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Home » Subtract consecutive equations to eliminate $ d $: - ToelettAPP

Subtract consecutive equations to eliminate $ d $: - ToelettAPP

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Divide by 12:

📌 v = rac{40}{12} = rac{10}{3}.

📌 Thus, the value of $v$ is $oxed{\dfrac{10}{3}}$.Question: What two-digit number represents the number of days in a cycle that is one more than a multiple of 7 and 11?

📌 Solution: To find the number, compute the least common multiple (LCM) of 7 and 11, then add 1. Since 7 and 11 are coprime, $ ext{LCM}(7, 11) = 7 imes 11 = 77$. Adding 1 gives $77 + 1 = 78$. The two-digit number is $oxed{78}$.

📌 Question: What is the base-ten number represented by the base-eight number $327_8$, which encodes a patient's health metric in an octal system?

📌 Solution: Convert $327_8$ to base-ten: $3 imes 8^2 + 2 imes 8^1 + 7 imes 8^0 = 3 imes 64 + 2 imes 8 + 7 = 192 + 16 + 7 = 215$. The base-ten equivalent is $oxed{215}$.

📌 Question: What is the remainder when the sum of annual ritual events (2023, 2025, 2027, 2029) is divided by 5, reflecting a cyclical calendar system?

📌 Solution: Compute the sum: $2023 + 2025 + 2027 + 2029 = 8104$. Divide by 5: $8104 \div 5 = 1620$ with a remainder of $8104 - 5 imes 1620 = 8104 - 8100 = 4$. The remainder is $oxed{4}$.

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