Geometry Hexagon

Geometry Hexagon

Hexagon is the two dimensional geometric closed figure with five sides.

Geometry Hexagon interior angle:

The angle that found inside the geometric figure is said to be interior angle of the Hexagon.

Geometry Hexagon Exterior angle:

The angle between any side of the Hexagon and the line extended from the next side is said to be exterior angle of the Hexagon.

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Formula:

Formula for calculating the exterior angle of the Hexagon:

Sum of the exterior angle of the Hexagon is 360 degrees.

Formula for calculating the interior angle of the Hexagon:

Sum of Interior angle of the Hexagon = (n-2) 180 degrees

Here n is the number of the Hexagon.

Regular Hexagons:

The regular Hexagon is the geometric figure  in which all sides are equal in length and all the angles are equal in degrees.

Interior angle of the regular Hexagon is `(((n-2) 180)/n)`

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Model Problems:

1.Find the sum of interior angle and each interior angle of the regular geometry Hexagon?

Solution:

To find the sum of the interior angle:

Here

Sum of the interior angle of Hexagon = (n-2) 180 degrees

Here n = 6 sides

= (6-2) 180

= (4) 180

Sum of the interior angle of Hexagon =720 degrees.

To find the each interior angle:

Here

Interior angle of the regular Hexagon =` (((n-2) 180)/n)`

= (((6-2)180)/5)

= (720/6)

Interior angle of the regular Hexagon = 120 degrees.

2. Find sixth interior angle of the Geometry Hexagon when first five angles are 108, 110, 106, 102, 104 degrees respectively?

Solution:

We know that sum of the interior angle of the Hexagon = 720 degrees

That is (angle 1+angle2+angle 3+angle 4+angle 5 +angle 6) = 720

(108+110+106+102+104+x) = 720

(530+x) = 720

x = 720-530

Sixth interior angle of the Hexagon x = 190 degrees

3. Find first interior angle of the Geometry Hexagon when last five angles are 108, 110, 108, 106, 104 degrees respectively?

Solution:

We know that sum of the interior angle of the Hexagon = 720 degrees

That is (angle 1+angle2+angle 3+angle 4+angle 5 +angle 6) = 720

(x+108+110+108+106+104) = 720

(x+536) = 720

x = 720-536

Sixth interior angle of the Hexagon x = 184 degrees

Fractionation Method

Introduction Fraction Method:

A fraction is a value that shows the number of equal parts taken of a whole quantity or unit. The denominator of a fraction is the number that shows how many equal parts are in the whole quantity. The numerator of a fraction is the number that shows how many equal parts of the, whose are taken.

The numerator and denominator are called the term of the fraction,

3 -(Numerator)
-------------------------
4-(Denominator)

A improper fraction is a fraction in which the numerator is larger than equal to the denominator, as in 3 / 2, 5 / 4, 11 / 8. A mixed number is a number composed of a whole number and a fraction, as examples 3 7/8, 7 1/2

A complex fraction is a fraction in which one or both of the terms are fraction or mixed number, as in example ¾ / 6.

I like to share this Converting Mixed Numbers to Improper Fractions with you all through my article.

Fraction methods - Addition and Subtraction:


Steps for fraction method - addition:

To add algebraic fraction, follow these steps:

Write the given fraction and common denominator.
Added the numerators value.
Solution for the problem
Example:

`= (1 / 2) + (5 / 2)`

`= (1 + 5) / 2`

`= 6 / 2`

= 3

Steps for fraction method - subtraction:

To subtraction algebraic fraction, follow these steps:

Write the given fraction and common denominator.
Subtracted the numerators value.
Solution for the problem
Example:

` = (7 / 3) - (4 / 3)`

` = (7 - 3) / 3`

= `4 / 3`

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Fraction methods – Multiplication and Division:


Steps for fraction method - multiplication:

To multiply algebraic fraction, follow these steps:

Write the given fraction and cancel any common factors.
Multiply the numerators.
Multiply the denominators.

