Maths-

General

Easy

Question

# Find the GCF (GCD) of the given pair of monomials.

Hint:

- The highest number that divides exactly into two or more numbers is known as GCF.
- An algebraic expression consisting only one term is called monomial.

## The correct answer is: So, The GCF 10x,25 is 5.

- We have been given a monomial in the question
- We have to find the GCF of the given pair of monomials.

Step 1 of 1:

We have given two monomials .

The highest factor in these two monomial is 5.

So, The GCF 10x , 25 is 5.

The highest factor in these two monomial is 5.

So, The GCF 10x , 25 is 5.

### Related Questions to study

Maths-

### Find the number of diagonals of a 100-gon.

Solution:

Hint:

We have to find the number of diagonals of a 100-gon

We know that the number of diagonal in n - side polygon =

Here, n = 100

So, Number of diagonals will be

= 4850

Hint:

- A hundred-sided polygon is known as 100-gon or hectogon. The sum of exterior angle of a 100-gon is 360 degrees.

- We have been given in the question the information about a polygon that is 100-gon having 100 sides
- We have to find the number of diagonals of the 100-gon from the four options provided.

We have to find the number of diagonals of a 100-gon

We know that the number of diagonal in n - side polygon =

Here, n = 100

So, Number of diagonals will be

= 4850

### Find the number of diagonals of a 100-gon.

Maths-General

Solution:

Hint:

We have to find the number of diagonals of a 100-gon

We know that the number of diagonal in n - side polygon =

Here, n = 100

So, Number of diagonals will be

= 4850

Hint:

- A hundred-sided polygon is known as 100-gon or hectogon. The sum of exterior angle of a 100-gon is 360 degrees.

- We have been given in the question the information about a polygon that is 100-gon having 100 sides
- We have to find the number of diagonals of the 100-gon from the four options provided.

We have to find the number of diagonals of a 100-gon

We know that the number of diagonal in n - side polygon =

Here, n = 100

So, Number of diagonals will be

= 4850

Maths-

### Factor out the GCF from the given polynomial.

Solution:

Hint:

We have to find the GCD of the given polynomial .

Now we will factorize the given polynomial and extract the greatest factor from it.

So,

So, The GCD of this polynomial will be 4y

Hint:

- The highest number that divides exactly into two or more numbers is known as GCF.
- A polynomial is a type of algebraic expression in which the exponents of all variable should be a whole number.

- We have been given a polynomial in the question
- We have to factor out the GCF of the given polynomial.

We have to find the GCD of the given polynomial .

Now we will factorize the given polynomial and extract the greatest factor from it.

So,

So, The GCD of this polynomial will be 4y

^{3}.### Factor out the GCF from the given polynomial.

Maths-General

Solution:

Hint:

We have to find the GCD of the given polynomial .

Now we will factorize the given polynomial and extract the greatest factor from it.

So,

So, The GCD of this polynomial will be 4y

Hint:

- The highest number that divides exactly into two or more numbers is known as GCF.
- A polynomial is a type of algebraic expression in which the exponents of all variable should be a whole number.

- We have been given a polynomial in the question
- We have to factor out the GCF of the given polynomial.

We have to find the GCD of the given polynomial .

Now we will factorize the given polynomial and extract the greatest factor from it.

So,

So, The GCD of this polynomial will be 4y

^{3}.Maths-

### Factor out the GCF from the given polynomial.

Solution:

Hint:

We have to find the GCD of the given polynomial .

Now we will factorize the given polynomial and extract the greatest factor from it.

So,

So, The GCD of this polynomial will be x.

Hint:

- The highest number that divides exactly into two or more numbers is known as GCF.
- A polynomial is a type of algebraic expression in which the exponents of all variable should be a whole number.

- We have been given a polynomial in the question
- We have to factor out the GCF of the given polynomial.

We have to find the GCD of the given polynomial .

Now we will factorize the given polynomial and extract the greatest factor from it.

So,

So, The GCD of this polynomial will be x.

### Factor out the GCF from the given polynomial.

Maths-General

Solution:

Hint:

We have to find the GCD of the given polynomial .

Now we will factorize the given polynomial and extract the greatest factor from it.

So,

So, The GCD of this polynomial will be x.

Hint:

- The highest number that divides exactly into two or more numbers is known as GCF.

