Center: (-5,-6)
Radius: 39
How to do it
Complete the square for
y
2
+
12
y
y
2
+
12
y
.
(
y
+
6
)
2
−
36
(
y
+
6
)
2
-
36
Substitute
(
y
+
6
)
2
−
36
(
y
+
6
)
2
-
36
for
y
2
+
12
y
y
2
+
12
y
in the equation
(
x
+
5
)
2
+
y
2
+
12
y
=
3
(
x
+
5
)
2
+
y
2
+
12
y
=
3
.
(
x
+
5
)
2
+
(
y
+
6
)
2
−
36
=
3
(
x
+
5
)
2
+
(
y
+
6
)
2
-
36
=
3
Move
−
36
-
36
to the right side of the equation by adding
36
36
to both sides.
(
x
+
5
)
2
+
(
y
+
6
)
2
=
3
+
36
(
x
+
5
)
2
+
(
y
+
6
)
2
=
3
+
36
Add
3
3
and
36
36
.
(
x
+
5
)
2
+
(
y
+
6
)
2
=
39
(
x
+
5
)
2
+
(
y
+
6
)
2
=
39
This is the form of a circle. Use this form to determine the center and radius of the circle.
1. Remove parentheses
-3x^2 + x^4 + x + 2x^4 - 7 + 4x
2. Collect like terms
-3x^2 + (x^4 + 2x^4) + (x + 4x) - 7
3. Simplify
-3x^2 + 3x^4 + 5x - 7
(-1,1)(1,4)
slope = (4 - 1) / (1 - (-1) = 3/(1 + 1) = 3/2
y = mx + b
slope(m) = 3/2
use either of ur points....(1,4)...x = 1 and y = 4
now sub and find b, the y int
4 = 3/2(1) + b
4 = 3/2 + b
4 - 3/2 = b
8/2 - 3/2 = b
5/2 = b
equation is y = 3/2x + 5/2...but we need it in standard form
y = 3/2x + 5/2
-3/2x + y = 5/2.....multiply both sides by -2
3x - 2y = -5 <==== ur standard form equation
D. Since we know that 1 ticket = $8 we would multiply to figure out how much 7 tickets were. (7x$8). And to figure out his change you would subtract the ticket amount from $100 :) Hope this helps
