Words That Mean Perfect

Introduction to Words That Mean Perfect:

Words that mean perfect in math is the operation in the expression done perfect with correct procedure. Each expression has different operation and different procedure. To get the result from or to solve the expression as by the corresponding procedure, we say as the words perfect. In this article, we see about the words that mean perfect.

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Example Problem – Words that Mean Perfect:


Example 1:

What is the words that mean perfect of the expression as (x + 1)?

Solution:

Given: (x + 1)

To find:  Words that mean perfect for the expression is the result of the given expression.

(x + 1) = (1 + 1) + (2 + 1) + (3 + 1) + (4 + 1)

= 2 + 3 + 4 + 5

= 14

Thus the words that mean perfect for the expression is the result of the expression is 14

Answer: Perfect 14

Example 2:

Which of the following is the words that mean perfect form the expression 33?

Option:

a)     9

b)    27

c)     9

d)    3

Solution:

Given: Expression is 3^3

The given expression is the 3 to the power of 3. Thus the number 3 is multiply itself as three times.

Step 1: 3^3 = 3 * 3 * 3 = 27

Thus 27 is the words that mean perfect to the expression as 33. Here the perfect words that given in option as b which is said to be as correct.

Answer: Option b - - - > 27

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Example Problem – Words that Mean Perfect:


Example 3:

Which of the following expression is correct for the words that mean perfect of the number 25?

Option:

a)     5 + 5

b)    20 * 5

c)     25 – 5

d)    5 * 5

Solution:

Step 1: To find the correct expression for the perfect number 25.

Step 2: Check each option which given the words that mean perfect as 25.

Option a: 5 + 5, the sum of 5 and 5 is 10

Option b: 20 * 5, the product of 20 and 5 is 100

Option c: 25 – 5, the result of 5 is subtracted from 25 is 20

Option d: 5 * 5. the product of 5 and 5 is 25

Thus the expression given in option d gives the words that mean perfect of 25.

Answer: Option d - - - > 25

Solve Perfect Triangles

Introduction to solve perfect triangles:

Triangles are three sided polygons. They are classified into equilateral triangles, isosceles, and right angled triangles. To solve perfect triangles, they should contain equal sides and angles. Perfect triangles include equilateral and right angled triangles. In triangles, we find the area, perimeter and the angles. Now we see some problems to solve perfect triangles.


Some basic properties of triangles and problems


Area formula = `1/2(b xx h)`

Perimeter formula = (a + b + c)

Interior angle = (n – 1) 180° and

Exterior angle = 360°/n

Where,

n – Number of sides

Problems to solve perfect triangles:

Example 1:

What is the area of an equilateral triangle, if it one of the side measures 5 cm?

Solution:

We know that, the equilateral triangle has same length in all the sides.

Formula to find the area of the triangle is given by,

Area =`1/2(b xx h)`

Here it has same breadth and length.

On substituting the side value, that is 5 in the areas formula,

Area =`1/2(5 xx 5)`

= `1/2(25)`

=12.5

Thus the area of the given equilateral triangle is 12.5 cm2.

Example 2:

Find the perimeter of the right angled triangle the sides are given as 3 cm, 6 cm, and 9 cm.

Solution:

We know the formula to find the perimeter of the given triangle

Perimeter = (a + b + c)

= (3 + 6 + 9)

= 18

Therefore the perimeter of the triangle is 18 cm.

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More problems to solve perfect triangles


Example 3:

Find the interior and exterior angles for the right angled triangle.

Solution:

Formula to find Interior angle = (n – 2) 180°

Here a right angled triangle has 3 sides. So n = 3

(n – 2) 180 = (3 – 2)180

= 180

The interior angle for a right angled triangle is 180°

Now to find the exterior angle, we know the formula as

`360/n = 360/3`

= 120

Hence the exterior angle is 120°.

Example 4:

A triangle has a total perimeter of 34 cm. If two sides are given as 12 cm and 14 cm, what is the length of the third side?

Solution:

Perimeter of the triangle is (a + b + c)

We know the two side’s length as 12 and 14.

So a = 12 cm and b = 14 cm

Let the third side be c.

