Do these ratios make a proportion? 4:10 and 6:15

I NEED THIS ASAP!!! Thanks!

To see if these ratios make a proportion let us first change them into fractions

= 4:10 = 4/10 = 4 ÷ 2 / 10 ÷ 2 = 2/5

= 6:15 = 6/15 = 6 ÷ 3 / 15 ÷ 3 = 2/5

= Since both these ratios are getting simplified into a same fraction , they are proportional .

Therefore , 4 : 10 :: 6 : 15 ( 4 : 10 is proportional to 6 : 15 )

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)