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saul85 [17]
2 years ago
10

Find an equation of the circle that satisfies the given conditions.

Mathematics
1 answer:
hodyreva [135]2 years ago
4 0
The equation of a circle:
(x-h)^2+(y-k)^2=r^2
(h,k) - the coordinates of the centre
r - the radius

The midpoint of the diameter is the centre of a circle.
The coordinates of the midpoint:
(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})
(x₁,y₁), (x₂,y₂) - the coordinates of endpoints

P(-1,1) \\
x_1=-1 \\ y_1=1 \\ \\ Q(5,9) \\ x_2=5 \\ y_2=9 \\ \\
\frac{x_1+x_2}{2}=\frac{-1+5}{2}=\frac{4}{2}=2 \\ \frac{y_1+y_2}{2}=\frac{1+9}{2}=\frac{10}{2}=5

The centre of the circle is (2,5).

The radius is the distance between an endpoint of the diameter and the centre.
The formula for distance:
d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

(-1,1) \\ x_1=-1 \\ y_1=1 \\ \\ (2,5) \\ x_2=2 \\ y_2=5 \\ \\ d=\sqrt{(2-(-1))^2+(5-1)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5

The radius is 5.

(x-2)^2+(y-5)^2=5^2 \\
\boxed{(x-2)^2+(y-5)^2=25}
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F(x) = x². What is g(x)?
Simora [160]

g(x) is the inverse of f(x)

f(x) = {x}^{2}

g(x) =  \sqrt{x}

8 0
2 years ago
If B is the midpoint of line AC, AC = CD, AB = 3x+4, AC=11x-17, and CE = 49, find DE. (Show work)
larisa [96]

Answer:

2(3x+4) = 11x-17

6x+8 = 11x-17

25=-5x

x=-5

11x-17

55-17

38

AC = 38

CD = 38

49-38 = 11

DE = 11

Let me know if this helps!

3 0
2 years ago
How do I solve this equation
Anestetic [448]
-x - y = 8
2x - y = -1

Ok, we are going to solve this in 2 parts.  First we have to solve for one of the variables in one of the equation in terms of the other variable.  I like to take the easiest equation first and try to avoid fractions, so let's use the first equation and solve for x.

-x - y = 8      add y to each side
-x = 8 + y      divide by -1
x = -8 - y

So now we have a value for x in terms of y that we can use to substitute into the other equation.  In the other equation we are going to put -8 - y in place of the x.

2x - y = -1
2(-8 - y) - y = -1      multiply the 2 through the parentheses
-16 - 2y - y = -1      combine like terms
-16 - 3y = -1            add 16 to both sides
-3y = 15                   divide each side by -3
y = -5

Now we have a value for y.  We need to plug it into either of the original equations then solve for x.  I usually choose the most simple equation.

-x - y = 8
-x - (-5) = 8            multiply -1 through the parentheses
-x + 5 = 8                subtract 5 from each side
-x = 3                      divide each side by -1
x = -3

So our solution set is

(-3, -5)

That is the point on the grid where the 2 equations are equal, so that is the place where they intersect.

4 0
3 years ago
How do I answer this?
Agata [3.3K]

Answer:

2k³ is the GCF.

Step-by-step explanation:

GCF of 10k^{3} ,6k^{3}

Finding the factors:

=10k³[Factoring 10k³]

=2×5×k×k×k

=6k³[Factoring 6k³]

=2×3×k×k×k

Common factors in 10k³ and 6k³.

=2×k³

=2k³

8 0
2 years ago
Read 2 more answers
I really need help someone
Ann [662]

with what english, science anything i no it all

8 0
3 years ago
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