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Write four solutions for the following equations: πx + y = 9

We have to find four solutions for the equation πx+y = 9 Solution Let us assume x = 0 and substitute in the given equation Then,... View Article

In given figure. (i) and (ii) , DE || BC. Find EC in (i) and AD in (ii) .

(i) Given, In △ ABC, DE∥BC AD/DB = AE/EC [By Basic proportionality theorem] ⇒1.5/3 = 1/EC ⇒EC = 3/1.5 EC = 3×10/15 =... View Article

Find the sum of first 40 positive integers divisible by 6.

We have find the sum of first 40 positive integers divisible by 6 The positive integers that are divisible by 6 are 6, 12, 18, 24 ….... View Article

In Fig find the values of x and y and then show that AB || CD.

Given, AB and CD are two lines intersected by a transversal at point x and y. We need to find the values of x and y and show that AB || CD.... View Article

Without adding, find the sum: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Solution The Sum of first n odd natural numbers is n2 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 = 144 The Sum of first... View Article

Show that the angles of an equilateral triangle are 60° each.

Solution Given ∆ABC is an equilateral ∆ To Prove ∠A=∠B=∠C=60° In ∆ABC, AB=AC ∠B=∠C... View Article

All squares are rhombuses and also rectangles. (True or False)

All squares are rhombuses and also rectangles. Ans: True Squares have a property similar to Rhombuses and also to rectangles. ... View Article

Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.

Given that A.P. is3, 8, 13, …, 253 Common difference, d= 5. Find out We need to find the 20th term from the last Solution The given series... View Article

Construct a triangle PQR in which QR = 6cm, ∠Q = 60° and PR-PQ = 2cm.

P Procedure 1. Draw a line segment of base QR = 6 cm 2. Measure and draw ∠Q = 60° and let the ray be QX 3. Using a compass... View Article

Simplify and solve the following linear equation: 3(t – 3) = 5(2t + 1)

3(t – 3) = 5(2t + 1) => 3t – 9 = 10t + 5 Rearranging the equation and combining like terms we get => 3t – 10t = 5 + 9... View Article

Find the length of the side of a square whose area is 441 m2.

Solution Let the side of square be x m. Area of square = x2 According to the given details, the equation becomes x2 = 441 x =... View Article

Solve the following equation and check your results: 3x = 2x + 18

Solution 3x – 2x =18 Rearranging the terms we get X = 18 Verification We will substitute the value of x in the given... View Article

The diagonals of a rhombus are 7.5 cm and 12 cm. Find its area.

Given d1 = 7.5 cm and d2 = 12 cm Formula We know that, Area of the rhombus = (½) × d1 × d2 = (½) × 7.5... View Article

Solve the following equation and check your results: 3m = 5m – 8/5

Solution 3m = 25m -8/5 15m = 25m – 8 Rearranging and combining the like terms 15m – 25m = -8 -10m = -8 m = 8/10 or m = 4/5... View Article

Solve the following equation and check your results: 2x – 1 = 14 – x

Solution 2x – 1 + x = 14 Rearranging and combining the like terms 2x + x = 14 + 1 3x = 15 x = 5 Verification... View Article

Solve the following equation and check your results: 4z + 3 = 6 + 2z

Solution 4z +3 – 2z =6 Rearranging and combining the like terms 4z – 2z = 6 – 3 2z = 3 z = 3/2 Verification... View Article

Solve the following equation and check your results: 5x + 9 = 5 + 3x

Solution 5x + 9 – 3x = 5 Rearranging the like terms we get 5x – 3x = 5 – 9 2x = -4 x = -2 Verification ... View Article

Solve the following equation and check your results: 5t – 3 = 3t – 5

Solution 5t – 3 – 3t = -5 Rearranging the like terms we get 5t – 3t = -5 + 3 2t = -2 t = -1 ... View Article

Construct a triangle ABC in which BC = 7cm, ∠B = 75° and AB + AC = 13 cm.

Construction Procedure for the given parameters 1. Draw a line segment of base BC = 7 cm 2. Measure and draw ∠B = 75° and extend... View Article

Find the square roots of 529 by the Prime Factorisation Method.

Solution We have to find the square root of 529 by the prime factorisation method 529 = 23 × 23 × 1 529 = (23)2... View Article