A birdwatcher on a cliff saw a eagle 70 feet above him. Earlier, he had spotted the eagle 30 feet above him. Which integer repre
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Given:
Number of males = h
Number of females = (h-2)
Total number of visitors = 80
To find:
The value of h.
Solution:
We have,
Number of males = h
Number of females = (h-2)
So, the total number of visitors is:
It is given that the total number of visitors is 80. So,
Divide both sides by 2.
Therefore, the correct option is D.
To prove that the diagonals are congruent, you need to formula to compute the distance between two points:
Using that formula, you may prove that , which means that the two diagonals have the same length.
To prove that they are perpendicular, you need the formula to compute the slope of a segment. The slope, knowing the enpoints, is given by
You can use this formula to prove that
In fact, if one slope is the opposite of the reciprocal of the other, the two segments are perpendicular.
Finally, to prove that they bisect each other, you first need to find the point where they meet. First of all, you need to find the line the segments lie on: the formula is
where is one of the points belonging to the line, and you already know how to find the slope. Then, you find the point of intersection, say A, by solving the system involving the two lines:
And use again the formula for the distance between two points to prove that