Example:

= `(3 / 7)xx (4 / 5)`

= `(3xx 4) / (7 xx5)`

= ` 12 / 35`

Steps for fraction method division:

To divide algebraic fraction, follow these steps:

Write the given fractions.
Change the division sign to a multiplication sign and invert the second fraction.
Write the given fraction and cancel any common factors.
Multiply the numerators.
Multiply the denominators.
Example:

= `( 1 / 6) / (3 / 4)` (divisor)

= `(1 /6)xx (4 / 3)`

=` (4 xx1) / (6xx 3)`

= `4 / 18`

= `2 / 9`

Solve One-to-one Function

Solve One-to-One Function

One-to-one function is a function, in which every element of the range of the function is corresponds to exactly one element of the domain of the function. One-to-one function is often written as 1–1 function.

Example:

Function: y = f(x) is a function, if it passes only the vertical line test.

One-to-function: y = f(x) is a one-to-one function, if it passes both the horizontal line test and the vertical line test.


Solve One-to-One Function – Example Problems


See these solved problems on one-to-one function.

Example 1: Show that the function f(x) = 4(x - 6)3 + 9 is one-to-one function.

Solution:

Let (x) = f(y)

4(x - 6)2 + 9 = 4(y - 6)3 + 9

Add -9 to both sides

4(x - 6)3 + 9 - 9 = 4(y - 6)3 + 9 - 9

4(x - 6)3 = 4(y - 6)3

Divide both sides by 4

(x - 6)3 = (y - 6)3

The above equation leads to two other equations

(x - 6) = (y - 6)

x = y

Therefore given function f(x) = 4(x - 6)2 + 9 is one-to-one function.

Example 2: Show that the rational function f(x) = `10 / (12x + 15)` is one-to-one function.

Solution:

Let f(x) = f(y)

`10 / (12x + 15)` = `10 / (12y + 15)`

Multiply both sides (12x + 15)(12y + 15) and simplify

12y + 15 = 12x + 15

Add -15 to both sides

12y = 12x

Divide both sides by 12

y = x

Therefore the given function f(x) = `10 / (12x + 15)` is one-to-one function.

Example 3: Show that the function f(x) = 15x + 18, is one-to-one function.

Solution:

Let f(x) = f(y) and show that this leads to x = y

15x + 18 = 15y + 18

Add -18 to both sides

15x = 15y

Divide both sides by 15

x = y

Therefore the given function f(x) = 15x + 18 is one-to-one.

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Solve One-to-One Function – Practice Problems


Solve these following practice problems

Problem 1: Show that the rational function f(x) = `7 / (11x + 6) ` is one-to-one function.

Problem 2: Show that the function f(x) = 5(x - 11)3 + 21 is one-to-one function.

Problem 3: Show that function f(x) = 19x + 4 is one-to-one function.

Exterior Angle Solve Online

Introduction - Exterior angle solve online:

In this article, we shall discuss about Exterior angle solve online. Online helps students to share their views as well as gather notes regarding their subject. In geometry, shapes play an important part. There are various kinds of shapes. Any plane figure which is formed at the vertex where two lines intersect are called angles. The angles formed at the outer part of each vertex are called as exterior angles. There are two methods to find the exterior angles.

Method 1:

Exterior angle = `360/n` ,

where n is the number of sides of the polygon.

Method 2:

Exterior angle = 180 - interior angle.

Now we shall solve some example problems regarding exterior angle solve online.


Example Problems - exterior angle solve online:


Example 1:

Solve for the exterior angle of a polygon whose interior angle is 108°. Also determine the number of sides of the polygon.

Solution:

Given, The interior angle of a polygon is 108°.

When the interior angle is given, the exterior angle of a polygon can be calculated by using the formula,

Exterior angle = 180 - Interior angle

Exterior angle = 180 - 108°

= 72°

The exterior angle of the polygon is 72°.

Now the number of sides of the polygon can be determined by using the formula,

Exterior angle = `360/n`

where n is the number of sides of the polygon.

