Renee is creating a rectangular garden in her backyard. the length of the garden is 8 feet. the perimeter of the garden must be at least 30 feet and no more than 32 feet. use a compound inequality to find the range of values for the width w of the garden.

The appropriate compound inequality is then 14 ft ≤ W ≤ 16 ft

Step-by-step explanation:

30 ft perimeter:  P = 30 ft = 2L + 2W = 2(8 ft) + 2W

Solving for W, we get:  30 ft - 16 ft = 14 ft.  The minimum width, W, is 14 ft.

32 ft perimeter:  

P = 32 ft = 2L + 2W = 2(8 ft) + 2W

Solving for W, we get:  32 ft - 16 ft = 16 ft.  The minimum width, W, is 16 ft.

The appropriate compound inequality is then 14 ft ≤ W ≤ 16 ft

step-by-step explanation:

what is the figure? attach a picture.

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)