Answer:
26
Step-by-step explanation:
40-32÷8+5×-2
40-4+5×-2
40-4+-10
36+-10
26
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.
5/6 x 2 3/4 = 5/6 x (2x4+3)/4 = 5/6 x 11/4 = 55/24 = 2 7/24
Answer: 14
The number to the right of the decimal point is either 5 or greater than that, so the 13 is increased by 1 which results in 14.
a) The equation represents an ellipse.
b) The equation represents a circle.
c) The equation represents a parabola.
<h3>How to infer the graphical form of a general equation</h3>
In this problem we have <em>general</em> equations of the form A · x² + B · y² + C · x + D · y + E = 0, which have to be modified into <em>standard</em> form to infer its <em>graphical</em> form. This procedure can be done by <em>algebra</em> properties:
16 · x² + 4 · y² + 96 · x - 8 · y + 84 = 0
[(4 · x)² + 2 · 12 · (4 · x)] + [(2 · y)² - 2 · 2 · (2 · y)] = - 84
[(4 · x)² + 2 · 12 · (4 · x) + 144] + [(2 · y)² - 2 · 2 · (2 · y) + 4] = 64
(4 · x + 12)² + (2 · y + 2)² = 64
4² · (x + 3)² + 2² · (y + 2)² = 64
(x + 3)² / 4 + (y + 2)² / 16 = 1 : Ellipse
x² + y² + 8 · x - 6 · y - 15 = 0
(x² + 8 · x) + (y² - 6 · y) = 15
(x² + 2 · 4 · x + 16) + (y² - 2 · 3 · y + 9) = 40
(x + 4)² + (y - 3)² = 40 : Circle
x² + 6 · x + 4 · y + 5 = 0
x² + 6 · x + 5 = - 4 · y
y = - (1 / 4) · x² - (3 / 2) · x - (5 / 4) : Parabola
To learn more on ellipses: brainly.com/question/19507943
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