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.
<h3>Yes, this is true.</h3>
To be considered similar triangles, the angles must be the exact same, and the sides must be proportional. The side lengths do not have to be exactly the same, but they must be proportional (like a ratio, suppose one triangle has a side length of 1, and the similar triangle has a side length of 3. The ratio is 1:3, and all sides will follow this ratio.)
To solve this problem, we have to figure out a rule for the function. We are told that it is a two-step rule, so it is most likely the input multiplied by a coefficient plus a constant. Let’s let the input be represented by the variable x and the output be represented by the variable y. Using our knowledge, we can see that the outputs are close to triple the input, so we set up the preliminary equation:
y = 3x + b,
where b is a constant. If we want to solve for b, we must plug in one of our input/output pairs. If we plug in (5,16), we get the following:
16 = 3(5) + b
16 = 15 + b
1 = b
Then, we should substitute in this value into our equation and check our work.
y = 3x + 1
If we plug in the other points, this equation yields a true statement, so we know it is correct.
Hope this helps!
Answer:
the two options that are equivalent would be the first option and the fourth option. (2x . 2y = 4xy) (5xyz = 5 . x . y . z)
Step-by-step explanation:
Answer:
The radius of the circle is 9 units.
Step-by-step explanation:
To calculate the area of the circle we need to find it's radius, since we have the area of the sector and it's angle, therefore we can calculate the radius by using the following formula:
sector area = (central angle)*pi*r²/360
27pi = 120*pi*r²/360
27pi = pi*r²/3
27 = r²/3
r² = 81
r = sqrt(81) = 9
The radius of the circle is 9 units.
