Maths-

General

Easy

Question

# Write the repeating decimal 0.6333....... as a fraction.

Hint:

### Perform necessary multiplications to make it as a fraction.

## The correct answer is: 19/30

### Complete step by step solution:

Let x = 0.6333…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 6.333

Now multiply by 100 on both the sides in (i),

100x = 63.33

On subtracting from both the sides, we have

100x - 10x = 63.33 - 6.333

90x = 57

x =

On simplification, we get

Hence 0.6333…. =

### Related Questions to study

Maths-

### △ ADB and △ CBD are congruent by HL-congruence postulate.

### △ ADB and △ CBD are congruent by HL-congruence postulate.

Maths-General

Maths-

### Use the given information to name two triangles that are congruent. Explain your reasoning

### Use the given information to name two triangles that are congruent. Explain your reasoning

Maths-General

Maths-

### Use the given information to name two triangles that are congruent. Explain your reasoning. ABCD is a square

### Use the given information to name two triangles that are congruent. Explain your reasoning. ABCD is a square

Maths-General

Maths-

### Determine whether each of the following are terminating or repeating

a) 5.692

b) 0.22222222222

c) 7.00001

d) 7.288888888888

e) 1.178178178178178.......

Complete step by step solution:

a) 5.692 - Terminating decimal

b) 0.22222222222 - Repeating decimal

c) 7.00001 - Terminating decimal

d) 7.288888888888 - Repeating decimal

e) 1.178178178178178.......- Repeating decimal

a) 5.692 - Terminating decimal

b) 0.22222222222 - Repeating decimal

c) 7.00001 - Terminating decimal

d) 7.288888888888 - Repeating decimal

e) 1.178178178178178.......- Repeating decimal

### Determine whether each of the following are terminating or repeating

a) 5.692

b) 0.22222222222

c) 7.00001

d) 7.288888888888

e) 1.178178178178178.......

Maths-General

Complete step by step solution:

a) 5.692 - Terminating decimal

b) 0.22222222222 - Repeating decimal

c) 7.00001 - Terminating decimal

d) 7.288888888888 - Repeating decimal

e) 1.178178178178178.......- Repeating decimal

a) 5.692 - Terminating decimal

b) 0.22222222222 - Repeating decimal

c) 7.00001 - Terminating decimal

d) 7.288888888888 - Repeating decimal

e) 1.178178178178178.......- Repeating decimal

Maths-

### Name the included angle between the given sides.

1) AB and AC

2) AB and BC

3) AC and CD

### Name the included angle between the given sides.

1) AB and AC

2) AB and BC

3) AC and CD

Maths-General

Maths-

### Find the length of the diagonal and area of a Rectangle whose sides are 10 cm and 12 cm. If the perimeter of a square is 2 ( 2x+4y) , find the area ?

Hint:-

Area of a rectangle = length × breadth

All angles in a rectangle are equal to 90°

Diagonal of a rectangle divides it into 2 right angled triangles.

Area of a square = side2

Perimeter of a square = 4 × side

ep-by-step solution:-

In the adjacent diagram, we can see that the diagonal divides the given rectangle into 2 right angled triangles.

Also, diagonal of the rectangle becomes the hypotenuse of the 2 triangles.

Hypotenuse of the given triangles = diagonal of the given rectangle

Now, sides of the rectangle = sides of the triangle (other than hypotenuse)

By applying Pythagorean theorem, For a right angled triangle-

Hypotenuse2 = sum of the squares of the remaining 2 sides

∴ Hypotenuse2 = 122 + 102

∴ Hypotenuse2 = 144 + 100

∴ Hypotenuse2 = 244

∴ Hypotenuse = 2 √61 cm .............................. (Taking square root both the sides)

Area of the given rectangle = length × breadth

∴ Area of the given rectangle = 12 × 10 ...................................................................................... (From given information & Equation i)

∴ Area of the given plot = 120 cm2

Perimeter of the given square = 4 × sides

∴ 2 (2x + 4y) = 4 × sides

∴ 4x + 8y = 4 × sides

∴ x + 2y = side .................. (Dividing both sides by 4) ................................ (Equation i)

Now, Area of the given square = side2

∴ Area of the given square = (x + 2y)2 ......................................................................................... (From Equation i)

Final Answer:-

∴ Length of the diagonal and area of the given Rectangle is 2 √61 cm & 120 cm2, respectively.

Area of the given square is (x + 2y)2 cm2.

