Question
,
Which of the following describes the sum p + (−q) where p
and q
are positive numbers??(1 point)
Responses
The sum p+(−q) is the number located a distance |q| from p in the positive direction.
The sum p plus left parenthesis negative q right parenthesis is the number located a distance Start Absolute Value q End Absolute Value from p in the positive direction.
The sum p+(−q) is the number located a distance |p| from q in the positive direction.
The sum negative p plus left parenthesis negative q right parenthesis is the number located a distance absolute value of p from q in the positive direction.
The sum p+(−q) is the number located a distance |q| from p in the negative direction.
The sum p plus left parenthesis negative q right parenthesis is the number located a distance Start Absolute Value q End Absolute Value from p in the negative direction.
The sum p+(−q) is the number located a distance |p| from q in the negative direction.
Which of the following describes the sum p + (−q) where p
and q
are positive numbers??(1 point)
Responses
The sum p+(−q) is the number located a distance |q| from p in the positive direction.
The sum p plus left parenthesis negative q right parenthesis is the number located a distance Start Absolute Value q End Absolute Value from p in the positive direction.
The sum p+(−q) is the number located a distance |p| from q in the positive direction.
The sum negative p plus left parenthesis negative q right parenthesis is the number located a distance absolute value of p from q in the positive direction.
The sum p+(−q) is the number located a distance |q| from p in the negative direction.
The sum p plus left parenthesis negative q right parenthesis is the number located a distance Start Absolute Value q End Absolute Value from p in the negative direction.
The sum p+(−q) is the number located a distance |p| from q in the negative direction.
Answers
GPT-4o mini
Let's analyze the expression \( p + (-q) \).
Given that \( p \) and \( q \) are positive numbers, the expression can be rewritten as:
\[
p + (-q) = p - q
\]
The sum \( p - q \) involves subtracting a positive number \( q \) from another positive number \( p \). There are two possible cases:
1. If \( p > q \), then \( p - q \) is positive, and the result is located a distance of \( q \) units to the left of \( p \) on a number line.
2. If \( p < q \), then \( p - q \) is negative, and the result is located a distance of \( q \) units in the negative direction from \( p \).
Now, let's look at the options. Since the options seem to discuss distances, we'll focus on those that describe the position of \( p - q \):
- The first option states: "The sum \( p + (-q) \) is the number located a distance \( |q| \) from \( p \) in the positive direction."
- The second option states: "The sum \( p + (-q) \) is the number located a distance \( |p| \) from \( q \) in the positive direction."
- The third option states: "The sum \( p + (-q) \) is the number located a distance \( |q| \) from \( p \) in the negative direction."
- The fourth option states: "The sum \( p + (-q) \) is the number located a distance \( |p| \) from \( q \) in the negative direction."
From our analysis, the most reasonable choice aligns with \( p - q \):
- If \( p > q \): We are going \( q \) units to the left from \( p \).
- If \( p < q \): We are \( |q| \) units away in the negative direction.
Given the provided responses, the most accurate description of \( p + (-q) \) is:
"The sum \( p + (-q) \) is the number located a distance \( |q| \) from \( p \) in the negative direction."
So the correct response is the option that states:
"The sum \( p + (-q) \) is the number located a distance \( |q| \) from \( p \) in the negative direction."
Given that \( p \) and \( q \) are positive numbers, the expression can be rewritten as:
\[
p + (-q) = p - q
\]
The sum \( p - q \) involves subtracting a positive number \( q \) from another positive number \( p \). There are two possible cases:
1. If \( p > q \), then \( p - q \) is positive, and the result is located a distance of \( q \) units to the left of \( p \) on a number line.
2. If \( p < q \), then \( p - q \) is negative, and the result is located a distance of \( q \) units in the negative direction from \( p \).
Now, let's look at the options. Since the options seem to discuss distances, we'll focus on those that describe the position of \( p - q \):
- The first option states: "The sum \( p + (-q) \) is the number located a distance \( |q| \) from \( p \) in the positive direction."
- The second option states: "The sum \( p + (-q) \) is the number located a distance \( |p| \) from \( q \) in the positive direction."
- The third option states: "The sum \( p + (-q) \) is the number located a distance \( |q| \) from \( p \) in the negative direction."
- The fourth option states: "The sum \( p + (-q) \) is the number located a distance \( |p| \) from \( q \) in the negative direction."
From our analysis, the most reasonable choice aligns with \( p - q \):
- If \( p > q \): We are going \( q \) units to the left from \( p \).
- If \( p < q \): We are \( |q| \) units away in the negative direction.
Given the provided responses, the most accurate description of \( p + (-q) \) is:
"The sum \( p + (-q) \) is the number located a distance \( |q| \) from \( p \) in the negative direction."
So the correct response is the option that states:
"The sum \( p + (-q) \) is the number located a distance \( |q| \) from \( p \) in the negative direction."