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or, y(y 2 ) 3 (y 2 ) 0 or, (y 2 )(y 3 ) 0 ? y 2 0 , or, y 3 0 If y 2 0 ,y 2 If y 3 0 ,y 3 Now, when y 2 , 1 2 x a x ...
0DWK,;;)RUPD Square of the fraction = 4 ( 4 )^2816 2 2 (^22) ̧^ ¹ · ̈ © § x x x x x x x Here, numerator =x^2 and ...
Example 15. Shahik bought some pens at Tk. 240. If he would get one more pen in that money, average cost of each pen would be le ...
the new student = 1 1984 1 1950 34 x x b. By the question, 1 1 1950 1984 x x or, 1 1 1950 1984 x x or, 1 ( 1 ) 195 ...
What is the coefficient of x in the equation 3 x^2 x 5 0? a. 3 b. 2 c. 1 d. 1 Observe the following equations : i. 2 x 3 ...
2 ( 1 ) ( 1 ) ( 1 ) ( 1 ) 2 2 3 3 x x x x Solve by forming equations (26−31) : 26. Sum of the two digits of a numb ...
Chapter Six Lines, Angles and Triangles Geometry is an old branch of mathematics. The word ‘geometry’ comes from the Greek wor ...
of geometry springs from the study of space occupied by solids and the shape, size, location and properties of the space. A soli ...
A linehas only length, but no breath and height. A straight line is a line which lies evenly with the points on itself. A surfa ...
0DWK,;;)RUPD without any proof. Since the fifth postulate is related to parallel lines, it will be discussed later. 6.3 P ...
According to postulate 5(c) one to one correspondence can be established between the set of points in every straight line and th ...
Proof by contradiction Philosopher Aristotle first introduced this method of logical proof. The basis of this method is: x A pro ...
State the postulat e of ruler placement. Define intersecting straight line and parallel straight line. Line, Ray and Line Segme ...
Perpendicular and Right Angle The bisector of a straight angle is called perpendicular and each of th related adjacent angle a r ...
Opposite Angles Two angles are said to be the opposite angles if the sides of one are the opposite rays of the other. In the adj ...
(a) 1 and 5 , 2 and 6 , 3 and 7 , 4 and 8 are corresponding angles, (b) 3 and 6 , 4 and 5 are alternate angles, (c) ...
Theorem 4 When a transversal cuts two straight lines, such that (a) pairs of corresponding angles are equal, or (b) pairs of alt ...
0DWK,;;)RUPD Equilateral Triangle An equilateral triangle is a triangle of three equal sides. In the adjacent figure, tri ...
9.3 Interior and Exterior Angles If a side of a triangle is produced, a new angle is formed. This angle is known as exterior ang ...
In the figure, 'ABCand'DEF are congruent. If two triangles ABC and DEF are congruent, by superposition of a copy of ABC on DEF w ...
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