In parallelogram MNPQ, side MN is seven inches longer than twice the length of side NP. If the perimeter of MNPQ is 68 inches, then determine the length of NP. Show how you solved for your answer.

NP = 9 inches

Step-by-step explanation:

In a parallelogram, the opposite sides are equal.

If the length of the longer side is MN, it means that the length of the two opposite longer sides is 2MN.

If the length of the shorter side is NP, it means that the length of the two opposite shorter sides is 2NP.

The perimeter is 2MN + 2NP

If the perimeter of MNPQ is 68 inches, it means that

2MN + 2NP = 68- - - - - - - - - - - -1

In parallelogram MNPQ, side MN is seven inches longer than twice the length of side NP. It means that

MN = 2NP + 7- - - - - - - - - - -2

Substituting equation 2 into equation 1, it becomes

2(2NP + 7) + 2NP = 68

4NP + 14 + 2NP = 68

4NP + 2NP = 68 - 14

6NP = 54

NP = 54/6

NP = 9 inches

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.