Area of a rectangle = length × breadth

All angles in a rectangle are equal to 90°

Diagonal of a rectangle divides it into 2 right angled triangles.

Area of a square = side2

Perimeter of a square = 4 × side

ep-by-step solution:-

In the adjacent diagram, we can see that the diagonal divides the given rectangle into 2 right angled triangles.

Also, diagonal of the rectangle becomes the hypotenuse of the 2 triangles.

Hypotenuse of the given triangles = diagonal of the given rectangle

Now, sides of the rectangle = sides of the triangle (other than hypotenuse)

By applying Pythagorean theorem, For a right angled triangle-

Hypotenuse2 = sum of the squares of the remaining 2 sides

∴ Hypotenuse2 = 122 + 102

∴ Hypotenuse2 = 144 + 100

∴ Hypotenuse2 = 244

∴ Hypotenuse = 2 √61 cm .............................. (Taking square root both the sides)

Area of the given rectangle = length × breadth

∴ Area of the given rectangle = 12 × 10 ...................................................................................... (From given information & Equation i)

∴ Area of the given plot = 120 cm2

Perimeter of the given square = 4 × sides

∴ 2 (2x + 4y) = 4 × sides

∴ 4x + 8y = 4 × sides

∴ x + 2y = side .................. (Dividing both sides by 4) ................................ (Equation i)

Now, Area of the given square = side2

∴ Area of the given square = (x + 2y)2 ......................................................................................... (From Equation i)

Final Answer:-

∴ Length of the diagonal and area of the given Rectangle is 2 √61 cm & 120 cm2, respectively.

Area of the given square is (x + 2y)2 cm2.

### Find the length of the diagonal and area of a Rectangle whose sides are 10 cm and 12 cm. If the perimeter of a square is 2 ( 2x+4y) , find the area ?

Maths-General

Hint:-

Area of a rectangle = length × breadth

All angles in a rectangle are equal to 90°

Diagonal of a rectangle divides it into 2 right angled triangles.

Area of a square = side2

Perimeter of a square = 4 × side

ep-by-step solution:-

In the adjacent diagram, we can see that the diagonal divides the given rectangle into 2 right angled triangles.

Also, diagonal of the rectangle becomes the hypotenuse of the 2 triangles.

Hypotenuse of the given triangles = diagonal of the given rectangle

Now, sides of the rectangle = sides of the triangle (other than hypotenuse)

By applying Pythagorean theorem, For a right angled triangle-

Hypotenuse2 = sum of the squares of the remaining 2 sides

∴ Hypotenuse2 = 122 + 102

∴ Hypotenuse2 = 144 + 100

∴ Hypotenuse2 = 244

∴ Hypotenuse = 2 √61 cm .............................. (Taking square root both the sides)

Area of the given rectangle = length × breadth

∴ Area of the given rectangle = 12 × 10 ...................................................................................... (From given information & Equation i)

∴ Area of the given plot = 120 cm2

Perimeter of the given square = 4 × sides

∴ 2 (2x + 4y) = 4 × sides

∴ 4x + 8y = 4 × sides

∴ x + 2y = side .................. (Dividing both sides by 4) ................................ (Equation i)

Now, Area of the given square = side2

∴ Area of the given square = (x + 2y)2 ......................................................................................... (From Equation i)

Final Answer:-

∴ Length of the diagonal and area of the given Rectangle is 2 √61 cm & 120 cm2, respectively.

Area of the given square is (x + 2y)2 cm2.

Area of a rectangle = length × breadth

All angles in a rectangle are equal to 90°

Diagonal of a rectangle divides it into 2 right angled triangles.

Area of a square = side2

Perimeter of a square = 4 × side

ep-by-step solution:-

In the adjacent diagram, we can see that the diagonal divides the given rectangle into 2 right angled triangles.

Also, diagonal of the rectangle becomes the hypotenuse of the 2 triangles.

Hypotenuse of the given triangles = diagonal of the given rectangle

Now, sides of the rectangle = sides of the triangle (other than hypotenuse)

By applying Pythagorean theorem, For a right angled triangle-

Hypotenuse2 = sum of the squares of the remaining 2 sides

∴ Hypotenuse2 = 122 + 102

∴ Hypotenuse2 = 144 + 100

∴ Hypotenuse2 = 244

∴ Hypotenuse = 2 √61 cm .............................. (Taking square root both the sides)

Area of the given rectangle = length × breadth

∴ Area of the given rectangle = 12 × 10 ...................................................................................... (From given information & Equation i)

∴ Area of the given plot = 120 cm2

Perimeter of the given square = 4 × sides

∴ 2 (2x + 4y) = 4 × sides

∴ 4x + 8y = 4 × sides

∴ x + 2y = side .................. (Dividing both sides by 4) ................................ (Equation i)

Now, Area of the given square = side2

∴ Area of the given square = (x + 2y)2 ......................................................................................... (From Equation i)

Final Answer:-

∴ Length of the diagonal and area of the given Rectangle is 2 √61 cm & 120 cm2, respectively.

