Answer:
(x + 1)² + (y + 3)² = 16
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² + 2x + 6y - 6 = 0
Collect the x and y terms together and add 6 to both sides
x² + 2x + y² + 6y = 6
To complete the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(1)x + 1 + y² + 2(3)y + 9 = 6 + 1 + 9
(x + 1)² + (y + 3)² = 16
with centre = (- 1, - 3) and r = = 4
I think that
Every point is moved so that it is 2/3 as far from the y axis
should be the answer
If 1/6 of the pan was left and there were 2 pieces left you just need to set 1/6 equal to 2/some number, this allows you to say that 1/6=2/x --> x/6=2-->x=12.
My explanation might be a little poor since this becomes fairly fundamental later on but hopefully it helps.
Total balance in Mr. Copley at the end of the month = $1473.61.
Initial deposite = $75 (not shown in his checkbook).
Let us assume his balance at the beginning of the month = x.
Total balance at the end of the month = The balance at the beginning of the month + total deposite.
$1473.61 = x + 75.
Subtracting 75 from both sides, we get
1473.61 -75 = x + 75 -75.
1398.61 = x.
Therefore, his balance at the beginning of the month was $1398.61.