If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent by

Solve:  and  by using elimination method.

ABCD is a parallelogram of area 162 sq., P is the point on AB such that AP:PB = 1:2, calculate the area of Triangle APD and the ratio PQ:QD, where Q is the point of intersection of AC and PD

How many litres of water flows out through a pipe having an area of cross-section of 5 cm² in one minute, if the speed of water in pipe is 30 cm/sec?

Curved surface area of a right circular cylinder of height 14 cm is 88 cm². Find the volume of the cylinder.

The sides of a parallelogram are 3cm and 2cm and the distance between two longer sides is 1.5cm. Find the distance between the shorter sides?

Solve:  and 

The cross section of a canal is atrapezium in shape. If the canal is 10m wide at the top and 6m wide at the bottom and the area of the cross section is 840 sq. m, find the depth of the canal ?

The total surface area of a cylinder of height 6.5 cm is 220 sq. cm. Find its volume.

In a trapezium, the two non parallel sides are equal in length, each being 5 units. The parallel sides are at a distance of 3 units apart. If the smaller side of the parallel side is of length 2 units, then what is the sum of the diagonals of the trapezium ?

The base radius of a cylinder is 5/3 times its height. The cost of painting its C.S.A. at 2 paise/cm² is Rs 92.40. What volume of the paint is required?

During mineral formation, the same chemical compound can beco me different minerals depending on the temperature and pressure at the time of formation. A phase diagram is a graph that shows the conditions that are needed to form each mineral. The graph above is a portion of the phase diagram for aluminosilicates, with the temperature t , in degrees Celsius  , on the horizontal axis, and the pressure p , in gigapascals (GPa), on the vertical axis.

An equation of the boundary line between the andalusite and sillimanite regions is approximated by the equation above. What is the meaning of the T-intercept of this line?

Note;
A phase diagram represents the different physical states of some substance under different conditions, such as termperature and pressure, graphically. It may seem like a complicated graph but we just needed to focus on the equation of one given line.

Solve the system of equation by using elimination: 

Farmer Joe had 35 customers for the whole morning. He knew 20 of them. How many new customers did he meet today ?

Read the problem carefully multiple times in order to understand it.

The budget for a school band was   in 2010 . The budget decreased by  from 2010 to 2011 and then increased by  from 2011 to 2012 . Which of the following expressions represents the budget, in dollars, for the school band in 2012?

Note:
The concept of percentages can be a little tricky. But we just need to remember a few basic things to get going. This is the standard way of finding the value after increasing or decreasing a quantity by a certain percentage

The perimeter of a trapezium is 52cm .Its non parallel sides are equal to 10cm each and its altitude is 8cm. Find the area of the trapezium ?