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Gennadij [26K]
2 years ago
12

Hey! pls help me with this question on angles. would really be appreciated. have a nice day.

Mathematics
1 answer:
Neko [114]2 years ago
7 0

Using supplementary angles, it is found that the measures of the angles are given as follows:

  • m<a = 30º.
  • m<b = 90º.

<h3>What are supplementary angles?</h3>

Supplementary angles are two angles whose sum is of 180º.

An interior angle is supplementary with it's exterior angle, hence:

m<a + 150º = 180º -> m<a = 30º.

The sum of the three interior angles of a triangle is of 180º, hence:

30º + m<b + 60º = 180º

90º + m<b = 180º

m<b = 90º.

More can be learned about supplementary angles at brainly.com/question/12919120

#SPJ1

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Option D:

\frac{25 a^{9} b^{10} }{6 } is equivalent to the given expression.

Solution:

Given expression:

$\frac{(5 a b)^{3}}{30 a^{-6} b^{-7}}

To find which expression is equivalent to the given expression.

$\frac{(5 a b)^{3}}{30 a^{-6} b^{-7}}

Using exponent rule: (ab)^m=a^mb^m

    $=\frac{5^3 a^3 b^{3}}{30 a^{-6} b^{-7}}

Using exponent rule: \frac{1}{a^{m}}=a^{-m}, \quad \frac{1}{a^{-m}}=a^{m}

     $=\frac{125 a^3 b^{3}a^{6} b^{7}}{30 }

     $=\frac{125 a^3 a^{6} b^{3} b^{7}}{30 }

Using exponent rule: a^{m} \cdot a^{n}=a^{m+n}

     $=\frac{125 a^{3+6} b^{3+7} }{30 }

    $=\frac{125 a^{9} b^{10} }{30 }

Divide both numerator and denominator by the common factor 5.

    $=\frac{25 a^{9} b^{10} }{6 }

$\frac{(5 a b)^{3}}{30 a^{-6} b^{-7}}=\frac{25 a^{9} b^{10} }{6 }

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