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Mathematics

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VARVARA [1.3K]3 years ago

7 0

Answer:

Here is the answer to your question it is in this picture

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Find the missing length

shutvik [7]

The small triangle and big triangle are similar - this means they have the same angles. So, if you know the ratio of a side of the big triangle (12) to a side of the small triangle inside it (4), you know the ratio of the other sides. In this case, the side ratio (small to big triangle) is 1/3. Thus, the missing side length is 18/3=6.
Brainliest? ;D

7 0

4 years ago

(01.02 HC)

Phoenix [80]

By applying radical, power and rational properties we have the following results after simplifying expressions:

$x^{\frac{3}{4} }$
x
$x^{\frac{11}{10} }$
x

<h3>How to reduce radical and rational expressions into a single power expression with rational exponent</h3>

In this question we need to simplify four given expressions by using the following radical and power properties:

$\sqrt[n]{x} = x^{\frac{1}{n} }$ (1)
$x^{m+n} = x^{m}\cdot x^{n}$ (2)
$x^{m-n} = \frac{x^{m}}{x^{n}}$ (3)
$(x^{m})^{n} = x^{m\cdot n}$ (4)

Now we proceed to simplify each of the four expressions:

$\sqrt[4]{x^{3}} = x^{3/4}$
$\frac{1}{x^{-1}} = (x^{-1})^{-1} = x$
$\sqrt[10]{x^{5}\cdot x^{4}\cdot x^{2}} = \sqrt[10]{x^{11}} = x^{\frac{11}{10} }$
$x^{\frac{1}{3} }\cdot x^{\frac{1}{3} }\cdot x^{\frac{1}{3} } = x$