/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 252 Simplify. \(5 \div 0.5+(3.9) 6... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 252

Simplify. \(5 \div 0.5+(3.9) 6-(0.7)^{2}\)

Short Answer

Expert verified
32.91

Step by step solution

01

- Division

First, perform the division operation: \(5 \div 0.5\). Dividing by 0.5 is the same as multiplying by 2. So, \(5 \div 0.5 = 5 \times 2 = 10\).
02

- Multiplication

Next, perform the multiplication operation: \((3.9) \times 6\). So, \(3.9 \times 6 = 23.4\).
03

- Exponentiation

Now, calculate the square of 0.7. So, \((0.7)^2 = 0.49\).
04

- Combine Results

Add the results of the previous steps and subtract the squared term: \(10 + 23.4 - 0.49\).
05

- Final Calculation

Perform the final addition and subtraction: \(10 + 23.4 - 0.49 = 32.91\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Division Operation
In this problem, we start with a division operation. The expression is: \(5 \div 0.5\).
When dividing by a fraction, it can be easier to think of it as multiplying by its reciprocal. The reciprocal of 0.5 is 2 because \( \frac{1}{0.5} = 2 \).
So, instead of dividing, we multiply: \( 5 \div 0.5 = 5 \times 2 = 10 \).
This simplifies our next steps.
Multiplication Operation
Next, we handle the multiplication operation in the expression: \((3.9) \times 6\).
Multiplication is straightforward here. We simply multiply the two numbers:
\(3.9 \times 6 = 23.4\).
Breaking it down, you multiply 3.9 by each part of 6:
  • 3.9 multiplied by 6 is 23.4
This intermediate result will be used in the final combination step.
Exponentiation
Now, we perform the exponentiation operation with the term \((0.7)^{2} \).
Raising 0.7 to the power of 2 means multiplying 0.7 by itself:
\(0.7 \times 0.7 = 0.49\).
So, \((0.7)^{2} = 0.49\).
Exponentiation simplifies calculating repeated multiplications, especially useful in algebra.
Step-by-Step Solution
Let's break down the solution step-by-step to make sure we understand each part. We have:
  • First, the division: \(5 \div 0.5 = 10\).
  • Second, the multiplication: \((3.9) \times 6 = 23.4\).
  • Third, the exponentiation: \((0.7)^{2} = 0.49\).
Each step simplifies an individual part of the expression. Using step-by-step methods ensures clarity and accuracy.
Combining Results
Finally, we combine all the results from previous steps:
  • The division result: 10
  • The multiplication result: 23.4
  • The exponentiation result: 0.49
We sum and subtract these values as per the original expression:
\(10 + 23.4 - 0.49\).
Adding 10 and 23.4 gives us 33.4.
Subtracting 0.49 from 33.4 gives us the final result:
\(33.4 - 0.49 = 32.91\).
This final step completes the problem, arriving at the simplified value of 32.91.

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