Lincoln has set up a lemonade stand outside his house and sells small cups and large cups of lemonade. Each small cup holds 6 ounces of lemonade and each large cup hold 18 ounces of lemonade. Lincoln used 780 ounces of lemonade and sold 4 times as many large cups as small cups. Write a system of equations that could be used to determine the number of small cups sold and the number of large cups sold. Define the variables that you use to write the system.

5/6

step-by-step explanation:

if i remember correctly with perpendicular stuff you just take away the negative

(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

6 adults and 9 children went.

a + c = 15

12a + 9c = 153

12(6) + 9(9) = 153

72 + 81 = 153