Question
hich 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 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 |p| from q in the negative direction. The sum p plus left parenthesis negative q right parenthesis is the number located a distance Start Absolute Value p End Absolute Value 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 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 |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.
Answers
Answer
Question Use properties of operations to add (−3) and (−17) .(1 point) Responses −14 negative 14 20 20 −20 negative 20 14
Answer
Add (4) and (−15).(1 point) Responses −19 negative 19 19 19 −11 negative 11 11
Answer
Add (−18) and (5) .(1 point) Responses −13 negative 13 23 23 −23 negative 23 13
Answer
Which number line shows the correct way to find the sum p+q if p is positive and q is negative?(1 point) Responses Image with alt text: A number line ranging from 0 in unit increments shows an arrow, labeled absolute value of q, starting at point p and ending 4 units to the right. Image with alt text: A number line is shown with arrows at both ends, and hash marks at unit intervals. Point p is marked on the seventh interval from the left. Zero is marked 2 intervals to the right of p. A leftward curved arrow, labeled absolute value of q, points from p to the second interval from the left. Image with alt text: A number line is shown with arrows at both ends, and hash marks at unit intervals. The second point from the left is labeled p. Zero is marked at 6 intervals to the right of point p. A rightward curved arrow, labeled absolute value of q, starts at p and ends 4 intervals to the right of p.
Answered by
GPT-4o mini
To analyze the sum \( p + (-q) \), we can rewrite it as \( p - q \). Since both \( p \) and \( q \) are positive numbers, the result will depend on their relative sizes.
1. If \( p > q \), then \( p - q \) is positive and represents the distance from \( q \) moving in the positive direction.
2. If \( p < q \), then \( p - q \) is negative and represents the distance from \( p \) moving in the negative direction.
3. If \( p = q \), then \( p - q = 0\).
Now, out of the given options, the correct interpretation of the sum \( p + (-q) \) or \( p - q \) can be summarized as follows:
- If \( p > q \): It is \( p - q \), and you can visualize this as starting at \( q \) and moving a distance of \( p \) to the right (positive direction).
- If \( p < q \): The absolute value \( |p| \) indicates how far you are from \( q \) in the negative direction.
The best choice to express this generally, without assuming more about the relationship between \( p \) and \( q \), is:
**The sum \( p + (-q) \) is the number located a distance \( |q| \) from \( p \) in the negative direction.**
When \( p < q\), you're moving left and vice versa, confirming that \( p + (-q) \) could represent different positions based on the values of \( p \) and \( q \).
1. If \( p > q \), then \( p - q \) is positive and represents the distance from \( q \) moving in the positive direction.
2. If \( p < q \), then \( p - q \) is negative and represents the distance from \( p \) moving in the negative direction.
3. If \( p = q \), then \( p - q = 0\).
Now, out of the given options, the correct interpretation of the sum \( p + (-q) \) or \( p - q \) can be summarized as follows:
- If \( p > q \): It is \( p - q \), and you can visualize this as starting at \( q \) and moving a distance of \( p \) to the right (positive direction).
- If \( p < q \): The absolute value \( |p| \) indicates how far you are from \( q \) in the negative direction.
The best choice to express this generally, without assuming more about the relationship between \( p \) and \( q \), is:
**The sum \( p + (-q) \) is the number located a distance \( |q| \) from \( p \) in the negative direction.**
When \( p < q\), you're moving left and vice versa, confirming that \( p + (-q) \) could represent different positions based on the values of \( p \) and \( q \).
Answered by
GPT-4o mini
To add \((-3)\) and \((-17)\), you can use the following steps:
\[
(-3) + (-17) = -3 - 17
\]
When adding two negative numbers, you add their absolute values and keep the negative sign:
\[
3 + 17 = 20
\]
Thus,
\[
(-3) + (-17) = -20
\]
So, the correct answer is:
**−20**
\[
(-3) + (-17) = -3 - 17
\]
When adding two negative numbers, you add their absolute values and keep the negative sign:
\[
3 + 17 = 20
\]
Thus,
\[
(-3) + (-17) = -20
\]
So, the correct answer is:
**−20**
Answered by
GPT-4o mini
To add \(4\) and \(-15\), you can set it up as follows:
\[
4 + (-15) = 4 - 15
\]
When you subtract a positive number from a smaller positive number, you get a negative result:
\[
4 - 15 = -11
\]
So, the correct answer is:
**−11**
\[
4 + (-15) = 4 - 15
\]
When you subtract a positive number from a smaller positive number, you get a negative result:
\[
4 - 15 = -11
\]
So, the correct answer is:
**−11**
Answered by
GPT-4o mini
To add \((-18)\) and \(5\), you can set it up as follows:
\[
-18 + 5
\]
This can be interpreted as starting at \(-18\) and moving \(5\) units to the right (towards the positive direction).
Calculating that:
\[
-18 + 5 = -13
\]
So, the correct answer is:
**−13**
\[
-18 + 5
\]
This can be interpreted as starting at \(-18\) and moving \(5\) units to the right (towards the positive direction).
Calculating that:
\[
-18 + 5 = -13
\]
So, the correct answer is:
**−13**
Answered by
GPT-4o mini
To find the sum \( p + q \) where \( p \) is a positive number and \( q \) is a negative number, you need to start at the position of \( p \) on the number line and then move left by the absolute value of \( q \).
Since \( q \) is negative, the arrow should point to the left from \( p \), indicating a decrease in value.
Given that understanding, the correct number line would be the one that shows:
- Point \( p \) on the number line, representing the positive value.
- An arrow pointing **leftward from \( p \)**, indicating that you are subtracting the absolute value of \( q \).
From your descriptions, the correct option would be:
**The number line where point p is marked on the seventh interval from the left and shows a leftward curved arrow labeled absolute value of q pointing from p to the second interval from the left.**
This correctly illustrates moving from the positive position \( p \) left by the magnitude of \( q \) to find the sum \( p + q \).
Since \( q \) is negative, the arrow should point to the left from \( p \), indicating a decrease in value.
Given that understanding, the correct number line would be the one that shows:
- Point \( p \) on the number line, representing the positive value.
- An arrow pointing **leftward from \( p \)**, indicating that you are subtracting the absolute value of \( q \).
From your descriptions, the correct option would be:
**The number line where point p is marked on the seventh interval from the left and shows a leftward curved arrow labeled absolute value of q pointing from p to the second interval from the left.**
This correctly illustrates moving from the positive position \( p \) left by the magnitude of \( q \) to find the sum \( p + q \).
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