16. solve the equation
3x + (2x + 6) = 6x + 1.152

x=4.848

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3x+2x+6=6x+1.152

(3x+2x)+(6)=6x+1.152(Combine Like Terms)

5x+6=6x+1.152

5x+6=6x+1.152

Step 2: Subtract 6x from both sides.

5x+6−6x=6x+1.152−6x

−x+6=1.152

Step 3: Subtract 6 from both sides.

−x+6−6=1.152−6

−x=−4.848

Step 4: Divide both sides by -1.

−x

−1

=

−4.848

−1

x=4.848

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