Sergio is making punch for a school party. the recipe he is using calls for 3 cups of fruit juice to make 7 cups of punch. he made a ratio table to him determine how much fruit juice he will need. cups of fruit juice 3 15 90 cups of punch 7 35 210 sergio thinks he will need 90 cups of fruit juice to make 210 cups of punch. explain his method. how many cups of fruit juice would sergio need to make 154 cups of punch? explain your calculations.

it would be 6xy and -16xy.

pi x^2

step-by-step explanation:

pi times x squared

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240