Answer:
(x-2)²+(y-4)²=4
Step-by-step explanation:
Answer:
<h2>45, 46, 47</h2>
Step-by-step explanation:
n, n + 1, n + 2 - three consecutive integers
The equation:
138 - n = (n + 1) + (n + 2)
138 - n = n + 1 + n + 2 <em>combile like terms</em>
138 - n = 2n + 3 <em>subtract 138 from both sides</em>
-n = 2n - 135 <em>subtract 2n from both sides</em>
-3n = -135 <em>divide both sides by (-3)</em>
n = 45
n + 1 = 46
n + 2 = 47
Perhaps the easiest way to find the midpoint between two given points is to average their coordinates: add them up and divide by 2.
A) The midpoint C' of AB is
.. (A +B)/2 = ((0, 0) +(m, n))/2 = ((0 +m)/2, (0 +n)/2) = (m/2, n/2) = C'
The midpoint B' is
.. (A +C)/2 = ((0, 0) +(p, 0))/2 = (p/2, 0) = B'
The midpoint A' is
.. (B +C)/2 = ((m, n) +(p, 0))/2 = ((m+p)/2, n/2) = A'
B) The slope of the line between (x1, y1) and (x2, y2) is given by
.. slope = (y2 -y1)/(x2 -x1)
Using the values for A and A', we have
.. slope = (n/2 -0)/((m+p)/2 -0) = n/(m+p)
C) We know the line goes through A = (0, 0), so we can write the point-slope form of the equation for AA' as
.. y -0 = (n/(m+p))*(x -0)
.. y = n*x/(m+p)
D) To show the point lies on the line, we can substitute its coordinates for x and y and see if we get something that looks true.
.. (x, y) = ((m+p)/3, n/3)
Putting these into our equation, we have
.. n/3 = n*((m+p)/3)/(m+p)
The expression on the right has factors of (m+p) that cancel*, so we end up with
.. n/3 = n/3 . . . . . . . true for any n
_____
* The only constraint is that (m+p) ≠ 0. Since m and p are both in the first quadrant, their sum must be non-zero and this constraint is satisfied.
The purpose of the exercise is to show that all three medians of a triangle intersect in a single point.
Answer:
Yes
Step-by-step explanation:
To be a function, the graph must pass the vertical line test.
The vertical line test is simple. Imagine you draw an infinite number of vertical lines. In all of these lines, it should never hit the function twice in the same x value.
For example, if it hits (4, 2) and (4, 7), the graph is not a function because there are two points with the same x value.
1/4 because 6/24 can be simplified all the way down to 1/4