Area of the given square is (x + 2y)2 cm2.

Maths-

### Evaluate 8.6 × 10^{-4} - 4.2 × 10^{-7}

Hint:-

In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as a

a

Step-by-step solution:-

8.6 × 10

= 0.00086 - 0.000000042

= 0.000859958

= 8.59958 × 10

Final Answer:-

∴ Simplifying the given expression, we get- 0.000859958 or 8.59958 × 10

In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as a

^{n}, where a is called the base and n is its power/ exponent.a

^{n}= a × a × ... × a n times.Step-by-step solution:-

8.6 × 10

^{-4}- 4.2 × 10^{-7}= 0.00086 - 0.000000042

= 0.000859958

= 8.59958 × 10

^{-4}Final Answer:-

∴ Simplifying the given expression, we get- 0.000859958 or 8.59958 × 10

^{-4}.### Evaluate 8.6 × 10^{-4} - 4.2 × 10^{-7}

Maths-General

Hint:-

In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as a

a

Step-by-step solution:-

8.6 × 10

= 0.00086 - 0.000000042

= 0.000859958

= 8.59958 × 10

Final Answer:-

∴ Simplifying the given expression, we get- 0.000859958 or 8.59958 × 10

In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as a

^{n}, where a is called the base and n is its power/ exponent.a

^{n}= a × a × ... × a n times.Step-by-step solution:-

8.6 × 10

^{-4}- 4.2 × 10^{-7}= 0.00086 - 0.000000042

= 0.000859958

= 8.59958 × 10

^{-4}Final Answer:-

∴ Simplifying the given expression, we get- 0.000859958 or 8.59958 × 10

^{-4}.Maths-

### A rectangular field has its length and breadth in the ratio 5 : 3. Its area is 3.75 hectares. Find the cost of fencing it at ~ 5 per metre.

Hint:-

i. Fencing refers to blocking or covering the boundaries of a land with fences i.e. wooden blocks/ wires to prevent livestock from getting away.

ii. Perimeter of a rectangle = 2 (length + breadth)

Step-by-step solution:-

For the given rectangle field, we are given that length : breadth = 5 : 3

Let x be the common factor

∴ length = 5x, breadth = 3x

1 hectare = 10,000 sq mt

∴ 3.75 hectares = 3.75 × 10,000 = 37,500 m2

Area of the given rectangular field = length × breadth

∴ 37,500 = 5x × 3x ............................................................. (From given information)

∴ 37,500 = 15 x2

∴ 37,500 / 15 = x2

∴ 2,500 = x2

∴ 50 = x .................................................................... (Taking square root both the sides)

∴ Length = 5x = 5 × 50 = 250 m

& Breadth = 3x = 3 × 50 = 150 m

We need to find the cost of fencing the field at Rs. 5 per mt.

Since fences are put on the boundaries of the field, we need to calculate the perimeter of the field to find the cost of fencing it

∴ Perimeter of the given field = 2 (length + breadth)

∴ Perimeter of the given field = 2 (250 + 150)

∴ Perimeter of the given field = 2 × 400

∴ Perimeter of the given field = 800 m

∴ cost of fencing the whole field (@ Rs. 5 per mt) = 800 m × Rs. 5/ mt

∴ cost of fencing the whole field (@ Rs. 5 per mt) = Rs. 4,000

Final Answer:-

∴ The cost of fencing the given rectangle field is Rs. 4,000.

i. Fencing refers to blocking or covering the boundaries of a land with fences i.e. wooden blocks/ wires to prevent livestock from getting away.

ii. Perimeter of a rectangle = 2 (length + breadth)

Step-by-step solution:-

For the given rectangle field, we are given that length : breadth = 5 : 3

Let x be the common factor

∴ length = 5x, breadth = 3x

1 hectare = 10,000 sq mt

∴ 3.75 hectares = 3.75 × 10,000 = 37,500 m2

Area of the given rectangular field = length × breadth

∴ 37,500 = 5x × 3x ............................................................. (From given information)

∴ 37,500 = 15 x2

∴ 37,500 / 15 = x2

∴ 2,500 = x2

∴ 50 = x .................................................................... (Taking square root both the sides)

∴ Length = 5x = 5 × 50 = 250 m

& Breadth = 3x = 3 × 50 = 150 m

We need to find the cost of fencing the field at Rs. 5 per mt.

