Question
Solve the following equation: \[ \sqrt{15}=\sqrt{6 \mathrm{k}-14} \] Provide an answer accurate to the nearest hundredth.
Ask by Wright Turnbull. in the United States
Nov 22,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution to the equation is \( k \approx 4.83 \).
Solution
To solve the equation
\[
\sqrt{15} = \sqrt{6k - 14},
\]
we start by squaring both sides to eliminate the square roots:
\[
15 = 6k - 14.
\]
Next, we isolate \(6k\) by adding 14 to both sides:
\[
15 + 14 = 6k,
\]
which simplifies to
\[
29 = 6k.
\]
Now, we solve for \(k\) by dividing both sides by 6:
\[
k = \frac{29}{6}.
\]
To express this as a decimal, we perform the division:
\[
k \approx 4.8333\ldots.
\]
Rounding this to the nearest hundredth, we find:
\[
k \approx 4.83.
\]
Thus, the solution to the equation is
\[
\boxed{4.83}.
\]
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Simplify this solution Mind Expander
To solve the equation \(\sqrt{15}=\sqrt{6k-14}\), we start by squaring both sides: \[ 15 = 6k - 14. \] Next, we isolate \(6k\) by adding \(14\) to both sides: \[ 15 + 14 = 6k, \] which simplifies to: \[ 29 = 6k. \] Now, we solve for \(k\) by dividing both sides by \(6\): \[ k = \frac{29}{6}. \] This is approximately: \[ k \approx 4.8333. \] To round to the nearest hundredth, we find: \[ k \approx 4.83. \] Thus, the solution rounded to the nearest hundredth is: \[ \boxed{4.83}. \]
