7x + 6y = 10 x+y = 9
1 answer:
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The equation (x + 2)² + (y - 1)² = 25 represents a circle that contain the point (-5 , -3) and has a center at (-2 , 1)
Step-by-step explanation:
The equation of a circle of center (h , k) and radius r is:
(x - h)² + (y - k)² = r²
The given is:
- The center of the circle is (-2 , 1)
- The circle passes through point (-5 , -3)
The length of the radius is the distance from the center of the circle
to a point on the circle
∵ The formula of the distance is
∵ The center of the circle is (-2 , 1)
∵ The circle passes through point (-5 , -3)
∴
∴
∴
∴
∴ r = 5
∵ The equation of the circle is (x - h)² + (y - k)² = r²
∵ The center of the circle is (-2 , 1)
∴ h = -2 and k = 1
∵ r = 5
∴ r² = (5)² = 25
- Substitute the values of h , k , r² in the equation of the circle
∴ (x - -2)² + (y - 1)² = 25
∴ (x + 2)² + (y - 1)² = 25
The equation (x + 2)² + (y - 1)² = 25 represents a circle that contains
the point (-5 , -3) and has a center at (-2 , 1)
Learn more:
You can learn more about the equation of the circle in brainly.com/question/9510228
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Answer:
{ - 2, 10 }
Step-by-step explanation:
Given
x² - 8x = 20
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 4)x + 16 = 20 + 16, that is
(x - 4)² = 36 ( take the square root of both sides )
x - 4 = ± = ± 6 ( add 4 to both sides )
x = 4 ± 6
Thus
x = 4 - 6 = - 2
x = 4 + 6 = 10