Sure, let's break down the word description and translate it step-by-step into an algebraic expression.
1. Understand the components in the description:
- "The quotient of nine and the sum of a number and one."
2. Translate the words into mathematical operations:
- "Quotient of" implies division.
- "Nine" is 9.
- "Sum of a number and one" can be represented as [tex]\( x + 1 \)[/tex], where [tex]\( x \)[/tex] is the variable representing the number.
3. Form the algebraic expression:
- The description asks for the quotient of 9 and the sum of a number and one. This means we need to divide 9 by [tex]\( x + 1 \)[/tex].
Thus, the algebraic expression that represents this description is:
[tex]\[ \frac{9}{x+1} \][/tex]
4. Identify the correct option from the given choices:
- Option A: [tex]\(\frac{x+1}{9}\)[/tex] does not match, as it represents the sum of a number and one divided by nine.
- Option B: [tex]\(\frac{9}{x+1}\)[/tex] matches the description exactly.
- Option C: [tex]\(\frac{9}{x}+1\)[/tex] does not match, as it adds one after dividing nine by the number.
- Option D: [tex]\(\frac{x}{9}+1\)[/tex] does not match, as it represents the number divided by nine and then adding one.
Therefore, the correct choice is:
[tex]\[ B. \frac{9}{x+1} \][/tex]
So the algebraic expression that represents the given word description is [tex]\( \frac{9}{x+1} \)[/tex], corresponding to choice B.
