is a linear polynomial
S<u>tep-by-step explanatio</u>n:
based on the highest power of the variables of a polynomial, it can be classified as linear,polynomial, quadratic polynomial,cubic polynomial etc.
In a linear polynomial, the highest power of the variable is 1. The general form of a linear polynomial is ax+b
In a quadratic polynomial, the highest power of the variables is 2.The general form of quadratic polynomial is ![ax^2+bx+c](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc)
In a cubic polynomial,the highest power of variable is 3.The general form of cubic polynomial is
.
Take the given question and simplify it
![r^2+3r+5-r^3/r=r^2+3r+5-r^2\\=3r+5](https://tex.z-dn.net/?f=r%5E2%2B3r%2B5-r%5E3%2Fr%3Dr%5E2%2B3r%2B5-r%5E2%5C%5C%3D3r%2B5)
It is of the form ax+b. Hence it is a linear polynomial.
Answer:
![(x-7)^2+(y-5)^2=1](https://tex.z-dn.net/?f=%28x-7%29%5E2%2B%28y-5%29%5E2%3D1)
Step-by-step explanation:
The two things that are required to formulate the equation of the circle is the center coordinate and the radius of the circle!
<u>Center of the circle:</u>
- The center of the circle always lies at the midpoint of the endpoints of its diameter: Let's call the endpoints A(6,5) and B(8,5).
Using the midpoint formula we'll get:
![(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)](https://tex.z-dn.net/?f=%28x_m%2C%20y_m%29%20%3D%20%5Cleft%28%5Cdfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%5Cdfrac%7By_1%2By_2%7D%7B2%7D%5Cright%29)
![(x_m, y_m) = \left(\dfrac{6+8}{2},\dfrac{5+5}{2}\right)](https://tex.z-dn.net/?f=%28x_m%2C%20y_m%29%20%3D%20%5Cleft%28%5Cdfrac%7B6%2B8%7D%7B2%7D%2C%5Cdfrac%7B5%2B5%7D%7B2%7D%5Cright%29)
![(x_m, y_m) = (7,5)](https://tex.z-dn.net/?f=%28x_m%2C%20y_m%29%20%3D%20%287%2C5%29)
This is the center coordinate of our circle.
<u>Radius: </u>
The radius of the circle is the distance from the center of the circle to any of the endpoints of the diameter (A or B)
We can use the distance formula:
![r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%28x_1-x_2%29%5E2%2B%28y_1-y_2%29%5E2%7D)
![r = \sqrt{(x_1-x_m)^2+(y_1-y_m)^2}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%28x_1-x_m%29%5E2%2B%28y_1-y_m%29%5E2%7D)
![r = \sqrt{(6-7)^2+(5-5)^2}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%286-7%29%5E2%2B%285-5%29%5E2%7D)
![r = \sqrt{1^2}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B1%5E2%7D)
![r = 1](https://tex.z-dn.net/?f=r%20%3D%201)
<u>Equation of the circle: </u>
The equation is written as:
![(x-a)^2+(y-b)^2=r^2](https://tex.z-dn.net/?f=%28x-a%29%5E2%2B%28y-b%29%5E2%3Dr%5E2)
here, (a,b) are the center points of the circle
in our case this is ![(a,b)=(x_m,y_m)=(7,5)](https://tex.z-dn.net/?f=%28a%2Cb%29%3D%28x_m%2Cy_m%29%3D%287%2C5%29)
and r = 1
![(x-7)^2+(y-5)^2=1^2](https://tex.z-dn.net/?f=%28x-7%29%5E2%2B%28y-5%29%5E2%3D1%5E2)
![(x-7)^2+(y-5)^2=1](https://tex.z-dn.net/?f=%28x-7%29%5E2%2B%28y-5%29%5E2%3D1)
This is the equation of the circle!
The train Chug-a-Lug must be going 153.5 miles to match the same speed as Old Steamy so they can arrive at the station at the same time.
150 more male bats need to be tagged
if you want 2/5 to be female you divide the 260 (<160+100) by 2 to get 130
then you multiply 130 by 3 to get the total amount of male bats that need to be tagged
130*3=390
then you subtract 240 from the 390 to find out how many more bats need to be tagged
390-240=150
Answer:
1 out of a 50% chance
Step-by-step explanation:
hope it helps