Answer:
m (2,6), L (3, -6), J (-6, -9), K (-1, -9)
Step-by-step explanation:
Answer:
When solving for x, answer = 
When solving for a, answer = 
Step-by-step explanation:
24 + 5x = -x + 6(5a - 4)
Start by multiplying 6 by the values in the parenthesis
24 + 5x = -x + 30a - 24
Add 24 to both sides of the equation
48 + 5x = -x + 30a
Add 1x to both sides of the equation
48 + 6x = 30a
Subtract 48 from both sides of the equation
6x = 30a - 48
Divide both sides of the equation by 6
x = 5a - 8 (Answer when solving for x)
Add 8 to both sides of the equation
x + 8 = 5a
Divide both sides of the equation by 5
a = 1/5x + 8/5 (Answer when solving for a)
-----------------------------------------
When solving for x, answer =
When solving for a, answer =
Hope this helps :)
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:
Step-by-step explanation:
The -4 makes the waves taller (Amplitude 4), and the negitive flips over x-axis.
In (3x-pi) The three compresses horizontally making the waves tighter. The -pi shifts the funtion pi to the right.
The +5 shifts up five.
A True
Congruent means to have the same shape and size or when we can cut them out and then match them up completely.
