A large equilateral triangle has sides 1m and a smaller equilateral triangle has sides x m, 0≤x≤1. They are positioned as pictured so that the top side of the large triangle and the bottom side of the small triangle is parallel. Find the length x that maximizes the area of the intersection of the two triangles.

Mrs. morton has a special reward system for her class. when all her students behave well, she rewards them by putting 3 marbles into a marble jar. when the jar has 100 or more marbles, the students have a party. right now, the the jar has 24 marbles. how could mrs. morton reward the class in order for the students to have a party?

Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial

Calculate the missing value. round the answer to on decimal place. start with 70, increase it by 21%, and end up with