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Multiple select📘 G.SRT.D.10🧠 DOK 1

Question:

Which of the following statements correctly describe the application of the Law of Sines or the Law of Cosines in solving triangles? Select all that apply.

Answer Choices:

  • A) The Law of Sines can be used to find the length of a side in a right triangle when two angles and one side are known.
  • B) The Law of Cosines can be used to find the length of a side in a non-right triangle when two sides and the included angle are known.
  • C) The Law of Sines is only applicable to right triangles.
  • D) The Law of Cosines applies only to isosceles triangles.
  • E) The Law of Sines can be used to find an unknown angle in a non-right triangle when two sides and one angle are known.
✅ Answer:
The Law of Sines can be used to find the length of a side in a right triangle when two angles and one side are known.;The Law of Cosines can be used to find the length of a side in a non-right triangle when two sides and the included angle are known.;The Law of Sines can be used to find an unknown angle in a non-right triangle when two sides and one angle are known.

💡 Explanation:

  • The Law of Sines is applicable for any triangle, not just right triangles, and can be used when we know two angles and one side or two sides and one angle.

  • The Law of Cosines, on the other hand, is useful for finding unknown sides or angles in any triangle, not just isosceles triangles, particularly when two sides and the included angle are known.

Standard: G.SRT.D.10 | DOK: 1

Recent Questions

Multiple choice📘 7.G.A.2🧠 DOK 4

Question:

You are given three line segments of lengths 7 cm, 10 cm, and 5 cm. Which of the following statements is true about constructing a triangle using these line segments?

Answer Choices:

  • A) A triangle can be constructed using these line segments because the sum of any two sides is greater than the third side.
  • B) A triangle cannot be constructed using these line segments because the sum of the two shorter sides is not greater than the longest side.
  • C) A triangle can be constructed using these line segments because the sum of all three sides is greater than 20 cm.
  • D) A triangle cannot be constructed using these line segments because all sides must be equal.
✅ Answer:
A triangle cannot be constructed using these line segments because the sum of the two shorter sides is not greater than the longest side.

💡 Explanation:

  • According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

  • In this case, 7 cm + 5 cm = 12 cm, which is not greater than 10 cm.

  • Therefore, a triangle cannot be constructed with these segments.

Standard: 7.G.A.2 | DOK: 4

Short answer📘 MS-ESS3-1🧠 DOK 2

Question:

Explain how the uneven distribution of Earth's mineral resources is related to past geoscience processes. Provide specific examples to support your explanation.

✅ Answer:
The uneven distribution of Earth's mineral resources is largely due to historical geoscience processes such as volcanic activity, tectonic plate movements, and erosion. For example, volcanic activity can bring minerals from deep within the Earth to the surface, leading to concentrated deposits in certain areas. Tectonic plate movements can create mountain ranges where minerals are exposed, while erosion can wear down rock and soil to reveal mineral deposits. An example of this is the concentration of gold in the Sierra Nevada mountains, which is due to ancient volcanic activity and erosion processes.

💡 Explanation:

  • Earth's mineral resources are not evenly distributed because of various geological processes that have occurred over millions of years.
  • Volcanic activity, tectonic shifts, and erosion are key processes that have led to the concentration of minerals in specific locations.
  • These processes cause minerals to be deposited, exposed, or eroded away in different areas, resulting in uneven distribution.

Standard: MS-ESS3-1 | DOK: 2

Dropdown📘 MS-PS1-6🧠 DOK 2

Question:

Which of the following scenarios best illustrates a device that absorbs thermal energy through a chemical process?

Answer Choices:

  • A) A hand warmer that releases heat when shaken
  • B) An ice pack that becomes cold when activated
  • C) A flashlight that turns on using batteries
  • D) A solar panel that generates electricity from sunlight
✅ Answer:
An ice pack that becomes cold when activated

💡 Explanation:

  • An ice pack absorbs thermal energy from the surroundings through an endothermic chemical reaction, resulting in a cooling effect, which matches the requirement of a device that absorbs thermal energy by chemical processes.

Standard: MS-PS1-6 | DOK: 2

Short answer📘 F.IF.C.8🧠 DOK 3

Question:

Consider the quadratic function f(x) = x^2 - 6x + 8. Write this function in vertex form and identify the vertex. Explain how writing the function in vertex form makes it easier to identify the properties of the function.

✅ Answer:
The function f(x) = x^2 - 6x + 8 can be written in vertex form as f(x) = (x - 3)^2 - 1. The vertex of the function is (3, -1). Writing the function in vertex form makes it easier to identify the vertex, which provides information about the maximum or minimum point of the quadratic function and its axis of symmetry.

💡 Explanation:

  • To convert the quadratic function into vertex form, complete the square.

  • Start with the original function f(x) = x^2 - 6x + 8.

  • Take half of the linear coefficient (-6), square it ((-6/2)^2 = 9), and add and subtract this square inside the function: f(x) = x^2 - 6x + 9 - 9 + 8.

  • This can be rewritten as f(x) = (x - 3)^2 - 1.

  • The vertex form reveals the vertex of the function at (3, -1), allowing us to easily identify the point of symmetry and the minimum value of the function, which are not immediately obvious in standard form.

Standard: F.IF.C.8 | DOK: 3

Multiple choice📘 MS-LS3-2🧠 DOK 4

Question:

Which of the following scenarios best illustrates the difference between asexual and sexual reproduction in terms of genetic variation?

Answer Choices:

  • A) A garden with a single type of plant that reproduces through budding, producing identical offspring.
  • B) A fruit tree that produces seeds through pollination involving two different parent trees, leading to diverse offspring.
  • C) A bacterium that divides to form two identical daughter cells.
  • D) A colony of ants where all members are clones of a single queen ant.
✅ Answer:
A fruit tree that produces seeds through pollination involving two different parent trees, leading to diverse offspring.

💡 Explanation:

  • Asexual reproduction results in offspring that are genetically identical to the parent, as seen in the examples of budding plants and clonal ants.
  • In contrast, sexual reproduction involves the combination of genetic material from two parents, resulting in offspring with genetic variation, as illustrated by the fruit tree scenario.

Standard: MS-LS3-2 | DOK: 4

Dropdown📘 F.IF.C.5🧠 DOK 1

Question:

Consider the rational function f(x)=(x−3)(x+2)(x−1)(x+4) f(x) = \frac{(x-3)(x+2)}{(x-1)(x+4)} . Identify the vertical asymptotes.

Answer Choices:

  • A) x = 1 and x = -4
  • B) x = 3 and x = -2
  • C) x = -3 and x = 4
  • D) x = 1 and x = 4
✅ Answer:
x = 1 and x = -4

💡 Explanation:

  • Vertical asymptotes occur where the denominator is zero.

  • Set the denominator (x−1)(x+4)=0(x-1)(x+4) = 0 which gives the solutions x = 1 and x = -4.

Standard: F.IF.C.5 | DOK: 1

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