- We have been given a polynomial in the question
- We have to factor out the GCF of the given polynomial.

We have to find the GCD of the given polynomial .

Now we will factorize the given polynomial and extract the greatest factor from it.

So,

So, The GCD of this polynomial will be x.

Maths-

Solution:

Hint:

We have a given figure

In this figure,

4x = 20

x = 5

So,

= 15

And

7(5) - 20

= 15

Now, we know that the sum of angle of triangle is 180

So,

Hint:

- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.

- We have been given in the question diagram of a triangle named ABC where ∠ABC=60.
- We have to find out angle A.

We have a given figure

In this figure,

4x = 20

x = 5

^{0}So,

= 15

^{0}And

7(5) - 20

= 15

^{0}Now, we know that the sum of angle of triangle is 180

^{0}.So,

Maths-General

Solution:

Hint:

We have a given figure

In this figure,

4x = 20

x = 5

So,

= 15

And

7(5) - 20

= 15

Now, we know that the sum of angle of triangle is 180

So,

Hint:

- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.

- We have been given in the question diagram of a triangle named ABC where ∠ABC=60.
- We have to find out angle A.

We have a given figure

In this figure,

4x = 20

x = 5

^{0}So,

= 15

^{0}And

7(5) - 20

= 15

^{0}Now, we know that the sum of angle of triangle is 180

^{0}.So,

Maths-

### Use Symmetric Property of Equality: If x = y, then

Hint :- The symmetric property states that for any real numbers, a and b, if a = b then b = a.

Ans :- Option B

Explanation :- The symmetric property states that for any real numbers, a and b, if a = b then b = a.

Similarly with x and y If x = y, then y = x

∴ Option B

Ans :- Option B

Explanation :- The symmetric property states that for any real numbers, a and b, if a = b then b = a.

Similarly with x and y If x = y, then y = x

∴ Option B

### Use Symmetric Property of Equality: If x = y, then

Maths-General

Hint :- The symmetric property states that for any real numbers, a and b, if a = b then b = a.

Ans :- Option B

Explanation :- The symmetric property states that for any real numbers, a and b, if a = b then b = a.

Similarly with x and y If x = y, then y = x

∴ Option B

Ans :- Option B

Explanation :- The symmetric property states that for any real numbers, a and b, if a = b then b = a.

Similarly with x and y If x = y, then y = x

∴ Option B

Maths-

### If and , find the value of x and

Solution:

Hint:

In the given figure,

So,

x = 9

So,

= 5(9) + 7

= 52

And,

= 2(9) + 34

= 52

Now we know that the sum of angle of triangle is 180

So,

Hint:

- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.

- We have been given in the question that if 𝑚∠𝐵 = (5𝑥 + 7) ° and 𝑚∠𝐶 = (2𝑥 + 34) °
- We have to find the value of x and 𝑚∠A

In the given figure,

So,

x = 9

So,

= 5(9) + 7

= 52

^{0}And,

= 2(9) + 34

= 52

^{0}Now we know that the sum of angle of triangle is 180

^{0}.So,

### If and , find the value of x and

Maths-General

Solution:

Hint:

In the given figure,

So,

x = 9

So,

= 5(9) + 7

= 52

And,

= 2(9) + 34

= 52

Now we know that the sum of angle of triangle is 180

So,

Hint:

- We have been given in the question that if 𝑚∠𝐵 = (5𝑥 + 7) ° and 𝑚∠𝐶 = (2𝑥 + 34) °
- We have to find the value of x and 𝑚∠A

In the given figure,

So,

x = 9

So,

= 5(9) + 7

= 52

^{0}And,

= 2(9) + 34

= 52

^{0}Now we know that the sum of angle of triangle is 180

^{0}.So,

Maths-

### Use Substitution Property of Equality: If PQ = 10 cm , then PQ + RS =

Hint :- substitute the given value and choose the option .

Ans :- Option C

Explanation :-

If PQ = 10 cm

then PQ + RS = 10 cm + RS

∴ Option C

Ans :- Option C

Explanation :-

If PQ = 10 cm

then PQ + RS = 10 cm + RS

∴ Option C

### Use Substitution Property of Equality: If PQ = 10 cm , then PQ + RS =

Maths-General

Hint :- substitute the given value and choose the option .

