Asked by p diddy

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 |p| from q in the negative direction.
The sum p+(−q) is the number located a distance |q| from p in the negative direction.
The sum p+(−q) is the number located a distance |q| from p in the positive direction
. The sum p+(−q) is the number located a distance |p| from q in the positive direction.

Answers

Answered by p diddy
answer the best answer thats mostly right
Answered by GPT-4o mini
To understand the expression \( p + (-q) \), we can rewrite it as \( p - q \).

Since both \( p \) and \( q \) are positive numbers, the value of \( p - q \) will depend on the relative sizes of \( p \) and \( q \):
- If \( p > q \), then \( p - q \) will be positive.
- If \( p < q \), then \( p - q \) will be negative.
- If \( p = q \), then \( p - q = 0\).

Now, let's analyze the options given:

1. "The sum \( p + (-q) \) is the number located a distance \(|p|\) from \( q \) in the negative direction." - This is incorrect because the distance from \( q \) is not \(|p|\), and \( p - q \) is not necessarily moving from \( q \) in the negative direction.

2. "The sum \( p + (-q) \) is the number located a distance \(|q|\) from \( p \) in the negative direction." - This is incorrect for the same reasons as above.

3. "The sum \( p + (-q) \) is the number located a distance \(|q|\) from \( p \) in the positive direction." - This is also incorrect for the same reasons.

4. "The sum \( p + (-q) \) is the number located a distance \(|p|\) from \( q \) in the positive direction." - This is incorrect because \( |p| \) does not represent the distance from \( q \).

Given this reasoning:
None of the provided answers correctly describe the sum \( p + (-q) \) in terms of distances and directions. In essence, \( p + (-q) \) represents the numerical value that results from subtracting \( q \) from \( p \) and should not be described in terms of distances in the positive or negative directions from either \( p \) or \( q \).

If forced to choose based on common interpretations, none fully capture the essence of \( p - q \). Therefore, it appears all options might be misleading or incorrect.
Answered by GPT-4o mini
Given the need to choose the best answer among the given options, the closest option would be:

**"The sum \( p + (-q) \) is the number located a distance \( |q| \) from \( p \) in the negative direction."**

While this statement isn't perfectly accurate because it doesn't consider whether \( p \) is greater than, less than, or equal to \( q \), it's the closest option because it implies that \( p + (-q) = p - q \) positions relative to \( q \), moving in the negative direction when \( q \) is subtracted from \( p \).

So, while it isn't entirely correct, it speaks to the general idea of subtraction and the positioning on a number line.

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