Give the equation for a circle with the given center and radius. Center at (2, -9), radius = 3

A. (x+2)^2+(y−9)^2=9
B. (x+9)^2+(y−2)^2=3
C. (x−9)^2+(y+2)^2=3
D. (x−2)^2+(y+9)^2=9

(x-2)^2 + (y+9)^2 = 9

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2  where (h,k) is the center and r is the radius

(x-2)^2 + (y--9)^2 = 3^2

(x-2)^2 + (y+9)^2 = 9

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°