Completing the squares and comparing to the standard equation, it is found that the diameter of the circle is of
units.
<h3>What is the equation of a circle?</h3>
- The equation of a circle of center
and radius r is given by:
![(x - x_0)^2 + (y - y_0)^2 = r^2](https://tex.z-dn.net/?f=%28x%20-%20x_0%29%5E2%20%2B%20%28y%20-%20y_0%29%5E2%20%3D%20r%5E2)
- The diameter is twice the radius, that is,
.
In this problem, the <em>equation </em>is:
![x^2 + 5x = -8y - y^2](https://tex.z-dn.net/?f=x%5E2%20%2B%205x%20%3D%20-8y%20-%20y%5E2)
Then:
![x^2 + 5x + y^2 + 8y](https://tex.z-dn.net/?f=x%5E2%20%2B%205x%20%2B%20y%5E2%20%2B%208y)
Completing the squares:
![\left(x + \frac{5}{2}\right)^2 + (y + 4)^2 = \left(\frac{5}{2}\right)^2 + 4^2](https://tex.z-dn.net/?f=%5Cleft%28x%20%2B%20%5Cfrac%7B5%7D%7B2%7D%5Cright%29%5E2%20%2B%20%28y%20%2B%204%29%5E2%20%3D%20%5Cleft%28%5Cfrac%7B5%7D%7B2%7D%5Cright%29%5E2%20%2B%204%5E2)
![\left(x + \frac{5}{2}\right)^2 + (y + 4)^2 = \frac{25}{4} + 16](https://tex.z-dn.net/?f=%5Cleft%28x%20%2B%20%5Cfrac%7B5%7D%7B2%7D%5Cright%29%5E2%20%2B%20%28y%20%2B%204%29%5E2%20%3D%20%5Cfrac%7B25%7D%7B4%7D%20%2B%2016)
![\left(x + \frac{5}{2}\right)^2 + (y + 4)^2 = \frac{89}{4}](https://tex.z-dn.net/?f=%5Cleft%28x%20%2B%20%5Cfrac%7B5%7D%7B2%7D%5Cright%29%5E2%20%2B%20%28y%20%2B%204%29%5E2%20%3D%20%5Cfrac%7B89%7D%7B4%7D)
Hence:
![r^2 = \frac{89}{4}](https://tex.z-dn.net/?f=r%5E2%20%3D%20%5Cfrac%7B89%7D%7B4%7D)
![r = \sqrt{\frac{89}{4}}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%5Cfrac%7B89%7D%7B4%7D%7D)
![r = \frac{\sqrt{89}}{2}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B%5Csqrt%7B89%7D%7D%7B2%7D)
Hence, the diameter is:
![d = 2r = 2\left(\frac{\sqrt{89}}{2}\right) = \sqrt{89}](https://tex.z-dn.net/?f=d%20%3D%202r%20%3D%202%5Cleft%28%5Cfrac%7B%5Csqrt%7B89%7D%7D%7B2%7D%5Cright%29%20%3D%20%5Csqrt%7B89%7D)
You can learn more about the equation of a circle at brainly.com/question/16505663
Direction: Opens Down
Vertex:
(
0
,
81
)
(0,81)
Focus:
(
0
,
323
4
)
(0,3234)
Axis of Symmetry:
x
=
0
x=0
Directrix:
y
=
325
4
y=3254
Select a few
x
x
values, and plug them into the equation to find the corresponding
y
y
values. The
x
x
values should be selected around the vertex.
Tap for more steps...
x
y
−
2
77
−
1
80
0
81
1
80
2
77
xy-277-180081180277
Graph the parabola using its properties and the selected points.
Direction: Opens Down
Vertex:
(
0
,
81
)
(0,81)
Focus:
(
0
,
323
4
)
(0,3234)
Axis of Symmetry:
x
=
0
x=0
Directrix:
y
=
325
4
y=3254
x
y
−
2
77
−
1
80
0
81
1
80
2
77
xy-277-180081180277
f
(
x
)
=
8
1
−
x
2
?
?
f(x)=81-x2??
f
(
x
)
=
81
−
x
2
x
?
f(x)=81-x2x?
f
(
x
)
=
81
−
x
2
x
2
?
f(x)=81-x2x2?
f
(
x
)
=
81
−
x
2
x
3
?
f(x)=81-x2x3?
