To determine which variable expression represents "the sum of the number of dogs and the 6 cats," let's break down the phrase step by step.
1. Identify the variable and constants in the phrase:
- The phrase mentions "the number of dogs," which we denote as [tex]\( d \)[/tex].
- It also mentions "6 cats," which is a constant value, 6.
2. Understand the operation required:
- The word "sum" indicates that we need to perform an addition operation.
3. Formulate the expression:
- Since we are looking for "the sum of the number of dogs and the 6 cats," we need to add the number of dogs ([tex]\( d \)[/tex]) to 6.
4. Write the expression:
- Adding [tex]\( d \)[/tex] (the number of dogs) to 6 (the number of cats), we get the expression [tex]\( d + 6 \)[/tex].
Now, let's compare this with the given options:
- A. [tex]\( d \cdot 6 \)[/tex]: This represents the product of the number of dogs and 6, not their sum.
- B. [tex]\( d - 6 \)[/tex]: This represents the difference between the number of dogs and 6, not their sum.
- C. [tex]\( d + 6 \)[/tex]: This correctly represents the sum of the number of dogs and 6 cats.
- D. [tex]\( d \div 6 \)[/tex]: This represents the division of the number of dogs by 6, not their sum.
Therefore, the variable expression that correctly represents "the sum of the number of dogs and the 6 cats" is [tex]\( d + 6 \)[/tex].
So, the correct answer is C. [tex]\( d + 6 \)[/tex].
