Mathematics: Asocial worker earns $760 gross pay. if he is married and claims 1 dependent, his state tax rate is 7%, and fica is 7.65%, what is his net pay?

Asocial worker earns $760 gross pay. if he is married

Ответ:

emmanolan112

16.04.2020

Mathematics

$x = \frac{7\sqrt{6}}{2}\\\\$

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Explanation:

Focus on the upper triangle. This is a 30-60-90 triangle. The short leg is 7 and the long leg is $7\sqrt{3}$ . The long leg is always sqrt(3) times that of the short leg (and this only works for 30-60-90 triangles).

In short, the horizontal length is $7\sqrt{3}$ units long.

Now move to the lower triangle. This is a 45-45-90 triangle with congruent legs (each are x units long). We just found the hypotenuse is $7\sqrt{3}$

We can use the pythagorean theorem to say the following:

$a^2 + b^2 = c^2\\\\x^2 + x^2 = (7*\sqrt{3})^2\\\\2x^2 = 147\\\\x^2 = \frac{147}{2}\\\\x = \sqrt{\frac{147}{2}}\\\\x = \frac{\sqrt{147}}{\sqrt{2}}\\\\x = \frac{\sqrt{147}*\sqrt{2}}{\sqrt{2}*\sqrt{2}}\\\\x = \frac{\sqrt{147}*\sqrt{2}}{2}\\\\x = \frac{\sqrt{147*2}}{2}\\\\x = \frac{\sqrt{294}}{2}\\\\x = \frac{\sqrt{49*6}}{2}\\\\x = \frac{\sqrt{49}*\sqrt{6}}{2}\\\\x = \frac{7\sqrt{6}}{2}\\\\$

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Asocial worker earns $760 gross pay. if he is married and claims 1
dependent, his state tax rate is 7%, and fica is 7.65%, what is his net
pay?

Ответ:

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