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aleksandr82 [10.1K]
3 years ago
13

Given m∠D = 70°, m∠E = 42, and m∠EHG = 68°, prove DF is parallel to GH.

Mathematics
1 answer:
Pie3 years ago
4 0

we know that

If DF is parallel to GH

then

the measure of the angle EGH must be equal to 70° by corresponding angles

so

<u>Find the measure of the angle EGH </u>

In the triangle EGH

the sum of the internal angles must be equal to 180 degrees

42°+68°+∠EGH=180°

solve for ∠EGH

∠EGH=180-(42+68)

∠EGH=180-110

∠EGH=70°

therefore

The lines DF and GH are parallel

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Answer:

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Which statement is true?​
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<h2>Hello!</h2>

The answer is:

The second option,

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<h2>Why?</h2>

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\sqrt[m]{x}\sqrt[m]{y}=\sqrt[2m]{xy}

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<h2>Second option,</h2>

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The statement is true, we can prove it by using the following properties of exponents:

(a^{b})^{c}=a^{bc}

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(\sqrt[m]{x^{a} } )^{b}

So, applying the properties, we have:

(\sqrt[m]{x^{a} } )^{b}=(x^{\frac{a}{m}})^{b}=x^{\frac{ab}{m}}\\\\x^{\frac{ab}{m}}=\sqrt[m]{x^{ab} }

Hence,

(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }

<h2>Third option,</h2>

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The statement is false, the correct form of the statement (according to the property of roots) is:

a\sqrt[n]{x}+b\sqrt[n]{x}=(a+b)\sqrt[n]{x}

<h2>Fourth option,</h2>

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The statement is false, the correct form of the statement (according to the property of roots) is:

\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=\sqrt[m]{\frac{x}{y} }

Hence, the answer is, the statement that is true is the second statement:

(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }

Have a nice day!

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