Prove that one of the diagonals of a kite bisects two of the
angles of the...
Prove that one of the diagonals of a kite bisects two of the
angles of the kite. What about the other diagonal — must it also be
an angle bisector? Explain your response.
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SECTION
Prove using the principle of mathematical induction:
(i) The number of diagonals of a convex polygon with n vertices
is n(n − 3)/2, for n ≥ 4,
(ii) 2n < n! for all n > k > 0, discover the value of k
before doing induction
High Kite is one of the foremost performance kite makers
in Australia. The company has always prepared a budget that is
calculated using only one estimated volume of sales. You recently
joined the company as a junior accountant. You are required to set
up a spreadsheet for sensitivity analysis in the budgeting process.
This year it appears that the company may not meet expectations,
which could result in a loss. Top manager is concerned that the
company will incur a...
Draw a convex quadrilateral ABCD, where the diagonals intersect
at point M. Prove: If ABCD is a parallelogram, then M is the
midpoint of each diagonal.
Two angles of a quadrilateral measure 140° and 80°. The other
two angles are in a ratio of 3:4. What is the value of x? What are
the measures of those two angles?
x =
Measures of two angles are?
1)
Prove the conjectures
a) The sum of the measures of the n interior angles of any
n-gon is 180 degrees(n-2).
b) For any polygon, the sum of the measures of a set of
exterior angles is 360 degrees.
Prove using the short north-east diagonals or any other
mathematical method of your preference, that if A is enumerable,
then it is also countable with an enumeration that lists each of
its members exactly three (3) times. Hint. Your proof will consist
of constructing an enumeration with the stated requirement.