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luisejr77

Answer: Third option.

Step-by-step explanation:

You can observe in the image provided that:

[tex]RT=RS+ST[/tex]

The measure of RT is represented with the following expression:

[tex]RT=4x+1[/tex]

And ST is represented with this expression:

[tex]ST=3x-4[/tex]

Then, the first step is to substitute each expression into [tex]RT=RS+ST[/tex]:

[tex]4x+1=RS+3x-4[/tex]

The second step is to solve for RS:

[tex]4x+1=RS+3x-4\\\\4x+1-3x+4=RS\\\\RS=4x+1-3x+4[/tex]

And the final step is to add the like terms:

[tex]RS=x+5[/tex]

akposevictor

Based on the segment addition theorem, the expression that represents the measure of segment RS is: x + 5.

What is the Segment Addition Theorem?

If S is a point that lies between points T and R, then, based on the segment addition theorem, we would have, TS + SR = TR.

Given:

  • TS = 3x - 4
  • RS = ?
  • TR = 4x + 1

Thus:

RS = TR - TS (segment addition theorem)

Substitute

TS = (4x + 1) - (3x - 4)

TS = 4x + 1 - 3x + 4

TS = x + 5

Therefore, based on the segment addition theorem, the expression that represents the measure of segment RS is: x + 5.

Learn more about segment addition theorem on:

https://brainly.com/question/1397818

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