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Home » Substitute \( a = 1 \) back into Equation 4: - Esdistancia

Substitute \( a = 1 \) back into Equation 4: - Esdistancia

📅 March 17, 2026 👤 scraface

Mar 17, 2026

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📌 $$ 4 = -a(9) + 10 \implies -9a = 6 \implies a = -rac{2}{3} \quad ext{(invalid)}. $$

📌 Re-evaluating, the standard form $ y = -ax^2 + bx + c $ with vertex $ (3, 10) $ gives $ b = 2a \cdot 3 = 6a $ and $ 10 = -a(9) + b(3) + c $. Substituting $ b = 6a $ and $ c = 4 $ (from $ (0, 4) $):

📌 $$ 10 = -9a + 18a + 4 \implies 10 = 9a + 4 \implies 9a = 6 \implies a = rac{2}{3}. $$

📌 Thus, the value of $ a $ is $ oxed{\dfrac{2}{3}} $.

📌 Question: An entomologist studies the growth of a bee colony, modeled by $ rac{t^2 + 5t + 6}{t + 2} $. Simplify the expression and find its value at $ t = 4 $.

📌 Solution: Factor the numerator:

📌 $$ rac{t^2 + 5t + 6}{t + 2} = rac{(t + 2)(t + 3)}{t + 2} = t + 3 \quad ext{(for } t

📌 eq -2 ext{)}. $$

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