To determine the correct algebraic expression for the given word description, let's carefully break down and interpret each part of the phrase:
Phrase: "The quotient of nine and the sum of a number and one."
1. Quotient of nine: "Quotient" means division. So, we are looking at dividing nine by some other expression.
2. The sum of a number and one: Let's denote the unknown number by [tex]\( x \)[/tex]. The sum of this number and one would be written as [tex]\( x + 1 \)[/tex].
Now, combining these parts, the "quotient of nine" divided by "the sum of a number and one" translates to the following algebraic expression:
[tex]\[
\frac{9}{x + 1}
\][/tex]
After evaluating each option, we find:
- Option A: [tex]\(\frac{x+1}{9}\)[/tex] represents "the sum of a number and one divided by nine."
- Option B: [tex]\(\frac{x}{9}+1\)[/tex] represents "a number divided by nine, plus one."
- Option C: [tex]\(\frac{9}{x}+1\)[/tex] represents "nine divided by a number, plus one."
- Option D: [tex]\(\frac{9}{x+1}\)[/tex] represents "the quotient of nine and the sum of a number and one."
Thus, the correct algebraic expression that matches the word description is:
[tex]\[
\frac{9}{x + 1}
\][/tex]
Therefore, the correct answer is:
D. [tex]\(\frac{9}{x+1}\)[/tex]
