:

The number of units in the length of the shortest side of the triangle is 6.325 units or 2 sqrt 10.

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Please help me with Algebra 2 questions (2).

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8. The simplified form of the expression is $- 5 x^{\frac{4}{5}}y^{3}$

11. The value of x is 4

<h3>Simplifying an expression</h3>

From the question, we are to simplify the give expression

The given expression is

$y^{3}\sqrt[5]{32x^{4} } - 7\sqrt[5]{x^{4}y^{15} }$

$y^{3} (32x^{4} )^{\frac{1}{5} } - 7(x^{4}y^{15} )^{\frac{1}{5}$

$y^{3} \times 32^{\frac{1}{5} } x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{\frac{15}{5}}$

$y^{3} \times 2^{5 \times} ^{\frac{1}{5} } \times x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{3}$

$y^{3} \times 2 \times x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{3}$

$2 x^{\frac{4}{5} } y^{3} - 7 x^{\frac{4}{5}}y^{3}$

$= - 5 x^{\frac{4}{5}}y^{3}$

11. $\frac{1}{2}(5x+7 )^{\frac{2}{3} } =\frac{9}{2}$

Multiply both sides by 2

$2 \times \frac{1}{2}(5x+7 )^{\frac{2}{3} } =2 \times \frac{9}{2}$

$(5x+7 )^{\frac{2}{3} } =9$

Multiply both sides by a power of 3/2

$(5x+7 )^{\frac{2}{3} \times {\frac{3}{2} } } =9^{\frac{3}{2} }$

$(5x+7 )=3^{2 \times} ^{\frac{3}{2} }$

$5x+7 =3^{3}$

$5x+7 =27$

$5x =27-7$

$5x = 20$

$x = \frac{20}{5}$

x = 4

Hence,

8. The simplified form of the expression is $- 5 x^{\frac{4}{5}}y^{3}$

11. The value of x is 4

Learn more on Simplifying expressions here: brainly.com/question/11688560

#SPJ1

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