Answer:
Eq: (x+a/2)²+(y+1)²=(a²-8)/4
Center: O(-a/2, -1)
Radius: r=0.5×sqrt(a²-8)
Mandatory: a>2×sqrt(2)
Step-by-step explanation:
The circle with center in O(xo,yo) and radius r has the equation:
(x-xo)²+(y-yo)²=r²
We have:
x²+y²+ax+2y+3=0
But: x²+ax=x²+2(a/2)x+a²/4-a²/4= (x+a/2)²-a²/4
And
y²+2y+3=y²+2y+1+2=(y+1)²+2
Replacing, we get:
(x+a/2)²-a²/4+(y+1)²+2=0
(x+a/2)²+(y+1)²=a²/4-2=(a²-8)/4
By visual inspection we note that:
- center of circle: O(-a/2, -1)
- radius: r=sqrt((a²-8)/4)=0.5×sqrt(a²-8). This means a²>8 or a>2×sqrt(2)
Answer:
Step-by-step explanation:
If you foil this equation you will get:
And by dividing it, you will get;
That is your answer!
(10+t)/(18+t)=8/10
8(18+t)=10(10+t)
144+8t=100+10t
44=2t
t = 22 throws
74,233 increased by 58,490 is 74,233 * 58,490 so its 4,341,888, 170. So 4 billion, 341 million, 888 thousand, 170.
Scientific notation is 4.34188817 * 10 to the 9th power.
-24a²- 6a +9 = - 3(8a² +6a - 9)
8a² +6a - 9 =0
x=(-b +/-√(b² - 4ac))/2a
x = (-6 +/-√(36+4*8*9) /(2*8) = (-6 +/-√(324) /16 = (-6 +/-18)/16
x1 = (-6 +18)/16 = 0.75
x2 = (-6 -18)/16 = - 1.5
-24a²- 6a +9 = - 3(8a² +6a - 9) = -3(a - 0.75)(a + 1.5)