Since fences are put on the boundaries of the field, we need to calculate the perimeter of the field to find the cost of fencing it

∴ Perimeter of the given field = 2 (length + breadth)

∴ Perimeter of the given field = 2 (250 + 150)

∴ Perimeter of the given field = 2 × 400

∴ Perimeter of the given field = 800 m

∴ cost of fencing the whole field (@ Rs. 5 per mt) = 800 m × Rs. 5/ mt

∴ cost of fencing the whole field (@ Rs. 5 per mt) = Rs. 4,000

Final Answer:-

∴ The cost of fencing the given rectangle field is Rs. 4,000.

### A rectangular field has its length and breadth in the ratio 5 : 3. Its area is 3.75 hectares. Find the cost of fencing it at ~ 5 per metre.

Maths-General

Hint:-

i. Fencing refers to blocking or covering the boundaries of a land with fences i.e. wooden blocks/ wires to prevent livestock from getting away.

ii. Perimeter of a rectangle = 2 (length + breadth)

Step-by-step solution:-

For the given rectangle field, we are given that length : breadth = 5 : 3

Let x be the common factor

∴ length = 5x, breadth = 3x

1 hectare = 10,000 sq mt

∴ 3.75 hectares = 3.75 × 10,000 = 37,500 m2

Area of the given rectangular field = length × breadth

∴ 37,500 = 5x × 3x ............................................................. (From given information)

∴ 37,500 = 15 x2

∴ 37,500 / 15 = x2

∴ 2,500 = x2

∴ 50 = x .................................................................... (Taking square root both the sides)

∴ Length = 5x = 5 × 50 = 250 m

& Breadth = 3x = 3 × 50 = 150 m

We need to find the cost of fencing the field at Rs. 5 per mt.

Since fences are put on the boundaries of the field, we need to calculate the perimeter of the field to find the cost of fencing it

∴ Perimeter of the given field = 2 (length + breadth)

∴ Perimeter of the given field = 2 (250 + 150)

∴ Perimeter of the given field = 2 × 400

∴ Perimeter of the given field = 800 m

∴ cost of fencing the whole field (@ Rs. 5 per mt) = 800 m × Rs. 5/ mt

∴ cost of fencing the whole field (@ Rs. 5 per mt) = Rs. 4,000

Final Answer:-

∴ The cost of fencing the given rectangle field is Rs. 4,000.

i. Fencing refers to blocking or covering the boundaries of a land with fences i.e. wooden blocks/ wires to prevent livestock from getting away.

ii. Perimeter of a rectangle = 2 (length + breadth)

Step-by-step solution:-

For the given rectangle field, we are given that length : breadth = 5 : 3

Let x be the common factor

∴ length = 5x, breadth = 3x

1 hectare = 10,000 sq mt

∴ 3.75 hectares = 3.75 × 10,000 = 37,500 m2

Area of the given rectangular field = length × breadth

∴ 37,500 = 5x × 3x ............................................................. (From given information)

∴ 37,500 = 15 x2

∴ 37,500 / 15 = x2

∴ 2,500 = x2

∴ 50 = x .................................................................... (Taking square root both the sides)

∴ Length = 5x = 5 × 50 = 250 m

& Breadth = 3x = 3 × 50 = 150 m

We need to find the cost of fencing the field at Rs. 5 per mt.

Since fences are put on the boundaries of the field, we need to calculate the perimeter of the field to find the cost of fencing it

∴ Perimeter of the given field = 2 (length + breadth)

∴ Perimeter of the given field = 2 (250 + 150)

∴ Perimeter of the given field = 2 × 400

∴ Perimeter of the given field = 800 m

∴ cost of fencing the whole field (@ Rs. 5 per mt) = 800 m × Rs. 5/ mt

∴ cost of fencing the whole field (@ Rs. 5 per mt) = Rs. 4,000

Final Answer:-

∴ The cost of fencing the given rectangle field is Rs. 4,000.

Maths-

### What additional information is necessary to prove that the triangles ABC and XYZ are congruent by HL-Congruence theorem?

### What additional information is necessary to prove that the triangles ABC and XYZ are congruent by HL-Congruence theorem?

