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anonymous

  • one year ago

Given that Y is the centroid of triangle STU, find X. I added 2x - 3 + 10 = 180

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  1. anonymous
    • one year ago
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  2. phi
    • one year ago
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    the medians are divided by the centroid into the ratio of 2/3 to 1/3

  3. anonymous
    • one year ago
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    So they are equal, I'm thinking..

  4. phi
    • one year ago
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    in other words, the "long side" is 2 times bigger than the "short side" here the long side is 10 and the short side is 2x-3

  5. anonymous
    • one year ago
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    Oh, I think I get it now.. so it's 2(20)-3

  6. phi
    • one year ago
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    re-think that. long side is 2 * short side replace "long side" with 10 replace "is" with = replace "short side" with (2x-3)

  7. anonymous
    • one year ago
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    oh okay, now I think it is 2 times 10 minus 3..

  8. phi
    • one year ago
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    can you do each of these steps: long side is 2 * short side replace "long side" with 10 replace "is" with = replace "short side" with (2x-3) can you do that ? what do you get ?

  9. anonymous
    • one year ago
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    I get that the long side is SU and ST and UT

  10. anonymous
    • one year ago
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    I get it now!!

  11. anonymous
    • one year ago
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    9 is the short side, 9 times 2 is 18. 18 minus 3 is 15.

  12. phi
    • one year ago
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    oh. we are talking about the median line XT which is divided by the point Y the short side is XY and the long side is YT

  13. phi
    • one year ago
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    in other words, the median XT is what is divided into two parts, where the short part is 1/2 of the longer part

  14. anonymous
    • one year ago
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    Aw, I thought I did it right..

  15. phi
    • one year ago
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    we want to find x so we concentrate on just the median XT it can be proved that 2* XY = YT

  16. phi
    • one year ago
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    so we start with 2* XY = YT and "put in" the info they give us about the length of XY and the length of YT

  17. anonymous
    • one year ago
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    (2*2 - 1) 10 1x = 10 x= 10

  18. phi
    • one year ago
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    do you see the "length" of XY ?

  19. anonymous
    • one year ago
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    well XT = 10, and XY is half of XT, so XY=5 ?

  20. phi
    • one year ago
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    yes, that is good thinking. but according to the label in your picture XY is also what ?

  21. anonymous
    • one year ago
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    Umm, X is the centroid but I'm not exactly sure what Y is..

  22. phi
    • one year ago
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    XY is way to say, "the line segment joining X to Y"

  23. phi
    • one year ago
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    and that line segment from X to Y has a label in your picture

  24. phi
    • one year ago
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    in other words, they say the length of XY is (2x-3)

  25. anonymous
    • one year ago
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    Thank you for all the help @phi I completely set up the equation wrong until you explained it to me!

  26. phi
    • one year ago
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    using XY=5 (which you figured out up above) you can write 2x-3 = 5 and now "solve for x"

  27. phi
    • one year ago
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    If I were doing it I would write 2*XY= YT then replace XY with (2x-3) and YT with 10 to get 2(2x-3)= 10 then solve for x if we divide both sides by 2 as the first step, we get 2x-3= 5 now add +3 to both sides 2x-3+3= 5+3 2x= 8 and finally divide both sides by 2

  28. anonymous
    • one year ago
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    When multiple numbers are given to me in diagrams I get so confused as to what to add, usually I start plugging in my options into the equations. Sometimes it works, sometimes it doesn't. Thank you again, it really did make sense when it was explained to me :)

  29. phi
    • one year ago
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    sorting out what info to use is the hard part. If you get good at that, then you will get good at thinking in general, and that is why you are studying math.

  30. anonymous
    • one year ago
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    You're definitely right. I've been struggling with math all through high school. It's not even that I don't try, it's that I get so confused. I have to draw separate images sometimes (for triangles)

  31. phi
    • one year ago
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    You can learn this, but it takes lots of work to learn how to tackle a problem. If I get confused and later get the answer I go back and ask, "why did I not see how to do it?" what was I not thinking? or thinking wrong? and then: if I see a problem like this again, "what will I do?" hopefully I will learn how to do the problem correctly.

  32. anonymous
    • one year ago
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    I totally agree with you, this sounds crazy, but when a math problem has multiple numbers and equations, I actually get stressed out..

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