We know that the exterior angle of the given polygon is 72°

72 = `360 / n`

Multiply by n on both sides,

`72 n = n[360/n]`

`72 n = 360`

Divide by 72 on both sides

`(72n) / 72 = 360/72`

`n = 5`

Therefore the number of sides of the polygon is 5.

Since n = 5, the name of the polygon is pentagon.

Example 2:

Solve for the exterior angle of a polygon whose number of sides is 8.

Solution:

When the number of sides of the polygon is given, the exterior angle can be calculated by using the formula,

Exterior angle = `360/n`

where n is the number of sides of the polygon.

By substituting n = 8 in the formula, we can obtain the exterior angle of the polygon.

Exterior angle = `360/8`

= 45°

Since n = 8, the name of the polygon is octagon.

Hence the exterior angle of octagon is 45°.

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Practice Problems - exterior angle solve online:


Problem 1:

Solve for the exterior angle of a polygon whose interior angle is 120°. Also determine the number of sides of the polygon.

Answer:

Exterior angle = 60°

Number of sides = 6

Problem 2:

Solve for the exterior angle of a polygon whose number of sides is 10.

Answer:

Exterior angle = 36°.

Third Grade Student

Introduction to Third grade student:

In this article we are going to discuss about third grade student math solving problems. Third grade student math solving problems are easy to understand and solve. The following topics are studied in the grade third.

Addition
Subtraction
Multiplication
Division
Place value
Third grade student math solving sheets examples and practice problems with solutions are given below.


Third grade student – Example problems:


Example 1:

Add the five digit numbers given 55649 + 21453

Solution:

5 5 6 4 9

2 1 4 5 3 +

-----------------

7 7 1 0 2

-----------------

The addition solution is 77102

Example 2:

Perform the subtraction of the given five digit number 81928 – 47256

Solution:

8 1 9 2 8

4 7 2 5 6 –

-------------

3 4 6 7 2

-------------

The subtracting solution is 34672

Example 3:

Add the given decimal digits given 45.35 + 21.32

Solution:

4 5.3 5

2 1.3 2 +

------------

6 6.6 7

------------

The adding decimal solution is 66.67

Example 4:

Subtract the decimal values given 78.98 – 52.65

Solution

7 8.9 8

5 2.6 5 –

---------------

2 6.3 3

----------------

The subtracting decimal solution is 26.33

Example 5:

Multiply 7.8 x 3.2

Solution:

7.8

3.2 x

-------

156

234   +

-------------

2 4.9 6

--------------

The multiplication solution is 24.96

Example 6:

Decimal multiplication: 0.07 by 1.2

Solution:

Primarily we start with 0.07 * 1.2

Multiplying without decimal points, we get 7 * 12 = 84

We place decimal places:

0.07 has the two decimal places

1.2 has one decimal place

Final answer has three decimal points are 0.084

The decimal multiplication solution is: 0.084


Third grade student – practice problems:


Problem 1: Add the given decimal digits given 75.32 + 31.58

Problem 2: Multiply 9.8 x 4.2

Problem 3: Perform the subtraction 45624 – 21983

Problem 4: Add 87123 + 12456

Problem 5: Subtract 97. 86 – 31.24

Problem 6: Decimal multiplication 0.08 * 10

Third grade student – answer key:

Problem 1: 106.90

Problem 2: 41.16

Problem 3: 23641

Problem 4: 99579

Problem 5: 66.62

Problem 6: 0.008

Solve Math Student Solutions

Introduction to solve math student solutions:

Mathematics is a vast area.Some of the main branches of mathematics are algebra, geometry, trigonometry and calculus. There are  number of math problems available under these branches for the students. In this article solve math student solutions, we are going to solve for some basic math solutions which are useful for the students. In addition, some practice problems are given to solve.

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Solved examples for math solutions:


Example 1:

Andrew bought a camera for `$` 100 and he sold it for `$` 110. Find the gain amount.

Solution:

cost price of camera  =  $ 100

selling price of camera  =  $ 110

Gain   =  selling price - cost price

=  110 - 100

=  $ 10

Example 2:

Find  the area of circle if the radius is 79 cm.