(
)
|
[
]
√
≥
π
7
8
9
Direction: Opens Down
Vertex:
(
0
,
81
)
(0,81)
Focus:
(
0
,
323
4
)
(0,3234)
Axis of Symmetry:
x
=
0
x=0
Directrix:
y
=
325
4
y=3254
Select a few
x
x
values, and plug them into the equation to find the corresponding
y
y
values. The
x
x
values should be selected around the vertex.
Tap for more steps...
x
y
−
2
77
−
1
80
0
81
1
80
2
77
xy-277-180081180277
Graph the parabola using its properties and the selected points.
Direction: Opens Down
Vertex:
(
0
,
81
)
(0,81)
Focus:
(
0
,
323
4
)
(0,3234)
Axis of Symmetry:
x
=
0
x=0
Directrix:
y
=
325
4
y=3254
x
y
−
2
77
−
1
80
0
81
1
80
2
77
xy-277-180081180277
f
(
x
)
=
8
1
−
x
2
?
?
f(x)=81-x2??
f
(
x
)
=
81
−
x
2
x
?
f(x)=81-x2x?
f
(
x
)
=
81
−
x
2
x
2
?
f(x)=81-x2x2?
f
(
x
)
=
81
−
x
2
x
3
?
f(x)=81-x2x3?
(
)
|
[
]
√
≥
π
7
8
9
Direction: Opens Down
Vertex:
(
0
,
81
)
(0,81)
Focus:
(
0
,
323
4
)
(0,3234)
Axis of Symmetry:
x
=
0
x=0
Directrix:
y
=
325
4
y=3254
Select a few
x
x
values, and plug them into the equation to find the corresponding
y
y
values. The
x
x
values should be selected around the vertex.
Tap for more steps...
x
y
−
2
77
−
1
80
0
81
1
80
2
77
xy-277-180081180277
Graph the parabola using its properties and the selected points.
Direction: Opens Down
Vertex:
(
0
,
81
)
(0,81)
Focus:
(
0
,
323
4
)
(0,3234)
Axis of Symmetry:
x
=
0
x=0
Directrix:
y
=
325
4
y=3254
x
y
−
2
77
−
1
80
0
81
1
80
2
77
xy-277-180081180277
f
(
x
)
=
8
1
−
x
2
?
?
f(x)=81-x2??
f
(
x
)
=
81
−
x
2
x
?
f(x)=81-x2x?
f
(
x
)
=
81
−
x
2
x
2
?
f(x)=81-x2x2?
f
(
x
)
=
81
−
x
2
x
3
?
f(x)=81-x2x3?
(
)
|
[
]
√
≥
π
7
8
9
Direction: Opens Down
Vertex:
(
0
,
81
)
(0,81)
Focus:
(
0
,
323
4
)
(0,3234)
Axis of Symmetry:
x
=
0
x=0
Directrix:
y
=
325
4
y=3254
Select a few
x
x
values, and plug them into the equation to find the corresponding
y
y
values. The
x
x
values should be selected around the vertex.
Tap for more steps...
x
y
−
2
77
−
1
80
0
81
1
80
2
77
xy-277-180081180277
Graph the parabola using its properties and the selected points.
Direction: Opens Down
Vertex:
(
0
,
81
)
(0,81)
Focus:
(
0
,
323
4
)
(0,3234)
Axis of Symmetry:
x
=
0
x=0
Directrix:
y
=
325
4
y=3254
x
y
−
2
77
−
1
80
0
81
1
80
2
77
xy-277-180081180277
f
(
x
)
=
8
1
−
x
2
?
?
f(x)=81-x2??
f
(
x
)
=
81
−
x
2
x
?
f(x)=81-x2x?
f
(
x
)
=
81
−
x
2
x
2
?
f(x)=81-x2x2?
f
(
x
)
=
81
−
x
2
x
3
?
f(x)=81-x2x3?
(
)
|
[
]
√
≥
π
7
8
9
vvvvv
Answer:
Step-by-step explanation:
(1-2z)(1+2z) = 1-4z^2
you don't have a correct choice given the problem
is it possible there is a negative out front of the problem
- (1-2z)(1+2z) = -(1-4z^2) = 4z^2 -1
Otherwise, send an email to your instructor
For number 9. its 34 × 65 = 65 × 34.. So that means its communicative property