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ACT Exam  >  ACT Questions  >  4x3 × 3xy2 × 2xy2 is equivalent t... Start Learning for Free
4x3 × 3xy2 × 2xy2 is equivalent to:
  • a)
    9x3 y4
  • b)
    9x5 y4
  • c)
    24x3 y4
  • d)
    24x5 y4
  • e)
    24x5 y6
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
4x3 × 3xy2 × 2xy2 is equivalent to:a)9x3 y4b)9x5 y4c)24x3 ...
The correct answer is d. To find an equivalent expression, multiply the constants (4 × 3 × 2 = 24), combine the x terms (x3 × x × x) → x3+1+1 → x5, and combine the y terms (y2 × y2 → y2+2 → y4).
The result is 24x5 y4.
The most common incorrect answers are a and c, which come from multiplying the exponents of the x and y terms instead of adding them. If you chose b, you probably added the constants instead of multiplying them.
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Adapted from "The Weakness, Unrest, and Defects of Man," from The Thoughts of Blaise Pascal (ed. 1901)We care nothing for the present. We anticipate the future as too slow in coming, as if we could make it move faster; or we call back the past, to stop its rapid flight. So imprudent are we that we wander through the times in which we have no part, unthinking of that which alone is ours; so frivolous are we that we dream of the days which are not and pass by without reflection those which alone exist. For the days of the present generally gives us pain; we conceal it from our sight because it afflicts us, and if it be pleasant, we regret to see it vanish away. We endeavor to sustain the present by the future, and think of arranging things not in our power, for a time at which we have no certainty of arriving.If we examine our thoughts, we shall find them always occupied with the past or the future. We scarcely think of the present, and if we do so, it is only that we may borrow light from it to direct the future. The present is never our end; the past and the present are our means, the future alone is our end. Thus we never live, but hope to live, and while we always lay ourselves out to be happy, it is inevitable that we can never be so.What is the best equivalent for the bolded "that we may borrow" in the passage?

Directions:Read the passages and choose the best answer to each question.PassageTurf grasses are used throughout the United States in many suburban lawns. Kentucky bluegrass is the most common type of turf grass used in the northern part of the United States. To keep lawns green and healthy, many homeowners apply fertilizer up to five times a year. Inorganic fertilizers are becoming more popular, and contain three common elements – nitrogen, phosphorous, and potassium – for the development of plant color, strength, and health. Most turf grass lawns do not use all of the nutrients provided in the fertilizer, which means that much of the nitrogen, phosphorous, and potassium remains in the soil. When water enters the soil, it accumulates a portion of the excess nitrogen from the soil. This water, now termed leachate, flows into surrounding waterways. The leaching of high concentrations of nitrogen into natural waterways can throw off the environmental equilibrium of the aquatic ecosystem, often resulting in an increase in plant growth that can have a negative impact on the native fish populations.A study was performed to examine the degree of nitrogen leaching in Kentucky bluegrass turf; 2 one-acre plots of turf were compared. The scientists conducting the study relied completely on natural rainwater to irrigate the test plots. Each plot received fertilizer applications containing different levels of nitrogen two times per week during the months of April and September for 5 years. The plots had a 5% slope to facilitate leaching; leachate was collected in one-liter jugs. The leachate collected from each plot was measured for nitrogen concentration.Plot A, received a low nitrogen application, 98 kilograms of N per acre from 2000 to 2004. Plot B, received an initially high nitrogen application, 245 kilograms of N per acre from 2000–2002. In the last year of the study, the amount of nitrogen in the fertilizer was decreased to 196 kilograms of N per acre for Plot B. Table 1 shows the average nitrogen concentration in milligrams per liter (mg/L) in the leachate collected from each plot during each year. Figure 1 shows the percent concentration of nitrogen in the leachate.Q.According to the Environmental Protection Agency, average nitrogen levels in leachate must be less than 10 mg/L to be safe for the environment. Based on this standard and the results of the study, which of the following fertilizer applications is considered safe?

Directions:Read the passages and choose the best answer to each question.PassageTurf grasses are used throughout the United States in many suburban lawns. Kentucky bluegrass is the most common type of turf grass used in the northern part of the United States. To keep lawns green and healthy, many homeowners apply fertilizer up to five times a year. Inorganic fertilizers are becoming more popular, and contain three common elements – nitrogen, phosphorous, and potassium – for the development of plant color, strength, and health. Most turf grass lawns do not use all of the nutrients provided in the fertilizer, which means that much of the nitrogen, phosphorous, and potassium remains in the soil. When water enters the soil, it accumulates a portion of the excess nitrogen from the soil. This water, now termed leachate, flows into surrounding waterways. The leaching of high concentrations of nitrogen into natural waterways can throw off the environmental equilibrium of the aquatic ecosystem, often resulting in an increase in plant growth that can have a negative impact on the native fish populations.A study was performed to examine the degree of nitrogen leaching in Kentucky bluegrass turf; 2 one-acre plots of turf were compared. The scientists conducting the study relied completely on natural rainwater to irrigate the test plots. Each plot received fertilizer applications containing different levels of nitrogen two times per week during the months of April and September for 5 years. The plots had a 5% slope to facilitate leaching; leachate was collected in one-liter jugs. The leachate collected from each plot was measured for nitrogen concentration.Plot A, received a low nitrogen application, 98 kilograms of N per acre from 2000 to 2004. Plot B, received an initially high nitrogen application, 245 kilograms of N per acre from 2000–2002. In the last year of the study, the amount of nitrogen in the fertilizer was decreased to 196 kilograms of N per acre for Plot B. Table 1 shows the average nitrogen concentration in milligrams per liter (mg/L) in the leachate collected from each plot during each year. Figure 1 shows the percent concentration of nitrogen in the leachate.Q. It was determined that during times of heavy rain, more nitrogen was leached from the soil. Based on the results of the study, which year most likely had times of heavy rain in April and September?

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4x3 × 3xy2 × 2xy2 is equivalent to:a)9x3 y4b)9x5 y4c)24x3 y4d)24x5 y4e)24x5 y6Correct answer is option 'D'. Can you explain this answer?
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