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Given that x, y, and z are real numbers that satisfy:
find x+y+z
A convex hexagon with sides 3x, 3x, 3x, 5x, 5x and 5x is inscribed in a unit circle. Find
the value of x.
prove that
Rick, Dan and Alan play table tennis with two players at one side of the table and the third one at the other side. Dan and Alan playing together beat Rick three times as often as Rick beats them, Dan wins the game against Rick and Alan as often as he loses it, and Alan wins the game against Rick and Dan twice as often as he loses it. Last time they played six games during the afternoon, two in each arrangement of players. What is the probability that Rick won at least once?
Jenny and Kenny are walking in the same direction, Kenny at 3 feet per second and Jenny at 1 foot per second, on parallel paths that are 200 feet apart. A tall circular building 100 feet in diameter is centered midway between the paths. At the instant when the building first blocks the line of sight between Jenny and Kenny, they are 200 feet apart. Let T be the amount of time, in seconds, before Jenny and Kenny can see each other again. If T is written as a fraction in lowest terms, what is the sum of the numerator and denominator?
find n
Let
be the three sides of a triangle , and let , be the angles opposite them. If ,find
Find the smallest positive integer solution to
Determine all triples
, satisfyingDetermine all real x
such that
is an integer for any integer n.
Let ABCDE be a convex pentagon such that BC = CD = DE
and each diagonal of the pentagon is parallel to one of its sides. Prove that
all the angles in the pentagon are equal, and that all sides are equal
Find all solutions of
sin x + sin 2x = sin 4x
Given ten numbers 2, 3, 5, 6, 7, 8, 10, 11, 12, 13,
one must cross
out several of them so that the total of any of the remaining numbers would
not be an exact square
(that is, the sum of any two, three, four, : : :, and of
all the remaining numbers would not be an exact square).
At most how many numbers can remain?
Let a be the length of a side and b be
the length of a diagonal in the regular pentagon
PQRST. Prove that
b/a - a/b=1
solve the system
solve
i know its 4 but how
if
andprove
Prove that if both midlines of a quadrilateral halve its area then the quadrilateral is a parallelogram.
a triangle ABC,D ∈ AC, m< A = 4x°, m< C = 3x°, m< CBD = 5x°,
and AB = CD. Find x°
(Here m< means "the degree of angle)
x° (xdeg)
x is acute angle and
find x
If
find 8x
but how olivia