Which of the following describes the sum in terms of p and q?(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 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 p from q in the positive direction.
The sum negative p plus left parenthesis negative q right parenthesis is the number located a distance p from q in the positive direction.
The sum p+(−q) is the number located a distance |q| from p in the negative direction.
Which number line shows the correct way to find the sum p+q if p is positive and q is negative?
To find the sum p+q when p is positive and q is negative, the correct number line should show p as a positive value and q as a negative value, with the sum represented by a point located between p and q, closer to p. The number line should have its positive values on the right side and negative values on the left side.
Use properties of operations to add (−3) and (−17).(1 point)
Responses
negative 14
14
20
−20
The correct response is: negative 20
Add (4) and (−15).(1 point)
Responses
negative 11
negative 19
19
11
The correct response is: negative 11
Add (−18) and (5).(1 point)
Responses
13
13
−23
negative 23
23
23
−13
The correct response is: -13
To determine which statement describes the sum in terms of p and q, we need to analyze each response and consider their explanations.
1) The sum p+(-q) is the number located a distance |q| from p in the positive direction.
Explanation: This statement correctly describes that the sum p+(-q) represents a number that is a distance |q| away from p, in the positive direction.
2) 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.
Explanation: This statement is providing the same information as the first statement, just in a different format. It also correctly describes that the sum p+(-q) represents a number that is a distance |q| away from p, in the positive direction.
3) The sum p+(-q) is the number located a distance |p| from q in the negative direction.
Explanation: This statement describes a different scenario than the ones mentioned in the previous two statements. Here, the sum p+(-q) is said to represent a number that is a distance |p| away from q, but in the negative direction. This is not consistent with the previous explanations.
4) 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.
Explanation: This statement also describes a different scenario where the sum p+(-q) represents a number that is a distance |p| away from q, but in the negative direction. This is inconsistent with the previous explanations.
5) The sum -p+(-q) is the number located a distance p from q in the positive direction.
Explanation: This statement describes a different sum, -p+(-q), which is not the same as the sum p+(-q) mentioned in the other statements. Therefore, it does not describe the sum in terms of p and q.
6) The sum negative p plus left parenthesis negative q right parenthesis is the number located a distance p from q in the positive direction.
Explanation: This statement also describes a different sum, negative p plus left parenthesis negative q right parenthesis, which is not the same as the sum p+(-q) mentioned in the other statements. Therefore, it does not describe the sum in terms of p and q.
7) The sum p+(-q) is the number located a distance |q| from p in the negative direction.
Explanation: This statement describes the sum p+(-q) as a number located a distance |q| from p, but in the negative direction. This is inconsistent with the previous explanations.
Based on the explanations provided, we can conclude that the first two statements (1 and 2) correctly describe the sum in terms of p and q, as they provide consistent and accurate explanations.