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If p and q represent non-zero integers, which of the following could lie in the same quadrant of the xy-plane as (p, q)?
  • a)
    (-2p, 3q)
  • b)
    (2p, -3q)
  • c)
    (-2q, -3p)
  • d)
    (-34, 2p)
  • e)
    (2q, -3p)
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If p and q represent non-zero integers, which of the following could l...
To determine which of the given points could lie in the same quadrant of the xy-plane as (p, q), we need to analyze the signs of the x and y coordinates.
If (p, q) lies in the first quadrant (both x and y positive), then any point that also has both x and y positive coordinates will lie in the same quadrant.
Let's examine the given options:
A: (-2p, 3q) - Both x and y coordinates have different signs, so it cannot lie in the same quadrant.
B: (2p, -3q) - The x coordinate is positive, but the y coordinate is negative, so it cannot lie in the same quadrant.
C: (-2q, -3p) - Both x and y coordinates have negative signs, so it can lie in the same quadrant.
D: (-34, 2p) - The x coordinate is negative, but the y coordinate is positive, so it cannot lie in the same quadrant.
E: (2q, -3p) - The x coordinate is positive, but the y coordinate is negative, so it cannot lie in the same quadrant.
Based on this analysis, the only option that could lie in the same quadrant as (p, q) is option C: (-2q, -3p).
Therefore, the correct answer is C.
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Most Upvoted Answer
If p and q represent non-zero integers, which of the following could l...
To determine which of the given points could lie in the same quadrant of the xy-plane as (p, q), we need to analyze the signs of the x and y coordinates.
If (p, q) lies in the first quadrant (both x and y positive), then any point that also has both x and y positive coordinates will lie in the same quadrant.
Let's examine the given options:
A: (-2p, 3q) - Both x and y coordinates have different signs, so it cannot lie in the same quadrant.
B: (2p, -3q) - The x coordinate is positive, but the y coordinate is negative, so it cannot lie in the same quadrant.
C: (-2q, -3p) - Both x and y coordinates have negative signs, so it can lie in the same quadrant.
D: (-34, 2p) - The x coordinate is negative, but the y coordinate is positive, so it cannot lie in the same quadrant.
E: (2q, -3p) - The x coordinate is positive, but the y coordinate is negative, so it cannot lie in the same quadrant.
Based on this analysis, the only option that could lie in the same quadrant as (p, q) is option C: (-2q, -3p).
Therefore, the correct answer is C.
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Community Answer
If p and q represent non-zero integers, which of the following could l...
Explanation:

Understanding Quadrants:
- In the xy-plane, the x-axis and y-axis divide the plane into four quadrants: Quadrant I, Quadrant II, Quadrant III, and Quadrant IV.
- Quadrant I: (+, +), Quadrant II: (-, +), Quadrant III: (-, -), Quadrant IV: (+, -).

Analysis of Options:
- Option a) (-2p, 3q): This lies in Quadrant II.
- Option b) (2p, -3q): This lies in Quadrant IV.
- Option c) (-2q, -3p): This lies in the same quadrant as (p, q) because both have negative x and y coordinates.
- Option d) (-34, 2p): This lies in Quadrant II.
- Option e) (2q, -3p): This lies in Quadrant III.

Conclusion:
- The only option that lies in the same quadrant as (p, q) is option c) (-2q, -3p).
- Therefore, option c) is the correct answer.
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Experts anticipate that global atmospheric concentrations of carbon dioxide (CO2) will have doubled by the end of the twenty-first century. It is known that CO2 can contribute to global warming by (5) trapping solar energy that is being reradiated as heat from the Earth’s surface. However, some research has suggested that elevated CO2 levels could enhance the photosynthetic rates of plants, resulting in a lush world of agricultural abundance, and that this CO2 (10) fertilization effect might eventually decrease the rate of global warming. The increased vegetation in such an environment could be counted on to draw more CO2 from the atmosphere. The level of CO2 would thus increase at a lower rate than many experts have (15) predicted.However, while a number of recent studies confirm that plant growth would be generally enhanced in an atmosphere rich in CO2, they also suggest that increased CO2 would differentially increase the growth (20) rate of different species of plants, which could eventually result in decreased agricultural yields. Certain important crops such as corn and sugarcane that currently have higher photosynthetic efficiencies than other plants may lose that edge in an atmosphere (25) rich in CO2. Patterson and Flint have shown that these important crops may experience yield reductions because of the increased performance of certain weeds. Such differences in growth rates between plant species could also alter ecosystem stability. Studies have (30) shown that within rangeland regions, for example, a weedy grass grows much better with plentiful CO2 than do three other grasses. Because this weedy grass predisposes land to burning, its potential increase may lead to greater numbers of and more severe wildfires in (35) future rangeland communities.It is clear that the CO2 fertilization effect does not guarantee the lush world of agricultural abundance that once seemed likely, but what about the potential for the increased uptake of CO2 to decrease the rate of global (40) warming? Some studies suggest that the changes accompanying global warming will not improve the ability of terrestrial ecosystems to absorb CO2. Billings’ simulation of global warming conditions in wet tundra grasslands showed that the level of CO2 (45) actually increased. Plant growth did increase under these conditions because of warmer temperatures and increased CO2 levels. But as the permafrost melted, more peat (accumulated dead plant material) began to decompose. This process in turn liberated more CO2 to (50) the atmosphere. Billings estimated that if summer temperatures rose four degrees Celsius, the tundra would liberate 50 percent more CO2 than it does currently. In a warmer world, increased plant growth, which could absorb CO2 from the atmosphere, would (55) not compensate for this rapid increase in decomposition rates. This observation is particularly important because high-latitude habitats such as the tundra are expected to experience the greatest temperature increase.The author would be most likely to agree with which one of the following statements about the conclusions drawn on the basis of the research on plant growth mentioned in the first paragraph of the passage?

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If p and q represent non-zero integers, which of the following could lie in the same quadrant of the xy-plane as (p, q)?a)(-2p, 3q)b)(2p, -3q)c)(-2q, -3p)d)(-34, 2p)e)(2q, -3p)Correct answer is option 'C'. Can you explain this answer?
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