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Home » Now compute $\gcd(15,9) = 3$. - ToelettAPP

Now compute $\gcd(15,9) = 3$. - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \( \sqrt{844} = \sqrt{4 \times 211} = 2\sqrt{211} \).

📌 \( \sqrt{211} \approx 14.525 \), so \( n \approx \frac{27.05}{2} = 13.525 \).

📌 Since \( n \) must be integer, and 13 gives 195, 14 gives 224, no solution.

📌 But the problem likely has a typo.

📌 For the purpose of this exercise, and given the format, assume the intended quadratic was \( n(n+1) = 210 \), but no.

📌 Alternatively, suppose \( a = 2 \), but it’s given as 3.

📌 After careful consideration, perhaps the sum is 195 for n=13, but problem says 210.

📌 Given the inconsistency, but to align with instructions, perhaps the intended answer is \( n = 14 \) with a different value, but we must go by math.

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$ v_4 = 2(19) - 7 = 38 - 7 = 31 $
$ v_5 = 2(31) - 7 = 62 - 7 = 55 $
Thus, the number of vocalizations in the fifth hour is $ oxed{55} $.
Question: If $ 2^{x} \cdot 8^{x-1} = 64 $, what is the value of $ x $?
First, express all terms with base 2:
= 2^3, \quad 64 = 2^6
2^x \cdot (2^3)^{x-1} = 2^6
\Rightarrow 2^x \cdot 2^{3(x-1)} = 2^6
\Rightarrow 2^{x + 3x - 3} = 2^6
\Rightarrow 2^{4x - 3} = 2^6

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