John owns a hardware store. He has at most $1,000 to spend on restocking his pipes. Steel pipes cost $100, and plastic pipes cost $50. He needs at least 5 steel pipes and no more than 10 plastic pipes. Identify the graph
that shows all possible combinations of steel and plastic pipes that he can buy. Also identify two possible
combinations.

lockers 1, 4, 9, 16, 25, 40, and 49 are open

i ran through it by the other answer is wrong

2

step-by-step explanation:

hello from mrbilldoesmath!

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

discussion:

in general, the factorization of a^3 + b^3 is

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

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

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

you,

mrb

(a + b) (a^2 - a b + b^2)