2. What is the center and the radius of a circle given by the equation
1 answer:
Answer:
C
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given x² + y² + 4x - 10y + 20 = 0
Collect x and y terms and subtract 20 from both sides. that is
x² + 4x + y² - 10y = - 20
To obtain standard form use the method of completing the square
add ( half the coefficient of the x/y term )² to both sides
x² + 2(2)x + 4 + y² + 2(- 5)y + 25 = - 20 + 4 + 25
(x + 2)² + (y - 5)² = 9 ← in standard form
with centre = (- 2, 5) and r = = 3 → C
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Answer:
Approximately 10.2 inches
Step-by-step explanation:
The area of a square is given by the formula:
Where A is the area and s is the side length.
Since we already know that the area A is 105, substitute:
Now, take the square root of both sides:
Use a calculator:
So, the side length is approximately 10.2 inches.