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kifflom [539]
3 years ago
7

For the equation y = 3.5x and y= 25x + 40.50, x represent time in hours and y represents cost in dollars. Which equation is not

the equation of a proportional relationship? Explain.
Mathematics
1 answer:
dem82 [27]3 years ago
5 0

We are given equations y =3.5x and y=25x +40.50.

Where x represent time in hours and y represents cost in dollars.

We need to determine that which equation is not the equation of a proportional relationship?

In first equation we have slope 3.5 and y-intercept 0.

In second equation, we have slope 25 and y-intercept 40.50.

<em>In order to have a a proportional relationship, there should be y-intercept =0.</em>

<h3>Therefore, y= 25x + 40.50 is not the equation of a proportional relationship.</h3>
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We have opposite = 17 and adjacent = x.

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substitute:

\dfrac{17}{x}=\dfrac{\sqrt3}{3}       cross multiply

x\sqrt3=(3)(17)     multiply both sides by √3

x(\sqrt3)(\sqrt3)=51\sqrt3

3x=51\sqrt3      divide both sides by 3

x=17\sqrt3

Use the Pythagorean theorem:

y^2=(17\sqrt3)^2+17^2\\\\y^2=289(\sqrt3)^2+289\\\\y^2=289\cdot3+289\\\\y^2=867+289\\\\y^2=1156\to y=\sqrt{1156}\\\\y=34

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Other method.

30^o-60^o-90^o triangle.

The sides are in the ratio 1:2:\sqrt3\to17:y:x

Therefore

17:(2\cdot17):(17\sqrt3)\to17:34:17\sqrt3\to x=34,\ y=17\sqrt3

 


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