What is -8/25(x-25)^2 + 32 in the standard form?

(-8 (x + -35) (x - 15))/25

Step-by-step explanation:

Simplify the following:

32 - (8 (x - 25)^2)/25

Hint: | Put the fractions in 32 - (8 (x - 25)^2)/25 over a common denominator.

Put each term in 32 - (8 (x - 25)^2)/25 over the common denominator 25: 32 - (8 (x - 25)^2)/25 = 800/25 - (8 (x - 25)^2)/25:

800/25 - (8 (x - 25)^2)/25

Hint: | Combine 800/25 - (8 (x - 25)^2)/25 into a single fraction.

800/25 - (8 (x - 25)^2)/25 = (800 - 8 (x - 25)^2)/25:

(800 - 8 (x - 25)^2)/25

Hint: | Factor out the greatest common divisor of the coefficients of 800 - 8 (x - 25)^2.

Factor -8 out of 800 - 8 (x - 25)^2:

(-8 ((x - 25)^2 - 100))/25

Hint: | Write 100 as a square in order to express (x - 25)^2 - 100 as a difference of squares.

(x - 25)^2 - 100 = (x - 25)^2 - 10^2:

(-8 ((x - 25)^2 - 10^2))/25

Hint: | Factor the difference of two squares.

Factor the difference of two squares. (x - 25)^2 - 10^2 = ((x - 25) - 10) ((x - 25) + 10):

(-8(x - 25 - 10) (x - 25 + 10))/25

Hint: | Group like terms in x - 25 + 10.

Grouping like terms, x - 25 + 10 = x + (10 - 25):

(-8 x + (10 - 25) (x - 25 - 10))/25

Hint: | Evaluate 10 - 25.

10 - 25 = -15:

(-8 (x - 25 - 10) (x + -15))/25

Hint: | Group like terms in x - 25 - 10.

Grouping like terms, x - 25 - 10 = x + (-25 - 10):

(-8 x + (-25 - 10) (x - 15))/25

Hint: | Evaluate -25 - 10.

-25 - 10 = -35:

(-8 (x + -35) (x - 15))/25

32/80  

91/140

the last one 54 doesn't go into 45. 54/100 ?

step-by-step explanation:

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.