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STatiana [176]
3 years ago
12

A gym teacher orders 42 tennis balls. Each package contains three tennis balls. Which of the following equations represents the

number X of packages? X+ 3=42 3x= 42 x/3= 42 or x=3/42
Mathematics
1 answer:
navik [9.2K]3 years ago
8 0
42 balls / 3 balls per package Equals 14 packages
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Verify the following identity and show steps<br><br> (Cos2 θ)/(1+sin2 θ)= (cot θ-1)/(cot θ+1)
Paul [167]

Answer:

Verified below

Step-by-step explanation:

We want to show that (Cos2θ)/(1 + sin2θ) = (cot θ - 1)/(cot θ + 1)

In trigonometric identities;

Cot θ = cos θ/sin θ

Thus;

(cot θ - 1)/(cot θ + 1) gives;

((cos θ/sin θ) - 1)/((cos θ/sin θ) + 1)

Simplifying numerator and denominator gives;

((cos θ - sin θ)/sin θ)/((cos θ + sin θ)/sin θ)

This reduces to;

>> (cos θ - sin θ)/(cos θ + sin θ)

Multiply top and bottom by ((cos θ + sin θ) to get;

>> (cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ)

In trigonometric identities, we know that;

cos 2θ = (cos² θ - sin²θ)

cos²θ + sin²θ = 1

sin 2θ = 2sinθcosθ

Thus;

(cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ) gives us:

>> cos 2θ/(1 + sin 2θ)

This is equal to the left hand side.

Thus, it is verified.

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2 years ago
What is the slope of the line y = -5 - 3x ?<br> o 3<br> O 5<br> 0 -3<br> 0 -8
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Answer:

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Step-by-step explanation:

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Compare and contrast the methods used by African and Asian nations to achieve independence.
goblinko [34]

Answer: Decolonization as a result of World War II.

Step-by-step explanation:

  • With the end of World War II, the process of decolonization of the African and Asian continents began. It is the result of the destruction brought with it by World War II, but also by the liberalization that took place in Europe after World War II. In this context, it isn't effortless to point out the particular methods used by nations on these two continents. Decolonization is, however, an independent will and intervention of European countries.
  • Yet the colonization of nations was not entirely passive in terms of resistance to the European invaders. There were several uprisings against the colonists. However, what characterizes both fights for independence is the emergence of nationalism. This is the pattern that African and Asian countries have taken over from Europeans. The form of resistance also consisted in the fact that there was a specific political will on the part of certain domestic elites, as in the case of the West African National Congress or the South African National Congress.
  • A particular form of struggle for independence existed in India. This Asian country led its effort by methods of civil disobedience, non-payment of taxes, and refusal to work. The creator of this form of struggle was the leader of the Indian independence movement Mahatma Gandhi. An example of diminishing "third country" influence was an international intervention. Such an example is evident in Korea, where the United States and the Soviet Union eliminated Japanese colonial pretensions by their impact.
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Vikentia [17]
If one third of t is 7 than t is equal to 21
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