Simplify \( \frac{1}{\sqrt{3}+2} \) in the form \( a+b\sqrt{3} \)

Find the midpoint of the line joining P(-3, 5) and Q(5, -3).

The graph above shows the cumulative frequency curve of the distribution of marks in a class test. What percentage of the students scored more than 20 marks?

Find the value of α2 + β2 if α + β = 2 and the distance between points (1, α) and (β, 1)is 3 units

Determine the locus of a point inside a square PQRS which is eqidistant from PQ and QR

The sum of the interior angles of a pentagon is 6x + 6y. Find y in the terms of x

The shaded region in the Venn diagram above is

In the diagram above, PQ = 4 cm and TS = 6 cm. If the area of parallelogram PQTU is 32 cm2, find the area of the trapezium PQRU

Find the value of x in the figure above