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.

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GPT-4o mini · Answer

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 $.

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

GPT-4o mini · Answer

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**

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

GPT-4o mini · Answer

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**

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

GPT-4o mini · Answer

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**

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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.

GPT-4o mini · Answer

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 $.