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.
To find the answer, you have to set up a rate! The easiest way to do this would be to have:
160 beats / 60 seconds
25 beats / 10 seconds
From here, you can just look at the numbers. You want to get the two to have the same divisor, so you should multiply (25 beats / 10 seconds) by 6, because 6 * 10 = 60 seconds!
In conclusion, her heart rate when playing basketball is 160bpm, while her heart rate when jogging is 150bpm.
This means that her heart rate goes up more when she is playing basketball than when she is jogging!
The inequality to determine the minimum number of hours he needs to practice on each of the two days will be x >= (5/3)/2.
<h3>How to calculate the inequality?</h3>
Let the minimum number of hours to practice be represented by x.
She had already used 5 1/3 hours. The remaining hour will be:
= 7 - 5 1/3
= 1 2/3 hours.
Therefore, the inequality to represent the situation will be:
= x >= (5/3)/2
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So, to start, circumference=pi*diameter. Diameter is 2*radius, or in this case, 5. So we have circumference=pi*10. So, in terms of pi, it is 10pi.
Sam paid $ 124.032 as tax deduction each week.
<h3>What is an Equation ?</h3>
An equation is a mathematical statement formed when an algebraic expression is equated by an equal sign by a constant or algebraic expression.
It is given that
weekly earnings of Sam is $912
Tax deduction is 13.6 %
Let the amount of Tax deduction is represented by $x
Then the equation formed is
x = 13.6 % 912
x = 13.6 *912 /100
x = $ 124.032
Therefore Sam paid $ 124.032 as tax deduction each week.
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