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suppose Q is the midpoint of PR. Use the information to find the missing value. PQ = 6x + 25 and QR = 16 - 3x; Find PR

Respuesta :

sqdancefan

Answer:

  38

Step-by-step explanation:

A graph shows PQ = QR when x=-1 and PQ = QR = 19.

Then ...

  PR = PQ + PR

  = 19 + 19

  PR = 38

_____

If you want to solve this algebraically, you can set PQ = QR:

  6x +25 = 16 -3x

  9x = -9 . . . . . add 3x -25

  x = -1

  PQ = 6(-1) +25 = 19 . . . . this is half the length of PR

  PR = 2×PQ = 2×19

  PR = 38

Ver imagen sqdancefan
MrRoyal

The midpoint of a line segment is the point equidistant from the endpoints of the line. Length PR is 38 units long.

Given that:

[tex]PQ = 6x + 25[/tex]

[tex]QR = 16-3x[/tex]

If Q is the midpoint, then the following conditions are true

  1. PQ = QR
  2. PR = 2 x PQ = 2 x QR

Using the first condition, we have:

[tex]6x + 25 = 16 - 3x[/tex]

Collect like terms

[tex]6x + 3x = 16 - 25[/tex]

[tex]9x = -9[/tex]

Divide both sides by 9

[tex]x=-1[/tex]

Using the second condition, we have:

[tex]PR = 2 \times PQ[/tex]

This gives

[tex]PR = 2 \times (6x + 25)[/tex]

Substitute -1 for x

[tex]PR = 2 \times (6 \times -1 + 25)[/tex]

[tex]PR = 2 \times 19[/tex]

[tex]PR = 38[/tex]

Hence, the length of PR is 38 units

Read more about midpoints at:

https://brainly.com/question/8943202

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