Question
Consider the following descriptions, each representing a relation.
Description #1: The number of chairs in the restaurant is equal to three times the number of tables.
Description #2: The number of tables in the restaurant is equal to one-third the number of chairs.
Description #3: The number of tables in the restaurant is equal to three times the number of servers.
Question 1
A. Identify the two descriptions that represent relations that are inverses. (2 points)
Description # and Description #
Question 2
B. Create a verbal description for the inverse of description whose inverse is not given,(2 points)
Description #1: The number of chairs in the restaurant is equal to three times the number of tables.
Description #2: The number of tables in the restaurant is equal to one-third the number of chairs.
Description #3: The number of tables in the restaurant is equal to three times the number of servers.
Question 1
A. Identify the two descriptions that represent relations that are inverses. (2 points)
Description # and Description #
Question 2
B. Create a verbal description for the inverse of description whose inverse is not given,(2 points)
Answers
GPT-4o mini
To determine which descriptions represent inverse relations, let's first analyze the given relations:
1. Description #1: The number of chairs (C) in the restaurant is equal to three times the number of tables (T).
- This can be represented as: \( C = 3T \)
2. Description #2: The number of tables (T) in the restaurant is equal to one-third the number of chairs (C).
- This can be represented as: \( T = \frac{1}{3}C \)
- This is the inverse of Description #1 because it expresses the relationship in terms of T instead of C.
3. Description #3: The number of tables (T) in the restaurant is equal to three times the number of servers (S).
- This can be represented as: \( T = 3S \)
Now, let's answer the questions:
### Question 1
A. Identify the two descriptions that represent relations that are inverses.
- **Description #1** and **Description #2**.
### Question 2
B. Create a verbal description for the inverse of the description whose inverse is not given.
- Description #3 does not have an inverse given. Its inverse can be described as follows:
"The number of servers in the restaurant is equal to one-third the number of tables."
This can be expressed mathematically as \( S = \frac{1}{3}T \), which is the inverse of Description #3.
1. Description #1: The number of chairs (C) in the restaurant is equal to three times the number of tables (T).
- This can be represented as: \( C = 3T \)
2. Description #2: The number of tables (T) in the restaurant is equal to one-third the number of chairs (C).
- This can be represented as: \( T = \frac{1}{3}C \)
- This is the inverse of Description #1 because it expresses the relationship in terms of T instead of C.
3. Description #3: The number of tables (T) in the restaurant is equal to three times the number of servers (S).
- This can be represented as: \( T = 3S \)
Now, let's answer the questions:
### Question 1
A. Identify the two descriptions that represent relations that are inverses.
- **Description #1** and **Description #2**.
### Question 2
B. Create a verbal description for the inverse of the description whose inverse is not given.
- Description #3 does not have an inverse given. Its inverse can be described as follows:
"The number of servers in the restaurant is equal to one-third the number of tables."
This can be expressed mathematically as \( S = \frac{1}{3}T \), which is the inverse of Description #3.