Question
Perform the following operations. Express your answers as fully reduced fractions if necessary. \( \left(5^{2}+(8-30)^{2}\right) \div(3-7)= \)
Ask by Kirk Chadwick. in Canada
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The final answer is \(-\frac{509}{4}\).
Solution
1. Compute \( 5^2 \):
\[
5^2 = 25
\]
2. Compute the expression \( 8 - 30 \):
\[
8 - 30 = -22
\]
3. Compute \( (-22)^2 \):
\[
(-22)^2 = 484
\]
4. Sum the results in the numerator:
\[
25 + 484 = 509
\]
5. Compute the denominator \( 3 - 7 \):
\[
3 - 7 = -4
\]
6. Form the fraction:
\[
\frac{509}{-4} = -\frac{509}{4}
\]
The final answer is:
\[
-\frac{509}{4}
\]
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Simplify this solution The Deep Dive
Let's break down the expression step by step. 1. Calculate \( 5^2 \): \[ 5^2 = 25 \] 2. Calculate \( (8 - 30)^2 \): \[ 8 - 30 = -22 \] Now, square it: \[ (-22)^2 = 484 \] 3. Now, add the results: \[ 25 + 484 = 509 \] 4. Calculate \( 3 - 7 \): \[ 3 - 7 = -4 \] 5. Now, divide \( 509 \) by \( -4 \): \[ 509 \div -4 = -\frac{509}{4} \] So, the final answer is: \[ -\frac{509}{4} \]
