Let's assume
number of birds with 2 wings is x
number of birds with 4 wings is y
A nature museum has 2008 specimens of early birds
so,
Total of wings of 2 wings bird =2x
Total of wings of 4 wings bird =4y
The specimens have a total of 4384 wings
so, we get
we can divide both sides by 2
so, we get system of equations as
we can solve for x and y
We can subtract both equations
so,
number of birds with 2 wings is 1824
number of birds with 4 wings is 184.............Answer
Given:
M=(x1, y1)=(-2,-1),
N=(x2, y2)=(3,1),
M'=(x3, y3)= (0,2),
N'=(x4, y4)=(5, 4).
We can prove MN and M'N' have the same length by proving that the points form the vertices of a parallelogram.
For a parallelogram, opposite sides are equal
If we prove that the quadrilateral MNN'M' forms a parallellogram, then MN and M'N' will be the oppposite sides. So, we can prove that MN=M'N'.
To prove MNN'M' is a parallelogram, we have to first prove that two pairs of opposite sides are parallel,
Slope of MN= Slope of M'N'.
Slope of MM'=NN'.
Hence, slope of MN=Slope of M'N' and therefore, MN parallel to M'N'
Hence, slope of MM'=Slope of NN' nd therefore, MM' parallel to NN'.
Since both pairs of opposite sides of MNN'M' are parallel, MM'N'N is a parallelogram.
Since the opposite sides are of equal length in a parallelogram, it is proved that segments MN and M'N' have the same length.