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Solve the following equation: 1.6 = y/15

Solution 1.6 = y/1.5 On rearranging the terms we get y/1.5 = 1.6 y = 1.6 × 1.5 y = 2.4 Answer y = 2.4... View Article

Solve the following equation: 14y – 8 = 13

Solution 14y – 8 = 13 Rearranging the like terms we get 14y = 13+8 14y = 21 y = 21/14 y = 3/2 Answer y = 3/2 ... View Article

Which term of the A.P. 3, 8, 13, 18, … is 78?

Given that The A.P. series 3, 8, 13, 18, … Find out We need to find out which term is 78 Solution First-term, a = 3 Common... View Article

Without adding, find the sum: 1 + 3 + 5 + 7 + 9

Solution The Sum of first n odd natural numbers is n2 (i) 1 + 3 + 5 + 7 + 9= 25 The sum of the first 5 odd natural numbers is 52 52 = 25.... View Article

In Fig.PQR = PRQ, then prove that PQS = PRT.

Given, ∠PQR = ∠PRQ Considering ST is a straight line, so the sum of all angles made on it is 180° => ∠PQS +... View Article

Solve the following equation: (8x – 3) /3x = 2

(8x – 3)/3x = 2 On multiplying we get ⇒ 8x/3x – 3/3x = 2 ⇒ 8/3 – 1/x = 2 ⇒ 8/3 – 2 = 1/x ⇒ (8... View Article

Simplify the following expression: (√5 + √2) 2

(iii) (√5+√2)2 On opening the brackets and solving, we get, (√5+√2)2 =... View Article

In Fig. AP || BQ || CR. Prove that ar(△AQC) = ar(△PBR) .

Solution Given: AP || BQ || CR Prove: ar(AQC) = ar(PBR) Proof: ar(ΔAQB) = ar(ΔPBQ) ------------------(1)(Lie on the same base... View Article

Solve the following equation: x/3 + 1 = 7/15

Solution x/3 + 1 = 7/15 Rearranging the like terms we get x/3 = 7/15 – 1 Making common denominator x/3 = (7 – 15)/15 ... View Article

Solve the following equation: 3/7 + x = 17/7

Solution 3/7 + x = 17/7 On rearranging the terms we get x = 17/7 – 3/7 x = 14/7 x = 2 Answer x = 2... View Article

Solve the following equation: z/(z + 15) = 4/9

z/(z + 15) = 4/9 ⇒ z = 4/9 (z + 15) ⇒ 9z = 4(z + 15) ⇒ 9z = 4z + 60 Rearranging the equation and combining like terms we get... View Article

Solve the following equation: 9x/(7 – 6x) = 15

9x/(7 – 6x) = 15 ⇒ 9x = 15(7 – 6x) On simplifying we get ⇒ 9x = 105 – 90x ⇒ 9x + 90x = 105 ⇒ 99x = 105... View Article

Express 121 as the sum of 11 odd numbers.

Solution 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 121 = 112 Therefore sum of first 11 odd natural numbers is 121.... View Article

All squares are trapeziums. (True or False)

All squares are trapeziums. Ans: True All squares have two sides that are parallel to each similar to Trapezium. ... View Article

All rectangles are squares. (True or False)

All rectangles are squares. Ans: False In square all sides are equal, but in rectangle length and breadth are different. All square are... View Article

Simplify the following expression: (3 + √3) (3-√3)

(ii) (3+√3)(3-√3) On opening the brackets and solving, we get, (3+√3)(3-√3) = 32-(√3)2 = 9-3... View Article

In Fig. if AB CD, CD EF and y : z = 3 : 7, find x.

Given AB || CD and CD || EF y : z = 3 : 7 => AB || CD || EF => AB || EF So, x=z [alternate interior angles] -------------(i) Again... View Article

Simplify the following expression: (√5-√2) (√5 + √2)

(iv) (√5-√2)(√5+√2) On opening the brackets and solving, we get, (√5-√2)(√5+√2) =... View Article

Find six rational numbers between 3 and 4.

Given The numbers 3 & 4 are given Find out We have to find out 6 rational numbers between 3 and 4 Solution There are infinite rational... View Article

Solve the following equation: (7y + 4) /(y + 2) = -4/3

(7y + 4)/(y + 2) = -4/3 ⇒ 7y + 4 = -4/3 (y + 2) ⇒ 3(7y + 4) = -4(y + 2) ⇒ 21y + 12 = -4y – 8 Rearranging the equation... View Article