To determine which algebraic expression accurately represents the given phrase "the product of 40 and the distance to the finish line," let’s analyze the phrase step by step.
1. Identify keywords and phrases:
- "Product" indicates multiplication.
- "40" is a constant.
- "The distance to the finish line" can be represented as a variable, typically denoted as [tex]\( d \)[/tex].
2. Translate the phrase into a mathematical expression:
- "The product of 40 and the distance to the finish line" translates to multiplying 40 by [tex]\( d \)[/tex].
3. Write the expression:
- Multiplication in algebra is denoted by placing the coefficient and the variable next to each other, separated by a multiplication sign or simply written together since multiplication is implied.
So, the algebraic expression that matches the phrase is:
[tex]\[ 40 \cdot d \][/tex]
Now, let's compare this with the given options:
- A. [tex]\( 40 - d \)[/tex]: This represents 40 minus the distance, which is incorrect for "the product of 40 and the distance."
- B. [tex]\( 40 + d \)[/tex]: This represents 40 plus the distance, which is also incorrect.
- C. [tex]\( \frac{40}{d} \)[/tex]: This represents 40 divided by the distance, again incorrect.
- D. [tex]\( 40 \cdot d \)[/tex]: This correctly represents the product of 40 and the distance.
Therefore, the correct option is:
D. [tex]\( 40 \cdot d \)[/tex]
