Answer:
Step-by-step explanation:
The segment addition theorem tells you ...
CD +DE = CE
x^2 +12x = 32 -2x
Subtract the right side to put this in standard form.
x^2 +14x -32 = 0
(x +16)(x -2) = 0
x = -16 or 2
In order for DE to have a positive length, we must have x > 0. So ...
CD = x^2 = 2^2 = 4
DE = 12x = 12(2) = 24
CE = 32 -2x = 32 -2(2) = 28
Answer:
3 1/2 cups
Step-by-step explanation:
Let's start by figuring out how much sugar Karen needs in total.
She needs (1+1/3) cups for her original recipe. To triple that, we need (1+1/3) 3 times. We can calculate this by multiplying it by 3.
(1+1/3) * 3 = 3 + 1 = 4
Karen needs 4 cups in total. She has 1/2 cup. The difference is how much more she needs. Therefore, she needs 4 - 1/2 = 3 1/2 cups
Let L and W be the length and width of the given rectangle, respectively. Perimeter is calculated through the equation,
P = 2L + 2W
Substituting the perimeter,
36 = 2L + 2W
Simplifying,
18 = L + W
The area is calculated by multiplying the length and width as below,
A = 80 = LW
Substituting the expressions,
80 = (L)(18 - L)
The value of L from the equation is 8. With this, the value of W is equal to 10.
Therefore, the dimensions of the rectangle are 8 m by 10 m.
