Explanation

Plane geometry has two dimensions

It deals with shapes like lines, circles, and polygons that exist on a flat plane.

Explanation

To determine the total number of fence poles used, we need to consider that each corner pole is counted twice when calculating the poles for each side.

Each side of the square plot has 27 poles.

Since the plot is square, it has 4 sides.

First, calculate the total number of poles if we didn't account for the corners:

27 poles/side×4 sides=108 poles

However, this calculation counts each corner pole twice.

A square has 4 corners, so we need to subtract the 4 extra poles that were counted twice:

108 poles−4 extra poles=104 poles

Explanation

Given:

Total pages in the book = 300

Total days to finish the book = 10

Calculate the number of pages the student should read per day:

 300 pages / 10 days = 30 pages per day

Explanation

Given:

The total of their current ages is 80 years.

Three years ago, each of them was 3 years younger, so:

Amar's age three years ago = Amar's current age - 3

Akbar's age three years ago = Akbar's current age - 3

Ali's age three years ago = Ali's current age - 3

The total of their ages three years ago would be:

(Amar ′ s current age−3)+(Akbar ′ s current age−3)+(Ali ′ current age−3)

This simplifies to:

(Amar  ′ s current age+Akbar′ s current age+Ali' s current age)−9

Since the total of their current ages is 80 years:

80−9=71

Therefore, the total of their ages three years ago was 71 years

Explanation

The range of a data set is defined as the difference between the maximum and minimum values in the data set.

It provides a measure of the spread or variability of the data.

Explanation

To find the range from a set of data, subtract the smallest value from the largest value.

Given data:

85, 87, 90, 92, 95

Smallest value: 85

Largest value: 95

Range=Largest value−Smallest value

Range=95−85

Range=10

So, the range of the data set is 10.

Explanation

Given equation: 2x + 5 = 13

Subtract 5 from both sides to isolate 2x:

2x = 13 - 5

2x = 8

Now, divide by 2 to solve for x:

x = 8 / 2

x = 4

Therefore, the solution to the equation 2x + 5 = 13 is x = 4.

Explanation

To determine the solutions of the equation 2x + 4 = 3x + 1, we need to solve for x.

Given equation: 2x + 4 = 3x + 1

Subtract 2x from both sides to isolate x:

4 = x + 1

Subtract 1 from both sides to solve for x:

x = 3

After solving for x, we find that x = 3.

This means there is one solution to the equation.

Explanation

Let Vinay’s present age be x

Then, his mother’s present age = 3x

After 5 years,

Vinay’s age = x + 5

Vinay's mother’s age = 3x + 5

Sum of Vinay and Vinay's Mother's age after 5 years = 70

⇒x + 5 + 3x + 5 = 70

⇒ 4x+10 = 70

⇒4 x = 60

⇒ x = 15

⇒ 3x45

∴Vinay’s age is 15 years and his 

mother’s age is 45 years

Explanation

To find the range of a data set, we need to determine the difference between the maximum and minimum values in the set.

Given data set of student ages: 16, 17, 18, 16, 19, 20

1. The minimum age in the data set is 16.

2. The maximum age in the data set is 20.

3. To calculate the range, we subtract the minimum age from the maximum age:

Range = 20 = 16 = 4