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Ilya [14]
3 years ago
5

Harold paid 5% in sales tax on his new "smart fabric" warm-ups.

Mathematics
1 answer:
natita [175]3 years ago
3 0

Answer:

The pre-tax price of "smart fabric" warm-ups is $745 .

Step-by-step explanation:

Let us assume that the pre-tax price of the "smart fabric" warm-ups be x .

As given

arold paid 5% in sales tax on his new "smart fabric" warm-ups.  

if harnold paid 37.25 in sales tax on the warm ups .

5% is written in the decimal form .

=\frac{5}{100}

= 0.05

Equations becomes

0.05 × x = 37.25

0.05x = 37.25

x = \frac{37.25}{0.05}

x = $745

Therefore the pre-tax price of "smart fabric" warm-ups is $745 .

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\huge\boxed{y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{2}{3}x+\dfrac{4\sqrt{13}}{3}}

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The equation of a line:

y=mx+b

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substitute:

y=\dfrac{2}{3}x+b

The formula of a distance between a point and a line:

General form of a line:

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Distance:

d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+b^2}}

Convert the equation:

y=\dfrac{2}{3}x+b     |<em>subtract y from both sides</em>

\dfrac{2}{3}x-y+b=0    |<em>multiply both sides by 3</em>

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substitute:

d=4

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4=\dfrac{|3b|}{\sqrt{13}}\qquad|    |<em>multiply both sides by \sqrt{13}</em>

4\sqrt{13}=|3b|\iff3b=-4\sqrt{13}\ \vee\ 3b=4\sqrt{13}   |<em>divide both  sides by 3</em>

b=-\dfrac{4\sqrt{13}}{3}\ \vee\ b=\dfrac{4\sqrt{13}}{3}

Finally:

y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{4\sqrt{13}}{3}

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