Answer:
center = (-2, 6)
radius = 6
Step-by-step explanation:
<u>Equation of a circle</u>
(where (a, b) is the center and r is the radius)
Therefore, we need to rewrite the given equation into the standard form of an equation of a circle.
Given equation:
Collect like terms and subtract 4 from both sides:
Complete the square for both variables by adding the square of half of the coefficient of and
to both sides:
Factor both variables:
Therefore:
The two friends have the shortest distance between them are Carrie and Nayla.
In order to determine the distance of the friends from each other, the value of the angles have to be determined. The given figure is a triangle. Sum of angles in the triangle equal 180 degrees.
The first step is to determine the value of x:
20x + 7) + (5x + 50) + (5x + 3) = 180
Add similar terms togethers
30x + 60 = 180
Combine similar terms
30x = 180 - 60
30x = 120
x = 120 / 30
x = 4
The second step is to determine the value of each angle
Nayla = 20(4) + 7 = 87
Carrie = Second angle = 5(4) + 50 = 70
Maria = Third angle = 180 - (70 + 87) = 23
Nayla and Carrie live closest to each other
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