ANSWER
The radius is 4
EXPLANATION
The given equation is:
![{x}^{2} + {y}^{2} - 10y + 6x + 18 = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%20%20%7By%7D%5E%7B2%7D%20%20-%2010y%20%2B%206x%20%2B%2018%20%3D%200)
We complete the square to get the expression in standard form:
![{x}^{2} + 6x + {y}^{2} - 10y + 18 = 0](https://tex.z-dn.net/?f=%7Bx%7D%5E%7B2%7D%20%20%2B%206x%20%2B%20%20%7By%7D%5E%7B2%7D%20%20-%2010y%20%20%2B%2018%20%3D%200)
![{x}^{2} + 6x + 9 + {y}^{2} - 10y + 25 = - 18 + 9 + 25](https://tex.z-dn.net/?f=%7Bx%7D%5E%7B2%7D%20%20%2B%206x%20%2B%20%209%20%2B%20%7By%7D%5E%7B2%7D%20%20-%2010y%20%20%2B%2025%20%20%3D%20%20-%2018%20%2B%209%20%2B%2025)
We factor using perfect squares to get:
![{(x + 3)}^{2} + {(y - 5)}^{2} = 16](https://tex.z-dn.net/?f=%7B%28x%20%2B%203%29%7D%5E%7B2%7D%20%20%2B%20%20%7B%28y%20-%205%29%7D%5E%7B2%7D%20%3D%20%2016)
This implies that,
![{(x + 3)}^{2} + {(y - 5)}^{2} = {4}^{2}](https://tex.z-dn.net/?f=%7B%28x%20%2B%203%29%7D%5E%7B2%7D%20%20%2B%20%20%7B%28y%20-%205%29%7D%5E%7B2%7D%20%3D%20%20%20%7B4%7D%5E%7B2%7D%20)
Comparing to
![{(x - h)}^{2} + {(y - k)}^{2} = {r}^{2}](https://tex.z-dn.net/?f=%7B%28x%20%20-%20h%29%7D%5E%7B2%7D%20%20%2B%20%20%7B%28y%20-%20k%29%7D%5E%7B2%7D%20%3D%20%20%20%7Br%7D%5E%7B2%7D%20)
The radius is r=4
Answer:
Length = 7, width = 1.
Step-by-step explanation:
7 and 1 are the only possible dimensions as 7 is a prime number.
To solve this we are going to use the formula for compounded interest:
![A=P(1+ \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%3DP%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
where
![A](https://tex.z-dn.net/?f=A)
is the final amount after
![t](https://tex.z-dn.net/?f=t)
years
![P](https://tex.z-dn.net/?f=P)
is the initial amount
![r](https://tex.z-dn.net/?f=r)
is the interest rate in decimal form
![n](https://tex.z-dn.net/?f=n)
is the number of times the interest is compounded per year
![t](https://tex.z-dn.net/?f=t)
is the time in years
We know for our problem that
![P=1380](https://tex.z-dn.net/?f=P%3D1380)
,
![r= \frac{5}{100} =0.05](https://tex.z-dn.net/?f=r%3D%20%5Cfrac%7B5%7D%7B100%7D%20%3D0.05)
, and
![t=3](https://tex.z-dn.net/?f=t%3D3)
. Since the interest is compounded daily, it is compounded 365 times in year; therefore,
![n=365](https://tex.z-dn.net/?f=n%3D365)
. Lets replace those values in our formula to find
![A](https://tex.z-dn.net/?f=A)
:
![A=P(1+ \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%3DP%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
![A=1380(1+ \frac{0.05}{365})^{(365)(3)}](https://tex.z-dn.net/?f=A%3D1380%281%2B%20%5Cfrac%7B0.05%7D%7B365%7D%29%5E%7B%28365%29%283%29%7D%20)
![A=1603.31](https://tex.z-dn.net/?f=A%3D1603.31)
We can conclude the amount in Diane's after 3 years will be <span>
$1,603.31</span>
Answer:
The other side is 7.48 yards.
Step-by-step explanation:
Given that,
Hypotenuse = 15 yards
One leg = 13 yards
We need to find the length of the other leg. We can use the Pythagoras theorem to find it such that,
![H^2=b^2+h^2](https://tex.z-dn.net/?f=H%5E2%3Db%5E2%2Bh%5E2)
Where
h is other leg
Put all the values,
![h=\sqrt{H^2-b^2} \\\\h=\sqrt{(15)^2-(13)^2} \\\\h=7.48\ yd](https://tex.z-dn.net/?f=h%3D%5Csqrt%7BH%5E2-b%5E2%7D%20%5C%5C%5C%5Ch%3D%5Csqrt%7B%2815%29%5E2-%2813%29%5E2%7D%20%5C%5C%5C%5Ch%3D7.48%5C%20yd)
So, the other side is 7.48 yards.
Answer:
Step-1 : Reflect the original figure around the x-axis.
Step-2 : Slide the new figure 7 units to the right.