Solution:

Area of circle  =  `pi` r^2

=  3.14 (79)2

=  3.14 * 6241

=  19596.74 cm^2



Example 3:

Spears bought an ornament that costs `$` 1000. If the sales tax rate is 10%. What is the total amount she must pay for the ornament?

Solution:

Sales tax  =  10% of the price tax

=  10%  x  1000

=  0.10 x  1000

=  100

Final price  =  price before the tax + sales tax

=  1000+ 100

=  $ 1100

Example 4:

A basket contains 750 eggs. 680 were not broken. What percentage of the eggs were broken?

Solution:

Total number of eggs          =  750

Number of eggs not broken =  680

Number of eggs broken     =  750 - 680

= 70

Percentage of eggs broken   =  `<< 70/750>>`  x 100

=  `<< 7/75>>` x 100

=  9.3

Example 5:

Find the area and perimeter of rectangle, if the length is 35 m and breadth is 15 m.

Solution:

Area of rectangle  =  l * b

=  35 * 15

=  525 m^2

Perimeter of  rectangle  =  2 ( l + b )

=  2 ( 35 + 15 )

=  2 ( 50 )

=  100 m


Practice problems to solve:

1) Sarah bought a ring for `$` 1800 and she sold it for `$` 1880. Find the gain amount.

Answer: Gain =  `$` 80

2) Find  the area of circle if the radius is 16 cm.

Answer: Area =  803.84 cm^2

3) Mercy bought an ornament that costs `$` 1700. If the sales tax rate is 9%. What is the total amount she must pay for the ornament?

Answer: Amount = `$` 1853

4) A basket contains 200 eggs. 180 were not broken. What percentage of the eggs were broken?

Answer: Percentage = 10

5) Find the area and perimeter of rectangle, if the length is 28 m and breadth is 7 m.

Answer: Area = 196 m^2   Perimeter = 70 m

Student Teaching Requirements

Introduction to student teaching requirements:

Here given the student teaching requirements is the basic teaching requirements needed to students to practice as a teacher. Student teaching requirements are to make the students understand the concepts and help the students to learn in every concepts. Here for student teaching requirements we let us see problems solved by teachers for the given article student teaching requirements.


Student teaching requirements:


Basic algebra problems:

Example 1 :
What is the sum of 7 and 8? Express this statement by using place holder.
Solution :

We can write this statement, in short, as
7 + 8 = ?.

The answer for this problem would be 7 + 8 = 15.

Example 2 :
What number added to 10 will give 15?
Solution :
It is 10 + x = 15

Example 3 :
Rabi has 18 rupees. She buys vegetables for 8 rupees. Find the remaining amount she will have in her hands.
Solution :
We can write it as 18 – 8 = ?

The answer for this problem would be 18 - 8 = 10.

Example 4 :
Find the product of 5 and 12
Solution :
5 × 12 =?

The answer for this problem would be 5 × 12 = 60.

Example 5 :
When a number is multiplied by 4, the product is 116
Solution :
x × 4 = 116.

x = `116 / 4` = 29.


Student teaching requirements:


Example 6:
What is the sum of 9 and 10? Express this statement by using place holder.
Solution:

We can write this statement, in short, as
9 + 10 = ?.

The answer for this problem would be 9 + 10 = 19.

Example 7:
What number added to 12 will give 17?
Solution:
It is 12 + x = 17
The answer would be x = 17 - 12 = 5.

Example 8:
Rabi has 28 rupees. She buys vegetables for 12 rupees. Find the remaining amount she will have in her hands.
Solution:
We can write it as 28 – 12 = ?

The answer for this problem would be 28 - 12 = 16.

Example 9:
Find the product of 6 and 12
Solution:
6 × 12 =?

The answer for this problem would be 6 × 12 = 72.

Example 10:
When a number is multiplied by 4, the product is 84
Solution:
x × 4 = 84.

x = `84 / 4` = 21.