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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) 📰 Change Microsoft Email In Minutesunlock Unlimited Productivity Today 6149174 📰 Unlock Mu Options Nowthese Hidden Features Will Blow Your Mind 8978467 📰 Mary Magdalene The Chosen 1922794 📰 You Wont Believe What Happens When You Convert 375 Ml To Ozits Shocking Size 5907839 📰 Areala Warrior 2657479 📰 Unlock Mysteries The Most Stunning Spine Tattoo Designs That Will Blow Your Mind 5638385 📰 From Casual Fun To Professional Thrills Our Top Pick For The Ultimate Ski Game Every Gamer Needs 3690209 📰 Xmxxm Just Hit 150The Secret Stock Trending Globally You Need To Invest Now 4527109 📰 Juegps Secrets Revealed The Game Changing Tech Gamers Are Too Sleepy To Think Of 3784429 📰 The Secret Route Saving Travelers Time At Punta Cana Airport 4461534 📰 Wells Fargo Financial Services 2481603 📰 Bashful Meaning Shy Expression That Undercuts Every Conversationheres Why 8631171 📰 Avoid These Mistakes Buru Stock Overnight Price Move Expected To Shock Markets 781302 📰 Absentia Season 3 8543375 📰 Kal Els Hidden Powers Revealedyou Wont Believe What He Can Do 5084427