Solve graphically: 2x +3y = 2, x – 2y = 8

Prove that, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pot have been placed at a distance 1 m from each other along AD, as shown in Fig. 5. Niharika runs 1/4 th the distance AD on the 2^nd line and posts are green flag. Preet runs 1/5^th the distance AD on the eight line and posts a red flag.

(i) what is the distance between the two flags?

(ii) If Rashmi has two post a blue flag exactly half way between the line segment joining the two flags, where should she post the blue flag?

A two-digit number is such that the product of its digit is 14. If 45 is added to the number; the digits interchange their places. Find the number.

If 4 times the 4^th term of an AP is equal to 18 times the 18^th term, then find the 22^nd term.

OR

How many terms of the AP: 24, 21, 18, ….. must be taken so that their sum is 78?