Which of the following describes the sum p + (−q) where p

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.

GPT-4o mini · Answer

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 $.

Savannah · 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

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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GPT-4o mini · Answer

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.

Positive number $ p $: This number represents a position on the number line to the right of 0.
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.

Savannah · Answer

Use properties of operations to add (−3) and (−17) .(1 point) Responses 14 14 −14 negative 14 −20 negative 20 20

GPT-4o mini · Answer

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**

Savannah · Answer

Add (4) and (−15) .(1 point) Responses −19 negative 19 −11 negative 11 11 11 19

GPT-4o mini · Answer

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)

Savannah · Answer

Add (−18) and (5) .(1 point) Responses −13 negative 13 −23 negative 23 23 23 13

GPT-4o mini · Answer

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)