Answer:
The length of each blue trim is 17.2 inches
Step-by-step explanation:
Given
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Required
The length of each blue trim
Since all 4 triangles are equal, then the dimension of 1 triangle is:
The hypotenuse (x) of the triangle blue trim is represented by the blue trim
So:
This gives
Take square root
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.
Answer: Choice C) -11
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Explanation:
The first equation given is y = 3 - 1/2x
In other words, y is the same as 3 - 1/2x.
We can replace y in the second equation with 3 - 1/2x
This is known as substitution (think of a substitute teacher who is a temporary replacement for your teacher)
Doing this leads to...
3x+4y = 1
3x+4*y = 1
3x+4*( y ) = 1
3x+4*( 3 - 1/2x ) = 1 <<--- y has been replaced with 3-1/2x
3x+4*(3) +4*(-1/2x) = 1
3x+12-2x = 1
3x-2x+12 = 1
x+12 = 1
x+12-12 = 1-12 <<-- subtracting 12 from both sides
x = -11
Which is why the answer is choice C) -11
Unfortunately, I don’t knooow :(
Answer:
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Step-by-step explanation:
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