Segment AB falls on line 6x + 3y = 9. Segment CD falls on line 4x + 2y = 8. What is true about segments AB and CD?

A. They are parallel because they have the same slope of −2.
B. They are perpendicular because they have slopes that are opposite reciprocals of −2 and one half.
C. They are parallel because they have the same slope of 2.
D. They are perpendicular because they have opposite reciprocal slopes 2 and negative one half.

Option A is the correct answer

Step-by-step explanation:

We are given that Segment AB falls on line 6x + 3y = 9. Segment CD falls on line 4x + 2y = 8. Thus let's make y the subject in each segment;

For segment AB;

6x + 3y = 9

Rearranging, we have;

3y = -6x + 9

Divide each term by 3 to give;

y = -2x + 3

For segment CD;

4x + 2y = 8

Rearranging ;

2y = -4x + 8

Divide each term by 2 to give;

y = -2x + 4

So, each line has a slope of -2 and are therefore parallel.

Option A is the correct answer

answer: f true

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