Tawnee is designing a playground in the shape of a rectangle as shown below. If Tawnee increases the length and width of the playground by a scale factor of 3, what will be the resulting effect on the perimeter of the new playground? The perimeter of the new playground will be one-ninth the perimeter of the original.
The perimeter of the new playground will be one-third the perimeter of the original.
The perimeter of the new playground will be nine times the perimeter of the original.
The perimeter of the new playground will be three times the perimeter of the original.

answer: b.

step-by-step explanation:

the y coordinate for point b is 0, and answer b is the only one with that y coordinate.

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)