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prisoha [69]
3 years ago
11

a circle with center (1,5) passes through the point (10,10). what is the area of the circle rounded to the nearest square unit?

Mathematics
1 answer:
alina1380 [7]3 years ago
6 0
The points of the circle satisfy the equation
.. (x -1)^2 +(y -5)^2 = r^2
Filling in the given information, we can find r^2.
.. (10 -1)^2 +(10 -5)^2 = r^2
.. 81 +25 = r^2 = 106

The area of the circle is
.. A = πr^2 = 106π ≈ 333 . . . . square units
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<1 and <2 form a linear pair. If m<1= 4m<2, find the measure of each of the two angles.
ozzi

Answer:

  • The angle ∠1 = x = 36°
  • The angle ∠2 = 4x = 4(36°) = 144°

Step-by-step explanation:

We know that when two lines meet or intersect, we get a linear pair of angles.

Linear pairs are basically two adjacent angles that form a line.

The measure of two adjacent angles forming a straight line is 180, meaning they are supplementary.

We are given that <1 and <2 forms a linear pair, and

m∠1 = 4m∠2

It means the angle ∠1 is 4 times the measure of angle ∠2.

Let the angle ∠1 be = x

As the angle 1 is 4 times the measure of angle ∠2, so

The angle 2 will be = 4x

As <1 and <2 forms a linear pair, thus the measure of the sum of <1 and <2 will be 180°, so

x + 4x = 180

5x = 180

divide both sides by 5

5x/5 = 180/5

x = 36°

Therefore,

  • The angle ∠1 = x = 36°
  • The angle ∠2 = 4x = 4(36°) = 144°
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