To solve this problem, we need to match the given algebraic expression [tex]\(\frac{1}{4} d + 7\)[/tex] to the correct descriptive phrase.
Let's break down the expression:
1. [tex]\(\frac{1}{4} d\)[/tex]: This part of the expression represents the product of one-fourth and a number [tex]\(d\)[/tex].
2. [tex]\(+ 7\)[/tex]: This part indicates that we are adding 7 to the previous product.
Now, analyzing each option:
a. "the product of one-fourth and a number, plus seven"
- This phrase correctly describes the expression [tex]\(\frac{1}{4} d + 7\)[/tex]. It states that we take one-fourth of a number [tex]\(d\)[/tex] and then add 7.
b. "the product of seven and a number"
- This phrase describes [tex]\(7d\)[/tex], which is not the same as [tex]\(\frac{1}{4} d + 7\)[/tex].
c. "the product of one-fourth and seven, plus a number"
- This phrase describes [tex]\(\frac{1}{4} \times 7 + d\)[/tex], which is equivalent to [tex]\(\frac{7}{4} + d\)[/tex], not [tex]\(\frac{1}{4} d + 7\)[/tex].
d. "the product of seven and one-fourth"
- This phrase describes [tex]\(7 \times \frac{1}{4}\)[/tex], which equals [tex]\(\frac{7}{4}\)[/tex], and does not mention the variable [tex]\(d\)[/tex] or the addition of 7.
Based on the detailed analysis of each option, the correct phrase that represents the algebraic expression [tex]\(\frac{1}{4} d + 7\)[/tex] is:
"The product of one-fourth and a number, plus seven."
Thus, the answer is option (a).
