Mr. Holloway is a craftsman who makes custom guitars by hand. His last order was for 2 guitars, and it took him 8 weeks to make them. He receives an order to make 7 guitars. If he makes the guitars at the same rate, how long will it take Mr. Holloway to make the guitars?

step-by-step explanation:

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

the answer is 40.

proof:

d. corresponding side lengths in similar triangles are proportional in length.

step-by-step explanation: