Asked by Savannah
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.
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
Answered by
Savannah
Which number line shows the correct way to find the sum p+q if p is positive and q is negative?(1 point)
Responses
A number line is shown with arrows at both ends, and hashmarks 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.
Image with alt text: A number line is shown with arrows at both ends, and hashmarks 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.
A number line is shown with arrows at both ends, and hashmarks at unit intervals. The second mark from the left is labeled 0. Point p is located 5 intervals to the right of 0. A leftward curved arrow, labeled absolute value of q, starts at p and ends 4 intervals to the left of p.
Image with alt text: A number line is shown with arrows at both ends, and hashmarks at unit intervals. The second mark from the left is labeled 0. Point p is located 5 intervals to the right of 0. A leftward curved arrow, labeled absolute value of q, starts at p and ends 4 intervals to the left of p.
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 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.
A number line is shown with arrows at both ends, and hashmarks 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 hashmarks 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.
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Responses
A number line is shown with arrows at both ends, and hashmarks 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.
Image with alt text: A number line is shown with arrows at both ends, and hashmarks 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.
A number line is shown with arrows at both ends, and hashmarks at unit intervals. The second mark from the left is labeled 0. Point p is located 5 intervals to the right of 0. A leftward curved arrow, labeled absolute value of q, starts at p and ends 4 intervals to the left of p.
Image with alt text: A number line is shown with arrows at both ends, and hashmarks at unit intervals. The second mark from the left is labeled 0. Point p is located 5 intervals to the right of 0. A leftward curved arrow, labeled absolute value of q, starts at p and ends 4 intervals to the left of p.
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 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.
A number line is shown with arrows at both ends, and hashmarks 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 hashmarks 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.
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Answered by
Savannah
Use properties of operations to add (−3) and (−17) .(1 point)
Responses
14
14
−14
negative 14
−20
negative 20
20
Responses
14
14
−14
negative 14
−20
negative 20
20
Answered by
Savannah
Add (4) and (−15) .(1 point)
Responses
−19
negative 19
−11
negative 11
11
11
19
Responses
−19
negative 19
−11
negative 11
11
11
19
Answered by
Savannah
Add (−18) and (5) .(1 point)
Responses
−13
negative 13
−23
negative 23
23
23
13
Responses
−13
negative 13
−23
negative 23
23
23
13
Answered by
GPT-4o mini
To analyze the expression \( p + (-q) \), we can simplify it to \( p - q \).
Given that both \( p \) and \( q \) are positive numbers, this means:
- If \( p > q \), then \( p - q \) is positive, and the result is still a positive number.
- If \( p < q \), then \( p - q \) is negative, indicating the result lies below zero.
Thus, the correct interpretation of the sum \( p + (-q) \) focuses on the fact that it represents the number \( p \) decreased by \( q \). This can be seen as moving a distance \( |q| \) from \( p \).
Among the options provided, the description that correctly encapsulates this idea is:
**The sum \( p + (-q) \) is the number located a distance |q| from p in the negative direction.**
This reflects that the outcome of \( p - q \) can be viewed as moving down \( q \) units from \( p \).
Given that both \( p \) and \( q \) are positive numbers, this means:
- If \( p > q \), then \( p - q \) is positive, and the result is still a positive number.
- If \( p < q \), then \( p - q \) is negative, indicating the result lies below zero.
Thus, the correct interpretation of the sum \( p + (-q) \) focuses on the fact that it represents the number \( p \) decreased by \( q \). This can be seen as moving a distance \( |q| \) from \( p \).
Among the options provided, the description that correctly encapsulates this idea is:
**The sum \( p + (-q) \) is the number located a distance |q| from p in the negative direction.**
This reflects that the outcome of \( p - q \) can be viewed as moving down \( q \) units from \( p \).
Answered by
GPT-4o mini
To determine which number line correctly represents the sum \( p + q \) when \( p \) is positive and \( q \) is negative, we need to consider how addition works with a positive and a negative number.
1. **Positive number \( p \)**: This number represents a position on the number line to the right of 0.
2. **Negative number \( q \)**: This number can be represented as \( -|q| \), indicating a movement to the left on the number line. To find \( p + q \), you essentially move left from \( p \) by the absolute value of \( q \).
Given this context, the correct number line would show:
- Point \( p \) marked a certain distance to the right of 0.
- A leftward arrow indicating a movement of \( |q| \) intervals from point \( p \).
From the given options, the description that matches this understanding is:
**A number line is shown with arrows at both ends, and hashmarks at unit intervals. The second mark from the left is labeled 0. Point p is located 5 intervals to the right of 0. A leftward curved arrow, labeled absolute value of q, starts at p and ends 4 intervals to the left of p.**
This reflects the movement from point \( p \) leftward, which correctly depicts the sum \( p + q \) when \( q \) is negative.
1. **Positive number \( p \)**: This number represents a position on the number line to the right of 0.
2. **Negative number \( q \)**: This number can be represented as \( -|q| \), indicating a movement to the left on the number line. To find \( p + q \), you essentially move left from \( p \) by the absolute value of \( q \).
Given this context, the correct number line would show:
- Point \( p \) marked a certain distance to the right of 0.
- A leftward arrow indicating a movement of \( |q| \) intervals from point \( p \).
From the given options, the description that matches this understanding is:
**A number line is shown with arrows at both ends, and hashmarks at unit intervals. The second mark from the left is labeled 0. Point p is located 5 intervals to the right of 0. A leftward curved arrow, labeled absolute value of q, starts at p and ends 4 intervals to the left of p.**
This reflects the movement from point \( p \) leftward, which correctly depicts the sum \( p + q \) when \( q \) is negative.
Answered by
GPT-4o mini
To add \((-3)\) and \((-17)\), we can apply the properties of addition. When adding two negative numbers, the result is negative, and their absolute values are added together.
1. Calculate the absolute values: \(|-3| = 3\) and \(|-17| = 17\).
2. Add the absolute values: \(3 + 17 = 20\).
3. Since both original numbers were negative, the result will also be negative: \(-20\).
Thus, the sum of \((-3)\) and \((-17)\) is:
\(-20\) (negative 20)
The correct response is:
**−20**
1. Calculate the absolute values: \(|-3| = 3\) and \(|-17| = 17\).
2. Add the absolute values: \(3 + 17 = 20\).
3. Since both original numbers were negative, the result will also be negative: \(-20\).
Thus, the sum of \((-3)\) and \((-17)\) is:
\(-20\) (negative 20)
The correct response is:
**−20**
Answered by
GPT-4o mini
To add \(4\) and \((-15)\), we can follow these steps:
1. Recognize that adding a negative number is the same as subtracting its absolute value. Thus, \(4 + (-15) = 4 - 15\).
2. Perform the subtraction:
\[
4 - 15 = -11
\]
So, the sum of \(4\) and \((-15)\) is \(-11\) (negative 11).
The correct response is:
**−11** (negative 11)
1. Recognize that adding a negative number is the same as subtracting its absolute value. Thus, \(4 + (-15) = 4 - 15\).
2. Perform the subtraction:
\[
4 - 15 = -11
\]
So, the sum of \(4\) and \((-15)\) is \(-11\) (negative 11).
The correct response is:
**−11** (negative 11)
Answered by
GPT-4o mini
To add \((-18)\) and \(5\), you can understand it as:
1. Adding a positive number to a negative number means you subtract the absolute value of the negative number from the positive number.
2. Calculate:
\[
5 + (-18) = 5 - 18
\]
3. Perform the subtraction:
\[
5 - 18 = -13
\]
Thus, the sum of \((-18)\) and \(5\) is \(-13\) (negative 13).
The correct response is:
**−13** (negative 13)
1. Adding a positive number to a negative number means you subtract the absolute value of the negative number from the positive number.
2. Calculate:
\[
5 + (-18) = 5 - 18
\]
3. Perform the subtraction:
\[
5 - 18 = -13
\]
Thus, the sum of \((-18)\) and \(5\) is \(-13\) (negative 13).
The correct response is:
**−13** (negative 13)
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