Featured Questions

Let the triangle ABC have the area S . The points D , E , F are in the order of AB , BC , CA such that AD = DB , BE = 1 part 2 EC , CF = 1 part 2 FA . Straight segments AE , BF , CD intersect to form a triangle . Calculate the area of the triangl e.

Given a fixed triangle ABC of height h . Find the set of points M with the sum of the distances to 3 of the triangle by the constant m ( m > h ) .

The net of a square pyramid, shown here, is a square with an equilateral triangle on each of its sides. The side length of the square can be expressed as 6x – 6 or 2x + 14, for the same value of x. When the net is folded to form a square pyramid, its surface area can be expressed in simplest radical form as a\(^2\)( b + c). What is the value of  + b + c?

The product of the 3-digit number ABC and its reverse, CBA, is 140,209. If A, B and C each represent a different digit, what is the value of A + B + C? 

Suppose f(x) is a polynomial of x.If f(x) has a remainder of 3 when it is divided by 2(x-1) and 2f(x) has a remainder of -4 when it is divided by 3(x+2).Thus when 3f(x) í divided by 4(\(x^2\) +x-2),the remainder is ax+b,where a and b are constants.Then a+b=...............

Find m,n are positive integer satisfy 

A box contains 15 slips of paper, each bearing a different natural number from 1 to 15, inclusive. If three of these slips are randomly drawn, one at a time, without replacement, what is the probability that three consecutive numbers are drawn in increasing order? Express your answer as a common fraction

Ali gives Stan a closed box that contains at least one of each token worth 5, 11 or 19 points. Ali says that the tokens have a combined value of 56 points. How many tokens are in the box?

The mean, the median and the mean of all modes of the integers 7, 4, 5, 6, 5, x are equal. How many possible values are there for x?

Xera and Yeta use this method to decide who will sit in the front passenger seat of the car. Xera throws a standard six-sided die, after which Yeta picks a card from a standard deck of 52 cards, with replacement. They continue to take turns die-throwing and card-picking until either Xera wins by rolling a four or Yeta wins by picking a card with a four. What is the probability that Yeta wins? Express your answer as a common fraction.