Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

enya.gold

  • one year ago

[Work Included] In ABC, centroid D is on median AM. AD = x + 5 and DM = 2x – 1 Find AM.

  • This Question is Closed
  1. enya.gold
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1357236456605:dw|

  2. enya.gold
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It looks more like an orthocenter, but for the sake of it, let's say it is a centroid.

  3. enya.gold
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ x + 5 = 2x - 1\]\[5 + x - 2x = 2x - 2x - 1\]\[5 - x = -1\]

  4. enya.gold
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Subtract five from both sides. \[-x = -1 - 5\]\[-x = -6\]

  5. enya.gold
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[x = 6\]

  6. enya.gold
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now I can plug in the missing numbers. \[6 + 5 = 2(6) - 1\]\[11 = 12 - 1\]\[= 11\]

  7. KingGeorge
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I think you're incorrect in assuming that \(x+5\) must equal \(2x-1\). The centroid of a triangle is located at a point 2/3 of the way along the median, and not 1/2 of the way along the median.

  8. enya.gold
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    In that case, I'll tweak a few things here. \[x + 5 = 2(2x - 1)\]\[x + 5 = 4x - 2\] Subtracting 4 from both sides.

  9. enya.gold
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[5 - 3x = -2\]\[-3x = -2 - 5\]\[-3x = -7\]

  10. enya.gold
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[x = \frac{ -7 }{ -3 }\]

  11. KingGeorge
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    That looks good to me. You can simplify that to \(\dfrac{7}{3}\) if you want.

  12. KingGeorge
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You're welcome.

  13. enya.gold
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @KingGeorge The answer was really 11. Guess I should have trusted my gut, ha.

  14. KingGeorge
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oops :( I guess that would be my fault.

  15. KingGeorge
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    However, I think we just forgot the last step in the problem. We found \(x=7/3\), but AM is equal to \((x+5)+(2x-1)\). If we plug in our value for \(x\) into this, we get\[\frac{7}{3}+4+\frac{14}{3}=\frac{21}{3}+4=7+4=11\]

  16. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.