Answer:
1.) Pray to Jesus. 2.) Go to the nurse, she'll give you an mint. 3.) If you're lucky an ice pack. 4.) Rethink life decisions. 5.) Go back to classroom
Step-by-step explanation:
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 answer is c. See explanation below.
Sin (A + B) = sin A cos B + cos A Sin B
<span>Cos (A - B) = cos A cos B + sin A sin B </span>
<span>=> (SinACosB+ CosASinB) (CosACosB +SinASinB) </span>
<span>=>SinACosACos^2B+Sin^2ACosBSinB+Cos^2A... </span>
<span>=>SinACosA(Cos^2B+Sin^2B) +SinBCosB(Sin^2A+Cos^2A) </span>
<span>we know that Sin^2+Cos^2=1 </span>
<span>=>SinACosA(1)+SinBCosB(1) </span>
<span>=SinACosA+SinBCosB </span>
<span>Proved
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