Sure, let's break down the phrase step-by-step to construct the appropriate mathematical expression.
1. Identify the sum part:
The phrase asks for the sum of 17 and 21. Mathematically, this is written as:
[tex]\[
17 + 21
\][/tex]
2. Double the sum:
To double means to multiply by 2. Therefore, we need to take the sum we found in the first step and multiply it by 2.
Combining both steps, the expression becomes:
[tex]\[
2 \times (17 + 21)
\][/tex]
This can also be written as:
[tex]\[
2(17 + 21)
\][/tex]
Now let's consider the given options one by one:
1. [tex]\(\frac{1}{2}(17+21)\)[/tex]: This represents half of the sum of 17 and 21, not double the sum.
2. [tex]\(2+17+21\)[/tex]: This adds 2, 17, and 21 directly, rather than doubling the sum of 17 and 21.
3. [tex]\(\frac{17+21}{2}\)[/tex]: This represents half of the sum of 17 and 21, again not double the sum.
4. [tex]\(2(17+21)\)[/tex]: This correctly represents double the sum of 17 and 21.
Thus, the correct mathematical representation of the phrase "double the sum of 17 and 21" is:
[tex]\[
2(17 + 21)
\][/tex]
When we compute [tex]\(17 + 21\)[/tex], we get 38. Doubling this result, we get:
[tex]\[
2 \times 38 = 76
\][/tex]
Therefore, the numerical results are:
[tex]\[
(38, 76)
\][/tex]
This confirms that the correct choice among the given options is:
[tex]\[
2(17 + 21)
\][/tex]
