Questions: Evaluate the expression. 31 ÷ (7.6 - -1 2/5) · (-7)^2 - 9 2/5 31 ÷ (7.6 - -1 2/5) · (-7)^2 - 9 2/5 = (Type an integer or a decimal.)

Evaluate the expression. 31 ÷ (7.6 - -1 2/5) · (-7)^2 - 9 2/5 31 ÷ (7.6 - -1 2/5) · (-7)^2 - 9 2/5 = (Type an integer or a decimal.)
Transcript text: Evaluate the expression. \[ 31 \div\left(7.6-\left|-1 \frac{2}{5}\right|\right) \cdot(-7)^{2}-9 \frac{2}{5} \] $31 \div\left(7.6-\left|-1 \frac{2}{5}\right|\right) \cdot(-7)^{2}-9 \frac{2}{5}=$ $\square$ (Type an integer or a decimal.)
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Solution

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Solution Steps

To evaluate the given expression, follow these steps:

  1. Simplify the absolute value expression \(\left|-1 \frac{2}{5}\right|\).
  2. Subtract the result from 7.6.
  3. Divide 31 by the result of step 2.
  4. Calculate \((-7)^2\).
  5. Multiply the result of step 3 by the result of step 4.
  6. Convert \(9 \frac{2}{5}\) to an improper fraction or decimal.
  7. Subtract the result of step 6 from the result of step 5.
Step 1: Evaluate the Absolute Value

First, we calculate the absolute value: \[ \left|-1 \frac{2}{5}\right| = \left|-1 - \frac{2}{5}\right| = 1.4 \]

Step 2: Subtract from 7.6

Next, we subtract the absolute value from 7.6: \[ 7.6 - 1.4 = 6.2 \]

Step 3: Divide 31 by the Result

Now, we divide 31 by the result from Step 2: \[ 31 \div 6.2 \approx 5.0000 \]

Step 4: Calculate \((-7)^2\)

We then calculate the square of \(-7\): \[ (-7)^2 = 49 \]

Step 5: Multiply the Results

Next, we multiply the result from Step 3 by the result from Step 4: \[ 5.0000 \cdot 49 = 245.0000 \]

Step 6: Convert \(9 \frac{2}{5}\) to Decimal

We convert \(9 \frac{2}{5}\) to decimal: \[ 9 \frac{2}{5} = 9 + \frac{2}{5} = 9.4 \]

Step 7: Subtract the Decimal from the Product

Finally, we subtract the result from Step 6 from the result of Step 5: \[ 245.0000 - 9.4 = 235.6000 \]

Final Answer

The final result is: \[ \boxed{235.6000} \]

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