"determine the location" or namely, is it inside the circle, outside the circle, or right ON the circle?
well, we know the center is at (1,-5) and it has a radius of 5, so the distance from the center to any point on the circle will just be 5, now if (4,-1) is less than that away, is inside, if more than that is outiside and if it's exactly 5 is right ON the circle.
well, we can check by simply getting the distance from the center to the point (4,-1).
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{center}{(\stackrel{x_1}{1}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d = \sqrt{[4-1]^2+[-1-(-5)]^2}\implies d=\sqrt{(4-1)^2+(-1+5)^2} \\\\\\ d = \sqrt{3^2+4^2}\implies d =\sqrt{9+16}\implies d=\sqrt{25}\implies \stackrel{\textit{right on the circle}}{d = 5}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20%5Cstackrel%7Bcenter%7D%7B%28%5Cstackrel%7Bx_1%7D%7B1%7D~%2C~%5Cstackrel%7By_1%7D%7B-5%7D%29%7D%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B4%7D~%2C~%5Cstackrel%7By_2%7D%7B-1%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20d%20%3D%20%5Csqrt%7B%5B4-1%5D%5E2%2B%5B-1-%28-5%29%5D%5E2%7D%5Cimplies%20d%3D%5Csqrt%7B%284-1%29%5E2%2B%28-1%2B5%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20d%20%3D%20%5Csqrt%7B3%5E2%2B4%5E2%7D%5Cimplies%20d%20%3D%5Csqrt%7B9%2B16%7D%5Cimplies%20d%3D%5Csqrt%7B25%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bright%20on%20the%20circle%7D%7D%7Bd%20%3D%205%7D)
Since this is simple interest, there's a formula to calculate the interest. Once you find the interest you can add that back to the principal and get your total amount paid.
Here's the formula: Interest = principal * rate * time.
We don't know the interest of the loan or the extra money you have to pay on top of the 10,000 borrowed. Anyways, plug in what you got to find the interest.
Interest = 10000 * .03 * 6
Interest = 1800.
This is the extra amount you've to pay while also paying the 10,000 back. To find out the total amount, just add the interest to the amount borrowed which is the 10,000.
So, 10,000 + 1800 = $11,800. That's the total amount that you'll pay. Hope this helped!
Answer: the money spend on ads to website is 4:3
Step-by-step explanation:
Answer:
<em>15 students visited both museums.</em>
Step-by-step explanation:
<u>Operations With Sets</u>
Sets are a collection of elements. Some sets have elements in common with other sets. These elements are said to be in their intersection. If we know the number of elements in the set A and in the set B, and also the total number of elements in both sets, we can say
![N(A\bigcup B)=N(A)+N(B)-N(A\bigcap B)](https://tex.z-dn.net/?f=N%28A%5Cbigcup%20B%29%3DN%28A%29%2BN%28B%29-N%28A%5Cbigcap%20B%29)
where
is the total number of elements, N(A) and N(B) are the number of elements in A and B respectively, and
is the number of elements in their intersection. If we wanted to know that last number, then we isolate it
![N(A\bigcap B)=N(A)+N(B)-N(A\bigcup B)](https://tex.z-dn.net/?f=N%28A%5Cbigcap%20B%29%3DN%28A%29%2BN%28B%29-N%28A%5Cbigcup%20B%29)
Let A= Students who visited the museum of natural history
B=Students who visited the natural air and space museum
We know ![N(A)=18, N(B)=22, N(A\bigcup B)=25,\ so](https://tex.z-dn.net/?f=N%28A%29%3D18%2C%20N%28B%29%3D22%2C%20N%28A%5Cbigcup%20B%29%3D25%2C%5C%20so)
![N(A\bigcap B)=18+22-25=15](https://tex.z-dn.net/?f=N%28A%5Cbigcap%20B%29%3D18%2B22-25%3D15)
Answer: 15 students visited both museums.
Note: We are assuming no students didn't visit at least one museum
Answer:
x = -3
Step-by-step explanation:
4x + 2 = x - 7
3x = -9
x = -3