Maths-General

Maths-

### Find the value of ( 5^{0} - 4^{0}) x 8^{-1}

Hint:-

In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as a

a

Step-by-step solution:-

(5

= (1-1) × 1/8 …............................... (b

= 0 × 1/8

= 0

Final Answer:-

∴ Simplifying the given expression, we get- 0.

In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as a

^{n}, where a is called the base and n is its power/ exponent.a

^{n}= a × a × ... × a n times.Step-by-step solution:-

(5

^{0}- 4^{0}) × 8^{-1}= (1-1) × 1/8 …............................... (b

^{0}= 1 & b^{-n}= 1/b^{n})= 0 × 1/8

= 0

Final Answer:-

∴ Simplifying the given expression, we get- 0.

### Find the value of ( 5^{0} - 4^{0}) x 8^{-1}

Maths-General

Hint:-

In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as a

a

Step-by-step solution:-

(5

= (1-1) × 1/8 …............................... (b

= 0 × 1/8

= 0

Final Answer:-

∴ Simplifying the given expression, we get- 0.

In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as a

^{n}, where a is called the base and n is its power/ exponent.a

^{n}= a × a × ... × a n times.Step-by-step solution:-

(5

^{0}- 4^{0}) × 8^{-1}= (1-1) × 1/8 …............................... (b

^{0}= 1 & b^{-n}= 1/b^{n})= 0 × 1/8

= 0

Final Answer:-

∴ Simplifying the given expression, we get- 0.

Maths-

### Are the given triangles congruent? Explain why or why not.

### Are the given triangles congruent? Explain why or why not.

Maths-General

Maths-

### Are the given triangles congruent? Explain why or why not

### Are the given triangles congruent? Explain why or why not

Maths-General

Maths-

### Find the value of

(67.542)^{2} - (32.458)^{2} / 75.458 - 40.374

Hint:-

In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as a

a

Step-by-step solution:-

(67.542)

= 4561.92 - 1053.52 / 35.084

= 3508.4 / 35.084

= 100

Final Answer:-

∴ Simplifying the given expression, we get- 100.

In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as a

^{n}, where a is called the base and n is its power/ exponent.a

^{n}= a × a × ... × a n times.Step-by-step solution:-

(67.542)

^{2}- (32.458)^{2}/ 75.458 - 40.374= 4561.92 - 1053.52 / 35.084

= 3508.4 / 35.084

= 100

Final Answer:-

∴ Simplifying the given expression, we get- 100.

### Find the value of

(67.542)^{2} - (32.458)^{2} / 75.458 - 40.374

Maths-General

Hint:-

In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as a

a

Step-by-step solution:-

(67.542)

= 4561.92 - 1053.52 / 35.084

= 3508.4 / 35.084

= 100

Final Answer:-

∴ Simplifying the given expression, we get- 100.

In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as a

^{n}, where a is called the base and n is its power/ exponent.a

^{n}= a × a × ... × a n times.Step-by-step solution:-

(67.542)

^{2}- (32.458)^{2}/ 75.458 - 40.374= 4561.92 - 1053.52 / 35.084

= 3508.4 / 35.084

= 100

Final Answer:-

∴ Simplifying the given expression, we get- 100.

Maths-

### Why is SSA not a valid method for proving that triangles are congruent?

Complete step by step solution:

SSA is not possible since the sides could be located in two different parts of the

triangles and not the corresponding sides of two triangles. There is chance that the

size and shape would be different for both triangles and for triangles to be congruent,

the triangles must be of the same length, shape and size.

SSA is not possible since the sides could be located in two different parts of the

triangles and not the corresponding sides of two triangles. There is chance that the

size and shape would be different for both triangles and for triangles to be congruent,

the triangles must be of the same length, shape and size.

### Why is SSA not a valid method for proving that triangles are congruent?

Maths-General

Complete step by step solution:

SSA is not possible since the sides could be located in two different parts of the

triangles and not the corresponding sides of two triangles. There is chance that the

size and shape would be different for both triangles and for triangles to be congruent,

the triangles must be of the same length, shape and size.

SSA is not possible since the sides could be located in two different parts of the

triangles and not the corresponding sides of two triangles. There is chance that the

size and shape would be different for both triangles and for triangles to be congruent,

the triangles must be of the same length, shape and size.

Maths-

### Prove that △ ACB ≅△ CAD by SAS postulate.

### Prove that △ ACB ≅△ CAD by SAS postulate.

Maths-General