Write the equation of the graph obtained when the graph of y=1/x is compressed vertically by a factor of 0.25, translated 4 units right, and then translated 3 units up.

The equation is y = 0.25/(x - 4) + 3

Step-by-step explanation:

If we have a function y = f(x)

A compression means that we multiply the function by a factor smaller than 1.

Then the vertical compression by a factor of 0.25 is:

y = 0.25*f(x)

a translation by A units to the right, means that we need to valuate the function in x - A.

So now we have:

y = 0.25*f(x - 4)

A translation in the y-axis means that we need to add a constant to the equation, then if we tralate it by 3 units up, we have:

y = 0.25*f(x - A) + 3

Then, if f(x) = 1/x

Our new equation is:

y = 0.25/(x - 4) + 3

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15

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