The equation of a circle is written as ( x-h)^2 + (y-k)^2 = r^2
h and k is the center point of the circle and r is the radius.
In the given equation (x+3)^2 + (y-1)^2 = 81
h = -3
k = 1
r^2 = 81
Take the square root of both sides:
r = 9
The center is (-3,1) and the radius is 9
Answer:
You can use Gaussian Elimination.
Double both sides of the first equation and add the second equation.
6x + 4y = 8
5x - 4y = 3
---------------
11x = 11
x = 1
5 - 4y = 3
-4y = -2
y = 1/2
Step-by-step explanation:
Answer:
<h2>The x-coordinate after the rotation is -10.</h2>
Step-by-step explanation:
A 810° rotation is equal to a 90° rotation. So, the transformation described gives the same result than rotating 90° only.
A 90° counterclockwise rotation is defined by the rule
The given coordinate is 
. Using the rule, we have
Therefore, the x-coordinate after the rotation is -10.
Answer:
A] The slope of f(x) is greater than the slope of g(x).
Step-by-step explanation:
First, you need to calculate the slope of f(x) and g(x) using the slope formula
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are points of the functions.
To calculate the slope of f(x) you can choose two points from the graph, in this case (0, -1) and (3, 1). Remember you can choose the points you want as long they are on the graph.
m = 1 - (-1) / 3 - 0
m = 1 + 1 / 3
m = 2 / 3
m = 0.66...
To calculate the slope of g(x) you can choose two points from the table, in this case (0, 2) and (5, 4).
m = 4 - 2 / 5 - 0
m = 2 / 5
m = 0.4
So the slope of f(x) is greater than the slope of g(x).
Two sandwiches divide by three brothers is:
2/3
So each brother gets two thirds of a sandwich.
