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📰 Final answer: $ \boxed{x^4 + 2x^2 + 9} $Question: A cartographer is analyzing elevation data from a triangular region defined by points $ A = (1, 2), B = (4, 6), C = (7, 3) $. If the elevation at each vertex is proportional to its respective $ z $-coordinate, and the average elevation over the triangle is $ 12 $, what is the $ z $-coordinate of the centroid of triangle $ ABC $? 📰 Solution: The centroid $ G $ of triangle $ ABC $ is the average of its vertices' coordinates: 📰 G = \left( \frac{1 + 4 + 7}{3}, \frac{2 + 6 + 3}{3} \right) = \left( 4, \frac{11}{3} \right) 📰 Getting Getting Over It 4458206 📰 The Harley Davidson Street Glide That Byte Back Into Your Heart 6708213 📰 Master Line Spacing In Wordboost Clarity And Fix Professionalism In Seconds 2931586 📰 Basketball Half Court 5155019 📰 How Many Mls To A Litre 5822098 📰 Grooming Bride Revealed The Secret Makeover That Made Her Unforgettable 518691 📰 Cannot Prove Itjust See How The Cfmoto 450Ss Runs Like A Beast In The Wild 3092675 📰 Best Credit Card In The World 3626009 📰 Cathead Biscuits 9497169 📰 From Puree Magic To Baby Friendly Delights That Guarantee Cheers 4266008 📰 The Ultimate Bassinet Bassinet Shop Now Before It Sells Out Experts Say Babies Sleep Deeper 153699 📰 From Laughs To Loyalty Discover The Secret Rise Of Toonle In The Mobile World 9909259 📰 People Are Obsessed The Ultimate Shiply Tool Youve Been Searching For Free 3234219 📰 Frugal Living Tips Everyones Talking Aboutcut Costs Without Sacrificing Style 627779 📰 Shocked By Hlns Price Spike Heres The Real Story Behind Todays Breaking Hlvn Movement 6995443