A recipe for fruit punch requires 5 cups of pineapple juice and 8 cups of ginger ale. Find the amounts of pineapple juice and ginger ale that must be used to produce different amounts of this punch.

answer below

Step-by-step explanation:

simply multiply by different numbers so...

5/8 x 2 = 10/16

5/8 x 3 = 15/24

and so on; as long as it can reduce to 5/8, it works!

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.