If 2/3 of the distance from the y-axis to point A (−30, −45) is equal to 1/4 of the distance from the x-axis to point B(5a, 2a), where a > 0, what is the value of a?

The value of a is 80

Step-by-step explanation:

The distance of a point from the y-axis can be written as  because the x-coordinate of the y-axis is zero.

Similarly, the distance of a point  from the x-axis can be written as

since the y-coordinate of the x-axis is zero.

In this problem:

- The distance of the point A (−30, −45) from the y-axis can be written as

- The distance of point B (5a,2a) from the x-axis can be written as

Since

We are told that 2/3 of the distance from the y-axis to point A (−30, −45) is equal to 1/4 of the distance from the x-axis to point B(a, a), which means

Therefore,

And solving for a,

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!