Ans :- Option C

Explanation :-

If PQ = 10 cm

then PQ + RS = 10 cm + RS

∴ Option C

Ans :- Option C

Explanation :-

If PQ = 10 cm

then PQ + RS = 10 cm + RS

∴ Option C

Maths-

### Find the length of each side of the given regular dodecagon.

Solution:

Hint:

We have given a regular dodecagon with sides represented as

Since, It is regular, then all sides are equal

So,

2x - 1 = 9x + 15

7x = - 16

X can not be negative

Wrong data

Hint:

- A regular dodecagon has 12 sides equal in length and all the angles have equal measures, all the 12 vertices are equidistant from the center of dodecagon.
- A regular dodecagon is a symmetrical polygon.

- We have been given in the question figure of a regular dodecagon
- We have also been given the two sides of it that is -
- We have to find length of each side of the regular dodecagon.

We have given a regular dodecagon with sides represented as

Since, It is regular, then all sides are equal

So,

2x - 1 = 9x + 15

7x = - 16

X can not be negative

Wrong data

### Find the length of each side of the given regular dodecagon.

Maths-General

Solution:

Hint:

We have given a regular dodecagon with sides represented as

Since, It is regular, then all sides are equal

So,

2x - 1 = 9x + 15

7x = - 16

X can not be negative

Wrong data

Hint:

- A regular dodecagon has 12 sides equal in length and all the angles have equal measures, all the 12 vertices are equidistant from the center of dodecagon.
- A regular dodecagon is a symmetrical polygon.

- We have been given in the question figure of a regular dodecagon
- We have also been given the two sides of it that is -
- We have to find length of each side of the regular dodecagon.

We have given a regular dodecagon with sides represented as

Since, It is regular, then all sides are equal

So,

2x - 1 = 9x + 15

7x = - 16

X can not be negative

Wrong data

Maths-

### Draw a quadrilateral that is not regular.

Solution:

Hint:

Hint:

- A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices, and four angles.

- We have been given information in the question to draw a quadrilateral that is not regular.

### Draw a quadrilateral that is not regular.

Maths-General

Solution:

Hint:

Hint:

- A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices, and four angles.

- We have been given information in the question to draw a quadrilateral that is not regular.

Maths-

### Which of the statements is TRUE?

Explanation:

Option A:

A semicircle is a polygon.

No this is not true, because polygon only contain straight lines.

Option B:

A concave polygon is regular

It is not necessary that a concave polygon is regular.

So, it is not true

Option C:

A regular polygon is equiangular

Yes this is true, a regular polygon is equiangular and equilateral.

Option D:

Every triangle is regular

This is not true, because mant triangles are not regulat.

Hence, Option C is correct.

- We have been given four statements in the question from which we have to choose which statement is true.
- In the given four statements we have been given information about the semicircle, concave polygon, triangle and regular polygon.

Option A:

A semicircle is a polygon.

No this is not true, because polygon only contain straight lines.

Option B:

A concave polygon is regular

It is not necessary that a concave polygon is regular.

So, it is not true

Option C:

A regular polygon is equiangular

Yes this is true, a regular polygon is equiangular and equilateral.

Option D:

Every triangle is regular

This is not true, because mant triangles are not regulat.

Hence, Option C is correct.

### Which of the statements is TRUE?

Maths-General

Explanation:

Option A:

A semicircle is a polygon.

No this is not true, because polygon only contain straight lines.

Option B:

A concave polygon is regular

It is not necessary that a concave polygon is regular.

So, it is not true

Option C:

A regular polygon is equiangular

Yes this is true, a regular polygon is equiangular and equilateral.

Option D:

Every triangle is regular

This is not true, because mant triangles are not regulat.

Hence, Option C is correct.

- We have been given four statements in the question from which we have to choose which statement is true.
- In the given four statements we have been given information about the semicircle, concave polygon, triangle and regular polygon.

Option A:

A semicircle is a polygon.

No this is not true, because polygon only contain straight lines.

Option B:

A concave polygon is regular

It is not necessary that a concave polygon is regular.

So, it is not true

Option C:

A regular polygon is equiangular

Yes this is true, a regular polygon is equiangular and equilateral.

Option D:

Every triangle is regular

This is not true, because mant triangles are not regulat.

