Answered

What is the correct order to solve this equation?

[tex]\[ \left(5 + 2^2\right) + 5 = \][/tex]

A. Calculate [tex]\(5 + 2\)[/tex], then calculate the exponent of [tex]\(2\)[/tex], then add [tex]\(5\)[/tex] to the results to get the final answer.

B. Calculate the exponent, then add [tex]\(5\)[/tex], then add [tex]\(5\)[/tex] to get the answer.

C. Calculate [tex]\(5\)[/tex] outside of the parentheses by the [tex]\(5\)[/tex] and [tex]\(2\)[/tex] inside the parentheses, then calculate the exponent to get the final answer.

D. Calculate the [tex]\(5\)[/tex] and [tex]\(2\)[/tex] inside the parentheses and add [tex]\(5\)[/tex] to the results.

E. None of the above.



Answer :

GinnyAnswer
To correctly solve the equation:

[tex]\[ \left(5 + 2^2\right) + 5 \][/tex]

you should follow the proper order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

1. Calculate the exponent first:
[tex]\[ 2^2 = 4 \][/tex]

2. Perform the addition inside the parentheses:
[tex]\[ 5 + 4 = 9 \][/tex]

3. Finally, add the result outside the parentheses:
[tex]\[ 9 + 5 = 14 \][/tex]

So, the step-by-step breakdown of the process is as follows:
- Calculate the exponentiation: [tex]\( 2^2 = 4 \)[/tex]
- Add the result of the exponentiation to 5 inside the parentheses: [tex]\( 5 + 4 = 9 \)[/tex]
- Add the resultant value 9 to 5 outside the parentheses: [tex]\( 9 + 5 = 14 \)[/tex]

The correct answer is 14.

Thus, the statement "Calculating the exponent, then adding 5, then adding 5 to get the answer" correctly describes the proper calculation order. Therefore, the closest correct option is the second one:

- Calculating the exponent, then adding 5, then adding 5 to get the answer.

However, it seems that this option might be phrased somewhat ambiguously regarding adding "5" twice, which could imply two separate additions. Hence, the better choice should correctly indicate the order derived from following PEMDAS and understanding the parentheses priority. Therefore, from the original options, we conclude that none of them correctly precisely align but understanding has been clarified here.