Solve and graph the inequality
6X + 32 > -4

Simplifying

6x + 32 = 180

Reorder the terms:

32 + 6x = 180

Solving

32 + 6x = 180

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-32' to each side of the equation.

32 + -32 + 6x = 180 + -32

Combine like terms: 32 + -32 = 0

0 + 6x = 180 + -32

6x = 180 + -32

Combine like terms: 180 + -32 = 148

6x = 148

Divide each side by '6'.

x = 24.66666667

Simplifying

x = 24.66666667

6x + 32> -4

6x > -4 - 32

6x > -36

x > -6

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.

arc length = 6.63311 ft.

step-by-step explanation:

the formula the arc measure is:

arc length s=2πr(c)/360

where:

c   is the central angle of the arc in degrees

r   is the radius of the arc

π   is pi, approximately 3.142

using the above formula we get

s =

thus we find that arc length of an arc for a circle of radius 20 feet and central angle 19 degrees is

6.63311 feet