Hence, Option C is correct.

Maths-

### The length of each side of a nonagon is 8 in. Find its perimeter

Solution:

Hint:

We have length of each side of a nanagon 8in

Now the perimeter will be

9 × 8in

72in

Hence, Option C is correct.

Hint:

- A nonagon is a polygon with nine sides and nine angles which can be regular, irregular, concave or convex depending upon its sides and interior angles.

- We have been given the length of each side of a nonagon that is 8 in.
- We have to find the perimeter of the given nonagon.

We have length of each side of a nanagon 8in

Now the perimeter will be

9 × 8in

72in

Hence, Option C is correct.

### The length of each side of a nonagon is 8 in. Find its perimeter

Maths-General

Solution:

Hint:

We have length of each side of a nanagon 8in

Now the perimeter will be

9 × 8in

72in

Hence, Option C is correct.

Hint:

- A nonagon is a polygon with nine sides and nine angles which can be regular, irregular, concave or convex depending upon its sides and interior angles.

- We have been given the length of each side of a nonagon that is 8 in.
- We have to find the perimeter of the given nonagon.

We have length of each side of a nanagon 8in

Now the perimeter will be

9 × 8in

72in

Hence, Option C is correct.

Maths-

### The lengths (in inches) of two sides of a regular pentagon are represented by the expressions 4x + 7 and x + 16. Find the length of a side of the pentagon.

Solution:

Hint:

The length of the two sides of a regular pentagon is represented by x + 16; 4x + 7

Now, We know that all sides of regular polygon are equal.

So,

X + 16 = 4x + 7

3x = 16 - 7

3x = 9

x = 3

And the measure of length will be

= x + 16

= 3 + 16

= 19

Hint:

- A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.

- We have been given the two sides of a regular pentagon in the form of expressions that is -
- 4x + 7 and x + 16
- We have to find the length of a side of the pentagon.

The length of the two sides of a regular pentagon is represented by x + 16; 4x + 7

Now, We know that all sides of regular polygon are equal.

So,

X + 16 = 4x + 7

3x = 16 - 7

3x = 9

x = 3

And the measure of length will be

= x + 16

= 3 + 16

= 19

### The lengths (in inches) of two sides of a regular pentagon are represented by the expressions 4x + 7 and x + 16. Find the length of a side of the pentagon.

Maths-General

Solution:

Hint:

The length of the two sides of a regular pentagon is represented by x + 16; 4x + 7

Now, We know that all sides of regular polygon are equal.

So,

X + 16 = 4x + 7

3x = 16 - 7

3x = 9

x = 3

And the measure of length will be

= x + 16

= 3 + 16

= 19

Hint:

- A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.

- We have been given the two sides of a regular pentagon in the form of expressions that is -
- 4x + 7 and x + 16
- We have to find the length of a side of the pentagon.

The length of the two sides of a regular pentagon is represented by x + 16; 4x + 7

Now, We know that all sides of regular polygon are equal.

So,

X + 16 = 4x + 7

3x = 16 - 7

3x = 9

x = 3

And the measure of length will be

= x + 16

= 3 + 16

= 19

Maths-

### Two angles of a regular polygon are given to be Find the value of and measure of each angle.

Solution:

Hint:

We know that a regulat polygon is equiangular

So,

2x + 27 = 3x - 3

x = 27 + 3

x = 30

And the value of each angle will be

= 2x + 27

= 2(30) + 27

= 87

Hint:

- A polygon whose length of all sides is equal with equal angles at each vertex is called regular polygon.

- We have been given the two sides of a regular polygon that is - (2𝑥 + 27)° 𝑎𝑛𝑑 (3𝑥 − 3)°
- We have to find the value of x and measure of each angle.

We know that a regulat polygon is equiangular

So,

2x + 27 = 3x - 3

x = 27 + 3

x = 30

And the value of each angle will be

= 2x + 27

= 2(30) + 27

= 87

### Two angles of a regular polygon are given to be Find the value of and measure of each angle.

Maths-General

Solution:

Hint:

We know that a regulat polygon is equiangular

So,

2x + 27 = 3x - 3

x = 27 + 3

x = 30

And the value of each angle will be

= 2x + 27

= 2(30) + 27

= 87

Hint:

- A polygon whose length of all sides is equal with equal angles at each vertex is called regular polygon.

