The Pappas family has two cats, Zeus and Athena. Together they weigh thirteen pounds. Zeus weighs 5 pounds less than Athena. How much does Athena weigh?

Given:

Combine weight of two cats, Zeus and Athena = 13 pounds

Zeus weighs 5 pounds less than Athena.

To find:

The weight of Athena.

Solution:

Let x pounds be the weight of Athena.

Zeus weighs 5 pounds less than Athena.

Weight of Zeus = x - 5 pounds

Combine weight of two cats, Zeus and Athena = 13 pounds

Add 5 on both sides.

Divide both sides by 2.

Therefore, the weight of Athena is 9 pounds.

the area of the rectangle is 35units^2.

step-by-step explanation:

graph it and find the distance.

it is a 5*7 rectangle.

therefore the area is 35units^2.

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0