A rope that is 168 ft long is to be cut into three pieces such that the second piece is 6 ft less than three times the first, and the third is 2 ft more than two-thirds of the second. Find the length of the longest piece.

Length of longest piece is 82 ft

Step-by-step explanation:

Let the measure of the second piece be x

First piece be y

second piece is 6 ft less than 3 times the first

x = 3y - 6

y = (x + 6)/3

3rd piece = 2 + 2/3 * x

= 2 + 2x/3

Adding all equals 168

we only add in terms of x

so we have;

x + (x + 6)/3 + 2 + 2x/3 = 168

Multiply through by 3

3x + x + 6 + 6 + 2x = 504

6x + 12 = 504

6x = 492

x = 492/6

x = 82 ft

So the other pieces are

(x + 6)/3 = 82+6/3 = 88/3 ft

And lastly

2 + 2x/3

= 2 + 164/3 ft

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet