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Short answer📘 N.RN.A.2🧠 DOK 2

Question:

Simplify the expression (x^(1/3) * y^(1/6))^6 using the properties of exponents.

✅ Answer:
x^2 * y

💡 Explanation:

  • Using the properties of exponents, when raising a power to a power, you multiply the exponents.

  • Therefore, (x^(1/3))^6 = x^(1/3 * 6) = x^2 and (y^(1/6))^6 = y^(1/6 * 6) = y^1 = y.

  • Hence, the expression simplifies to x^2 * y.

Standard: N.RN.A.2 | DOK: 2

Recent Questions

Dropdown📘 A.APR.C.2🧠 DOK 2

Question:

Given the expression (x+y)5(x + y)^5, use the Binomial Theorem to determine the coefficient of the x3y2x^3y^2 term.

Answer Choices:

  • A) 10
  • B) 5
  • C) 20
  • D) 30
✅ Answer:
10

💡 Explanation:

  • The Binomial Theorem states that (x+y)n=∑k=0n(nk)xn−kyk(x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k.

  • For the term x3y2x^3y^2, we need k=2k = 2 and n−k=3n-k = 3, and n=5n = 5.

  • The coefficient is (52)=10\binom{5}{2} = 10.

Standard: A.APR.C.2 | DOK: 2

Short answer📘 6.2.8.GeoHE.2.a🧠 DOK 4

Question:

Explain how the geographic features of early river valley civilizations influenced their settlement patterns, development of trade networks, technological innovations, and overall sustainability. Provide specific examples from at least two different river valley civilizations to support your explanation.

✅ Answer:
Geographic features such as fertile land, access to water, and natural barriers significantly influenced early river valley civilizations. In Mesopotamia, the Tigris and Euphrates rivers provided rich soil for agriculture, leading to settled farming communities and technological innovations like irrigation systems. The rivers also facilitated trade networks with neighboring regions. Similarly, the Nile River in Egypt offered predictable flooding patterns that supported agriculture and trade routes that connected Egypt with Africa and the Middle East. Natural barriers, such as deserts surrounding the Nile, provided protection, contributing to the civilization's sustainability.

💡 Explanation:

  • The geographic features of river valleys, such as fertile soil, water access, and natural protective barriers, played a crucial role in the settlement and development of civilizations.
  • These features allowed for stable agriculture, which supported population growth and technological advancements.
  • Trade networks flourished along these rivers, encouraging cultural exchange and economic wealth.
  • By examining Mesopotamia and Egypt, we see how geography shaped their growth and sustainability, with innovations like irrigation and trade routes stemming from their unique environments.

Standard: 6.2.8.GeoHE.2.a | DOK: 4

Dropdown📘 6.2.8.GeoPP.3.a🧠 DOK 2

Question:

How did the availability of natural resources influence the development of classical civilizations? Choose the correct option to complete the sentence: The abundance of natural resources such as fertile land and water in ancient Egypt led to the development of a strong political system because it allowed the civilization to:

Answer Choices:

  • A) expand their trade networks significantly
  • B) sustain a large population and organized society
  • C) create advanced tools and technologies
  • D) develop a system of writing and record keeping
✅ Answer:
sustain a large population and organized society

💡 Explanation:

  • The availability of natural resources like fertile land and water allowed ancient Egypt to sustain a large population, which in turn supported the development of a complex and organized political system.

Standard: 6.2.8.GeoPP.3.a | DOK: 2

Dropdown📘 W.NW.7.3.e🧠 DOK 2
After hiking for hours, Sarah finally reached the summit of the mountain. The view was breathtaking, with endless forests stretching out beneath her and the sky painted in hues of orange and pink. As she sat down to rest, she felt a sense of accomplishment wash over her, realizing that all her training had paid off. Reflecting on her journey, she knew this moment would inspire her future adventures.

Question:

What can be inferred about Sarah's feelings at the end of her hike?

Answer Choices:

  • A) She feels disappointed with the view.
  • B) She feels a sense of accomplishment.
  • C) She regrets the effort it took to reach the summit.
  • D) She is worried about the descent.
✅ Answer:
She feels a sense of accomplishment.

💡 Explanation:

  • The passage indicates that Sarah feels a sense of accomplishment and inspiration from her successful hike to the mountain summit, suggesting a positive reflection on her experience.

Standard: W.NW.7.3.e | DOK: 2

Multiple select📘 6.3.8.CivicsPR.4🧠 DOK 4

Question:

Which of the following pieces of evidence and quantitative data could be used to propose or defend a public policy aimed at reducing carbon emissions to combat climate change? Select all that apply.

Answer Choices:

  • A) A report showing a 20% increase in average global temperatures over the past century.
  • B) Data indicating a 15% reduction in air pollution levels in cities that have implemented strict emission regulations.
  • C) A survey of public opinion showing 80% support for renewable energy initiatives.
  • D) A study demonstrating a correlation between deforestation and increased carbon dioxide levels in the atmosphere.
  • E) Graphs illustrating a decrease in ice cap size over the last 50 years.
✅ Answer:
Data indicating a 15% reduction in air pollution levels in cities that have implemented strict emission regulations.; A study demonstrating a correlation between deforestation and increased carbon dioxide levels in the atmosphere.; Graphs illustrating a decrease in ice cap size over the last 50 years.

💡 Explanation:

  • The selected options provide data and evidence that can be used to support policies aimed at reducing carbon emissions: reduction in air pollution in cities with emission regulations, correlation between deforestation and carbon dioxide levels, and decreasing ice cap size are all relevant to climate change policy making.

Standard: 6.3.8.CivicsPR.4 | DOK: 4

Multiple select📘 W.AW.7.1.b🧠 DOK 2
Recent studies have shown that urban green spaces, such as parks and community gardens, play a crucial role in improving air quality. These areas help in reducing pollution by absorbing carbon dioxide and releasing oxygen. Furthermore, they provide residents with opportunities for physical activities, which can promote overall health. Experts argue that increasing the number of green spaces in cities can lead to a healthier and more sustainable urban environment.

Question:

Which of the following statements are supported by the passage?

Answer Choices:

  • A) Urban green spaces contribute to better air quality.
  • B) Parks and gardens are a source of pollution.
  • C) Green spaces encourage physical activity among residents.
  • D) Increasing urban green spaces harms the urban environment.
✅ Answer:
Urban green spaces contribute to better air quality.; Green spaces encourage physical activity among residents.

💡 Explanation:

  • The passage states that urban green spaces improve air quality by absorbing carbon dioxide and releasing oxygen.
  • It also mentions that these areas provide opportunities for physical activities, promoting overall health.

Standard: W.AW.7.1.b | DOK: 2

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