A board is 65 inches long into two pieces, so that one piece is 7 inches shorter than twice the length of the other pieces. Find the length of two pieces

24 in, 41 in

Step-by-step explanation:

Set shorter piece is x in, and another longer one is y.

1. x + y = 65

2. y = 2x - 7

plug in the second equation into y of the first equation, we get:

x + (2x - 7) = 65

x + 2x - 7 = 65

    3x - 7 = 65  （Add 7 to the both side)

          3x = 72     (Divide 3 to both side)

            x = 24 in

Plug x in the second equations to slove y.

y = 2x - 7

y = 2(24) - 7

y = 41 in

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)