There is more than one solution because there are two different numbers whose square is 9. One of them is +3. The other is -3.
The fundamental theorem of algebra says every non-zero single-variable polynomial of degree N has exactly N roots, counting multiplicity. Your polynomial is degree 2, so has 2 roots.
Pa, Pb,Pc,Ya, Yb,Yc,Ta, Tb, Tc
9 total outcomes choosing one balloon
Step-by-step explanation:
The center of a circle with 2 end points of a di diameter is the midpoint of the two endpoints.
The formula needed to find the minpoints is
(x,y) = (x2 + x1)/2, (y2 + y1)/2
x2 = 3
x1 = 3
y2 = 0
y1 = -7
midpoint = (3 + 3)/2, (0 - 7)/2
midp[oint = 3,-3.5
The midpoint is the center of the circle. Observe that the signs get changed when entering the values for (x,y)
So far what you have is (x - 3)^2 + (y + 3.5)^2 = r^2
To determine r^2 you need only take the distance from the center to oneof the endpoints.
r^2 = (3 - 3)^2 + (3.5 - 0)^2
r^2 = 3.5^2
r^2 = 12.25
Answer: (x - 3)^2 + (y + 3.5)^2 = 12.25
Given two points, (x1, y1) and (x2, y2), the slope can be found by ...
... slope = (change in y)/(change in x) = (y2-y1)/(x2-x1)
For your given points, the slope is
... slope = (79 -(-20))/(9 -(-2)) = 99/11 = 9
The point-slope equation for a line with slope m through point (h, k) is
... y -k = m(x -h)
You have m=9, h=-2, k=-20, so the equation is
... y +2 = 9(x +20)