Which expressions represent the product of exactly two factors?
Choose 2 answers
A: x+y
B: 5(x+y)
C: (x-y)(x+y)
D: xyz

B, C,

Step-by-step explanation:

A - This is addition. Finding a product refers to multiplication, so this is not correct.

B - This is multiplication of 5x × 5y, exactly two factors, so this is correct.

C - This is multiplication of (x-y) × (x+y). Each equation inside the parenthesis equals one factor, so this is multiplication of exactly two factors. This answer is also correct.

D - This is multiplication of three factors, x × y × z, and is not correct.

2nd one in the first row is correct

(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