- We have been given the two sides of a regular polygon that is - (2𝑥 + 27)° 𝑎𝑛𝑑 (3𝑥 − 3)°
- We have to find the value of x and measure of each angle.

We know that a regulat polygon is equiangular

So,

2x + 27 = 3x - 3

x = 27 + 3

x = 30

And the value of each angle will be

= 2x + 27

= 2(30) + 27

= 87

Maths-

### Solve the equation. Write a reason for each step.

8(−x − 6) = −50 − 10x

Hint :- using the additive property and subtraction property ,division property on both sides .solve for x.

Ans:- x = 1

Explanation :-

Given ,8(-x − 6) = -50-10x.

By left distributive property - 8x − 48 = - 50 -10x

Adding 48 on both sides by additive property of equality both sides remain equal.

- 8x − 48 + 48 = - 50 -10x + 48

- 8x = -10x - 2

Adding 10x on both sides by additive property of equality both sides remain equal.

- 8x +10x = -10x - 2 +10x

2x = - 2

Dividing 2 by division property of equality both sides remains equal.

x = -1

∴ x = -1

Ans:- x = 1

Explanation :-

Given ,8(-x − 6) = -50-10x.

By left distributive property - 8x − 48 = - 50 -10x

Adding 48 on both sides by additive property of equality both sides remain equal.

- 8x − 48 + 48 = - 50 -10x + 48

- 8x = -10x - 2

Adding 10x on both sides by additive property of equality both sides remain equal.

- 8x +10x = -10x - 2 +10x

2x = - 2

Dividing 2 by division property of equality both sides remains equal.

x = -1

∴ x = -1

### Solve the equation. Write a reason for each step.

8(−x − 6) = −50 − 10x

Maths-General

Hint :- using the additive property and subtraction property ,division property on both sides .solve for x.

Ans:- x = 1

Explanation :-

Given ,8(-x − 6) = -50-10x.

By left distributive property - 8x − 48 = - 50 -10x

Adding 48 on both sides by additive property of equality both sides remain equal.

- 8x − 48 + 48 = - 50 -10x + 48

- 8x = -10x - 2

Adding 10x on both sides by additive property of equality both sides remain equal.

- 8x +10x = -10x - 2 +10x

2x = - 2

Dividing 2 by division property of equality both sides remains equal.

x = -1

∴ x = -1

Ans:- x = 1

Explanation :-

Given ,8(-x − 6) = -50-10x.

By left distributive property - 8x − 48 = - 50 -10x

Adding 48 on both sides by additive property of equality both sides remain equal.

- 8x − 48 + 48 = - 50 -10x + 48

- 8x = -10x - 2

Adding 10x on both sides by additive property of equality both sides remain equal.

- 8x +10x = -10x - 2 +10x

2x = - 2

Dividing 2 by division property of equality both sides remains equal.

x = -1

∴ x = -1

Maths-

### Find the measure of each angle of an equilateral triangle using base angle theorem.

Solution:

Hint:

Let a triangle be ABC

Here,

AB = AC

Using base angle theorem

And,

So,

Therefore,

Step 2 of 2:

We know that the sum of all angles of a triangle is 180

Now,

So,

Hint:

- An equilateral triangle is a triangle with all the three sides of equal length.

- We have to find the measure of each angle of an equilateral triangle using base angle theorem.

Let a triangle be ABC

Here,

AB = AC

Using base angle theorem

And,

So,

Therefore,

Step 2 of 2:

We know that the sum of all angles of a triangle is 180

^{0}.Now,

So,

### Find the measure of each angle of an equilateral triangle using base angle theorem.

Maths-General

Solution:

Hint:

Let a triangle be ABC

Here,

AB = AC

Using base angle theorem

And,

So,

Therefore,

Step 2 of 2:

We know that the sum of all angles of a triangle is 180

Now,

So,

Hint:

- An equilateral triangle is a triangle with all the three sides of equal length.

- We have to find the measure of each angle of an equilateral triangle using base angle theorem.

Let a triangle be ABC

Here,

AB = AC

Using base angle theorem

And,

So,

Therefore,

Step 2 of 2:

We know that the sum of all angles of a triangle is 180

^{0}.Now,

So,