Find the center of a circle with the equation: x2+y2−32x−60y+1122=0

(16, 30)

Step-by-step explanation:

First the equation of a circle is:

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

We rewrite the equation and set them equal :

(x-h)^2 + (y-k)^2 - r^2 = x^2+y^2− 32x − 60y +1122=0

x^2 - 2hx + h^2 + y^2 - 2ky + k^2 - r^2 = x^2 + y^2 - 32x - 60y +1122 = 0

We solve for each coeffiecient meaning if the term on the LHS contains an x then its coefficient is the same as the one on the RHS containing the x or y.

-2hx = -32x => h = 16.

-2ky = -60y => k = 30. => the center is at (16, 30)

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

b.-4 units

all you   do is count how many times you move