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Makovka662 [10]
4 years ago
8

How many pairs of vertical angles are formed by five distinct lines that have a common point of intersection?

Mathematics
1 answer:
Bess [88]4 years ago
7 0

25 pairs of vertical angles are formed.

<u>Step-by-step explanation:</u>

Suppose there are N distinct lines, which produces N squared pairs of vertical angles.

If we have 2 distinct lines, then we have 4 pairs of vertical angles are formed.

2 distinct lines, then 2² = 4 pairs of vertical angles

3 distinct lines, then 3² = 9 pairs of vertical angles

4 distinct lines, then 4² = 16 pairs of vertical angles  

Here we have 5 distinct lines, and these lines produces 5² pairs of vertical angles.

So here 25 pairs of vertical angles are formed by 5 distinct lines.

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In ΔIJK, the measure of ∠K=90°, KJ = 65, IK = 72, and JI = 97. What is the value of the cosine of ∠J to the nearest hundredth?
kow [346]

Answer:

\cos(J) = 0.67

Step-by-step explanation:

Given

\angle K = 90^o

KJ = 65

IK = 72

JI = 97

Required

\cos(J)

The question is illustrated with the attached image.

From the image, we have:

\cos(J) = \frac{KJ}{JI}

This gives:

\cos(J) = \frac{65}{97}

\cos(J) = 0.67010309278

\cos(J) = 0.67 --- approximated

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3 years ago
10. The probability of buying pizza for dinner is 34% and the probability of buying
kipiarov [429]

Answer:

The probability of eating pizza given that a new car is bought is 0.952

Step-by-step explanation:

This kind of problem can be solved using Baye’s theorem of conditional probability.

Let A be the event of eating pizza( same as buying pizza)

while B is the event of buying a new car

P(A) = 34% = 0.34

P(B) = 15% = 15/100 = 0.15

P(B|A) = 42% = 0.42

P(B|A) = P(BnA)/P(A)

0.42 = P(BnA)/0.34

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Now, we want to calculate P(A|B)

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P(A|B = P(A n B)/P(B)

Kindly know that P(A n B) = P(B n A) = 0.1428

So P(A|B) = 0.1428/0.15

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Yuliya22 [10]

Answer:

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Step-by-step explanation:

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We have to prove that in a parallelogram the diagonals bisect each other.

Assume that the diagonals of ABCD i.e. AC and BD intersect at point O.

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