The homeowner's association is sponsoring a spaghetti supper. tickets to the event cost $10.50 per person. sixty-two people have already purchased tickets. the total number of tickets available is 245. if y = 10.50x represents the amount of money that can be received from the number of tickets that remain to be sold, what values are appropriate for the domain of the function? a) x > 62 b) 1 < x ≤183 c) 0 ≤ x ≤183 d) 62 ≤ x ≤245

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step-by-step explanation:

(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