M <N=...the scale factor is 2

Mathematics

1 answer:

aivan3 [116]2 years ago

7 0

We know that the sum of the internal angles in each triangle is 180°.

Therefore we have the equation:

$m\angle C+m\angle D+m\angle E=180^o$

substitute and solve:

$79+(6x+11)+(7x-14)=180\\(6x+7x)+(79+11-14)=180\\13x+76=180\ \ \ |-76\\13x=104\ \ \ |:13\\x=8$

We have

$m\angle N=3x+18$

substitute the value of x to the expression:

$m\angle N=3(8)+18=24+18=42$

Answer: m∠N = 42 degrees

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The population of a local species of dragonfly can be found using an infinite geometric series where a1=42 and the common ratio

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$\bf \textit{sum of an infinite geometric serie}\\\\
\stackrel{for~~|r|\ \textless \ 1}{S=\sum\limits_{i=0}^{\infty}~a_1r^i\implies \cfrac{a_1}{1-r}}\qquad 
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\end{cases}
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Scale factor is 3/2.4
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