4n=1/2(2n-12) check the solution to the example problem by replacing n in the original equation with -2 and evaluating both sides. what true statement do you get?

The true statement is that the expression is satisfied for n = -2.

Step-by-step explanation:

Given:

To check:

Left hand side = Right-hand side ( for n = -2)

Proof :

For n = -2

Consider  Left hand side of the equation given above.

∴ Left hand side = 4n

                            = 4×(-2)   ......................for n = -2

                            = -8

Consider Right-hand side of the equation given above

∴ Right-hand side =

Now we get Left hand side equal to Right hand side

i.e. Left hand side = Right hand side

i.e. is true for n = -2

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.

(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