Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Triangle R Q S is cut by line segment T V. Line segment T V goes from side Q R to side R S. The length of R V is x + 10, the length of V S is x, the length of R T is x + 4, and the length of T Q is x minus 3. Which value of x would make Line segment T V is parallel to Line segment Q S?
PLEASE HURRY

Sagot :

sqdancefan

9514 1404 393

Answer:

  x = 10

Step-by-step explanation:

In order for TV to be parallel to QS, it must divide the sides of the triangle proportionally.

  RT/TQ = RV/VS

  (x+4)/(x-3) = (x+10)/(x)

  1 +7/(x-3) = 1 +10/x . . . . expand each fraction

  7/(x -3) = 10/x . . . . . . . . subtract 1

  7x = 10(x -3) . . . . . . . . . cross multiply

  30 = 3x . . . . . . . . . . . . add 30-7x, simplify

  10 = x . . . . . . . . . . . . . . divide by 3

The value of x that makes the segments parallel is 10.

_____

Alternate solution

You can cross multiply the first fraction we wrote to get ...

  x(x +4) = (x -3)(x +10)

  x^2 +4x = x^2 +7x -30 . . . eliminate parentheses

  30 = 3x . . . . . . subtract x^2+4x-30 from both sides

Answer: C. 10

Step-by-step explanation:

i got it right on the test

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.