Let s s be the universal set, where: s = { 1 , 2 , 3 , , 18 , 19 , 20 } s = { 1 , 2 , 3 , , 18 , 19 , 20 } let sets a a and b b be subsets of s s , where: set a = { 2 , 4 , 6 , 12 , 16 , 17 , 19 } a = { 2 , 4 , 6 , 12 , 16 , 17 , 19 } set b = { 3 , 4 , 6 , 7 , 9 , 14 , 16 , 17 } b = { 3 , 4 , 6 , 7 , 9 , 14 , 16 , 17 } find the following: list the elements in the set ( a ∪ b a ∪ b ): ( a ∪ b ) ( a ∪ b ) = { } enter the elements as a list, separated by commas. if the result is the empty set, enter dne list the elements in the set ( a ∩ b a ∩ b ): ( a ∩ b ) ( a ∩ b ) = { } enter the elements as a list, separated by commas. if the result is the empty set, enter dne you may want to draw a venn diagram to answer this question. can someone me

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

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