A21-foot rope is cut into 2 pieces. seven less than three times the length of the longer rope piece x is five times the length of the shorter piece, which is (21 − x) ft. find the length of the longer rope piece x in ft

The length of the longer rope piece is 14 ft

Step-by-step explanation:

Let

x -----> the longer piece

y ----> the shorter piece

we know that

The sum of the longer piece plus the shorter piece must be equal to the length of the original piece

x+y=21

y=(21-x) -----> equation A

3x-7=5y ----> equation B

substitute equation A in equation B and solve for x

therefore

The length of the longer rope piece is 14 ft

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3