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3 years ago

Does the table show a direct proportional relationship? If so, what is the constant of proportionality? X 4 7 12 Y 32 56 96

Mathematics

1 answer:

dalvyx [7]3 years ago

6 0

<h3>Answer: Yes we have a direct proportional relationship</h3><h3>constant of proportionality = 8</h3>

equation is y = 8x

=============================================

Explanation:

Divide each x and y pair like so: y/x

If we get the same result each time, then we have a direct proportion.

y/x = 32/4 = 8

y/x = 56/7 = 8

y/x = 96/12 = 8

Each time we get the same result 8, which is the constant of proportionality. The table does show a direct proportional relationship. The equation is y = 8x which is in the form y = kx. The k value is the constant of proportionality. So k = y/x.

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3 years ago

What is the equation of the quadratic graph with a focus of (8, −8) and a directrix of y = −6?

sp2606 [1]

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$y=-\frac{223}{28}(x-8)^2-7$

Step-by-step explanation:

we are given a quadratic equation

we know that quadratic equation is same as equation of parabola

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$(h,k+\frac{1}{4a} )$

now, we can compare it with given focus

=(8,-8)

we get

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$k+\frac{1}{4a}=-8$

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$y=k-\frac{1}{4a}$

we are given directrix =-6

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we got two equations as

$k+\frac{1}{4a}=-8$

$k-\frac{1}{4a}=-6$

now, we can add both equations

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now, we can plug back all values

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3 years ago