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Home » where \(a = 3\), \(b = -4\), and \(c = 1\). Substituting: - Abu Waleed Tea

where \(a = 3\), \(b = -4\), and \(c = 1\). Substituting: - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: The average of $ 4x+1 $, $ x+7 $, and $ 2x+4 $ is $ 5x - 2 $. Solve for $ x $.

📌 \frac{(4x+1) + (x+7) + (2x+4)}{3} = \frac{7x + 12}{3}.

📌 Set equal to $ 5x - 2 $:

📌 \frac{7x + 12}{3} = 5x - 2 \implies 7x + 12 = 15x - 6 \implies -8x = -18 \implies x = \frac{9}{4}.

📌 The solution is $ \boxed{\frac{9}{4}} $.

📌 Solution: The smallest 4-digit number divisible by 11 is $ 1001 $ (since $ 1001 \div 11 = 91 $), and the largest is $ 9999 $ (since $ 9999 \div 11 = 909 $). The count is $ 909 - 91 + 1 = 819 $.

📌 The answer is $ \boxed{819} $.Question: A digital literacy advocate is organizing a workshop with 8 distinct tech tutorials and 5 community centers. How many distinct ways can the tutorials be assigned to centers if each center can receive any number of tutorials?

📌 Solution: Each of the 8 distinct tutorials can be assigned to any of the 5 centers. Since assignments are independent, the total number of ways is $5^8 = 390625$. Thus, the answer is $\boxed{390625}$.

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