The plan for a city park shows that the park is a quadrilateral with straight paths along the diagonals. For what values of the variables is the park a parallelogram? In this case, what are the lengths of the paths?

Step-by-step explanation:

Diagonals of parallelogram bisect each other;

Substitute values:

11y + 33 = 14y - 12 ⇒ 14y - 11y = 33+12 ⇒ 3y = 45 ⇒ y = 15

3x + 5y = 6x + 3y ⇒ 6x - 3x = 5y - 3y ⇒ 3x = 2y ⇒ 3x = 30 ⇒ x = 10

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3

x=6 and x=3

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