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
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* 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.
The form (x - p)^2 = q is the form that completing the square will leave us with.
---Add 5 to both sides
x^2 - 8x = 5
---Divide the b term by 2, and square it. Then, add that number to both sides.
-8/2 = -4
(-4)^2 = 16
x^2 - 8x + 16 = 5 + 16
x^2 - 8x + 16 = 21
---Factor!
(x - 4)^2 = 21
p = 4
q = 21
Hope this helps!! :)
Answer:
y = mx + b
Step-by-step explanation:
The reason is, x is always the hour, and m is the amount of money you earn in the hours.
Answer:
5
Step-by-step explanation:
they are equal to one another soo make an equation and solve it 2x-10 then divide that and get 5
1. <span>true
example:
2+3=3+2
5=5
2. </span><span>true
</span>example:
3*4=4*3
12=12
<span>
3. false
</span>example:
6-3=3-6
3≠-3
<span>
4. </span><span>true
</span>example:
(4 + 3) + 2= 4 + (3 + 2)
7 + 2 = 4 + 5
9 = 9
<span>
5. false
</span>example:<span>
(9 - 6) - 3 = 9 - (6 - 3)
</span>3 - 3 = 9 - 3
0 ≠ 6
6. true
example:
<span>2(3+4)= 2*3+2*4
2 * 7 = 6 + 8
14 = 14</span>
