Two cars got an oil change at the same auto shop. The shop charges customers for each quart of oil plus a flat fee for labor. The oil change for one car required 5 quarts of oil and cost $21.90. The oil change for the other car required 7 quarts of oil and cost $25.40. How much is the labor fee and how much is each quart of oil?

Step-by-step explanation:

Let x = the fee and let y = the cost per quart of oil

x + 5y = 22.45

x + 7y = 25.45     Multiply this equation by (-1) and add it to the 1st equation

-x -7y = -25.45

x + 5y = 22.45

     -2y = -3

        y = $1.50 /quart

x + 5(1.50) = 22.45

     x + 7.50 = 22.45

                 x = $14.95   is the basic fee

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .