Graph the following expression on the number line by placing the dot in the proper location. |2 - x | = 4

Plot two points. One point is at -2. The other point is at 6.

Step-by-step explanation:

The rule we'll use is

if |y| = k, then y = k or y = -k

where k is some positive number.

In this case, y = 2-x and k = 4

So we go from

|2-x| = 4

to these two equations

2-x = 4 or 2-x = -4

From here we solve each equation for x

2-x = 4

2-x+x = 4+x

2 = 4+x

4+x = 2

x+4 = 2

x+4-4 = 2-4

x = -2 which is one solution

and

2-x = -4

2-x+x = -4+x

2 = -4+x

-4+x = 2

x-4 = 2

x-4+4 = 2+4

x = 6 is the other solution

answer: 7

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