Up and running auto shop keeps track of their regular customers' data to see if there is a relationship between the life of a car's engine (y) and the number of times the oil is changed (x). when the data is shown on a scatter plot, the equation for the line of best fit is y = 0.4125x + 0.1576. what is the relationship between 0.4125 and the life of the car's engine?

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb

for the free

< < < emily> > >

well in order to answer the question, you have to give us the dimensions of the prism first.

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