We do the midpoint formula to find the center of the circle to get the left side of the equation.
Midpoint = [(X₁ + X₂) / 2 , (Y₁ + Y₂) / 2]
Now plug in:
[(8 + 4) / 2 , (- 6 - 2) / 2]
(12 / 2 , - 8 / 2)
(6, - 4)
The center of the circle is (6, -4)
Now we plug it into the equation of a circle:
(x - h)² + (y - k)² = r² where (h, k) is the center of the circle and r is the radius.
(x - 6)² + (y + 4)² = r² is the left side of the equation. This will eliminate options A and C
Now we do the distance formula using the center and an endpoint to get the radius. The formula for distance is:
√((X₂ - X₁)² + (Y₂ - Y₁)²)
We plug in using either of the endpoints.
√((4 - 6)² + (- 2 - (- 4))²)
√((-2)² + 2²)
√(4 + 4)
√8
√8 is your radius
(√8)² = 8
Your correct answer is (x - 6)² + (y + 4)² = 8, Option D
Answer:
5% or 0.05
Step-by-step explanation:
The null hypothesis will be rejected if p-value is less than significance level.
The null hypothesis can be rejected on 5% and 10% level of significance, but 5% level of significance is a suitable choice because when the 5% significance level is used the confidence level is 95% where as in case of 10% the confidence level is 90%. In short, the significance level indicates the probability of rejection of null hypothesis when the null hypothesis is true and the lesser probability of taking that risk will be better.
So, the scenario indicates the suitable significance level as 0.05.
Please see attached image for the graph.
a.
Yes, it is mathematically possible because the
degree of vertices for P=3, T=3, M=2, C=4, and R=2 and in Euler’s theorem, the
graph has to be connected, which in this case it is and the number of vertices
in the graph whose vertices is odd, is 0 or 2. And in this case, we have 2 that
have a degree of vertices that are odd, therefore mathematically this is
possible for the driver. The route would be P > R > C > M > T > C
> P > T.
b.
<span>It is mathematically possible. The router would be P
> C > R > T > M > C > T. Essentially, you travel each road
once.
</span>
c.
The driver would use a Hamiltonian circuit. The route
would be J > R > A > C > V > M > T > P > J.
Answer:
x=35
Step-by-step explanation:
For a polygon with n sides, the sum of its interior angles is equal to
(n-2) * 180
Here, there are 6 sides, so the sum of this polygon's interior angles is equal to (6-2)* 180 = 720
Therefore, the sum of the interior angles is 720. We can add them up to get
(4x-5) + 117 + (3x-3) + (3x+6) + 118 + 4x-3
= 14x +230 = 720
subtract 230 from both sides to isolate the x and its coefficint
14x = 490
divide both sides by 14 to get x
x=35
