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Home » Ancestry Detectives Reveal Hidden Treasures in These 10 Iconic Mexican Last Names! - Abbey Badges

Ancestry Detectives Reveal Hidden Treasures in These 10 Iconic Mexican Last Names! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 The area $ A $ is:

📌 A = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{15(15 - 7)(15 - 10)(15 - 13)} = \sqrt{15 \cdot 8 \cdot 5 \cdot 2} = \sqrt{1200}

📌 \sqrt{1200} = \sqrt{100 \cdot 12} = 10\sqrt{12} = 10 \cdot 2\sqrt{3} = 20\sqrt{3} ext{ cm}^2

📌 The altitude $ h $ corresponding to a side $ b $ is given by:

📌 A = rac{1}{2} b h \Rightarrow h = rac{2A}{b}

📌 To find the longest altitude, we use the shortest side, since altitude is inversely proportional to the base. The shortest side is $ 7 $ cm.

📌 h_{ ext{longest}} = rac{2 \cdot 20\sqrt{3}}{7} = rac{40\sqrt{3}}{7} ext{ cm}

📌 Thus, the length of the longest altitude is $ oxed{rac{40\sqrt{3}}{7}} $ cm.Question: A paleobotanist studying fossilized ferns models the growth pattern of a prehistoric plant using the equation $ 4x^2 - 12xy + 9y^2 + 8x - 36y + 20 = 0 $. Determine whether this equation represents a degenerate conic section and, if so, identify the type of degeneracy.

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