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

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enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1357236456605:dw

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1It looks more like an orthocenter, but for the sake of it, let's say it is a centroid.

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1\[ x + 5 = 2x  1\]\[5 + x  2x = 2x  2x  1\]\[5  x = 1\]

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1Subtract five from both sides. \[x = 1  5\]\[x = 6\]

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1Now I can plug in the missing numbers. \[6 + 5 = 2(6)  1\]\[11 = 12  1\]\[= 11\]

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1I think you're incorrect in assuming that \(x+5\) must equal \(2x1\). 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.

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1In that case, I'll tweak a few things here. \[x + 5 = 2(2x  1)\]\[x + 5 = 4x  2\] Subtracting 4 from both sides.

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1\[5  3x = 2\]\[3x = 2  5\]\[3x = 7\]

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1\[x = \frac{ 7 }{ 3 }\]

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1That looks good to me. You can simplify that to \(\dfrac{7}{3}\) if you want.

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1@KingGeorge The answer was really 11. Guess I should have trusted my gut, ha.

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Oops :( I guess that would be my fault.

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1However, I think we just forgot the last step in the problem. We found \(x=7/3\), but AM is equal to \((x+5)+(2x1)\). If we plug in our value for \(x\) into this, we get\[\frac{7}{3}+4+\frac{14}{3}=\frac{21}{3}+4=7+4=11\]
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