12 + 14 + c = 34

26 + c = 34

Subtract by 26 on both sides, we get

26 – 26 + c = 34 – 26

c = 8

Therefore the third side’s length is 8 cm.

These are some example problems to solve perfect triangles.

Definition of Perfect Square

Introduction to definition of perfect square:

The definition of perfect square is defined as the important topics in mathematics. Product of two integer gives another integer is known as the perfect square. The rational number with the square root is known as the perfect square.  For example, 16 is known as the perfect square integer, since it has 4  `xx`  4 is the two product for 16. This article shows the definition of perfect square with brief explanation and some example problems.


Explanation to definition of perfect square


The explanation given for the perfect square definition is as follows,

Trinomial and binomial functions are also written as the perfect square.
Trinomial Perfect square = x2 + 6x + 9
Trinomial Perfect square  = (x + 3)2 .
Perfect square Example:

0 , 1 , 4, 9, 16, 25, etc.

`16/36` , `16/25` are also the examples of perfect squares.


Example problems to definition of perfect square


Problem 1: Which of the following integer when added to 12 to make perfect square.

Options:

a) 2

b) 3

c) 1

d) 4

Solution:

Step 1: Given:

Number = 12

Step 2: To find:

Perfect square

Step 3: Solve:

12 + 4 = 16

16 = 42

16 = 4 `xx` 4

Therefore 4 is the integer when added to 12 to give perfect square.

Answer: Option d

Problem 2: Which of the following integer when added to 24 to make perfect square.

Options:

a) 2

b) 3

c) 1

d) 4

Solution:

Step 1: Given:

Number = 24

Step 2: To find:

Perfect square

Step 3: Solve:

24 + 1 = 25

25 = 52

16 = 5 `xx` 5

Therefore 1 is the integer when added to 24 to give perfect square.

Answer: Option c

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Practice problems to definition of perfect square


Problem 1: Which of the following integer when added to 25 to make perfect square.

Options:

a) 2

b) 1

c) 3

d) 4

Answer: Option b

Problem 2: Which of the following integer when added to 33 to make perfect square.

Options:

a) 2

b) 1

c) 3

d) 4

Answer: Option c

Perfect Square Definition

Introduction to perfect square definition:
Perfect square is defined as one of the most important topics in mathematics. Perfect square is defined as the product of integer gives the integer. Also, the perfect square is defined as the rational number with the square root. For example, 9 is called as the perfect square, since it has 3  `xx`  3 is the product terms. In this article, we are going to study about the perfect square definition in detail.

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Explanation to perfect square definition


The explanation given for the efinition of perfect square is as follows,

Perfect square can also written using the trinomial and binomials.
Perfect square trinomial = x^2 + 4x + 4
Perfect square binomial = (x + 2)^2 .
Example of perfect square:

0 , 1 , 4, 9, 16, 25, etc.

`9/16` , `16/25` are also known as the perfect squares.


Example problems to perfect square definition


Problem 1: Find the integer which the number 17 as the perfect square.

Options:

a) 2

b) 3

c) 1

d) 4

Solution:

Step 1: Given:

Number = 17

Step 2: To find:

Perfect square

Step 3: Solve:

17 - 1 = 16

16 = 42

16 = 4 `xx` 4

Therefore 1 is the number which makes 17 as the perfect square.

Answer: Option c

Problem 2: Find the integer which the number 27 as the perfect square.

Options:

a) 2

b) 3

c) 1

d) 4

Solution:

Step 1: Given:

Number = 27

Step 2: To find:

Perfect square

Step 3: Solve:

27 - 2 = 25

25 = 52

125 = 5 `xx` 5

Therefore 2 is the number which makes 27 as the perfect square.

Answer: Option a

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Practice problems to perfect square definition


Problem 1: Find the integer which the number 19 as the perfect square.

Options:

a) 2

b) 3

c) 1

d) 4

Answer: Option b

Problem 2: Find the integer which the number 29 as the perfect square.

Options:

a) 2

b) 3

c) 1

d) 4

Answer: Option d

Perfect Square Formula

Introduction to the perfect square formula :
In the mathematics, the perfect square is sometimes known as a square number. The perfect square is the integer square or also represented as the perfect square is the product of some of the integer with itself. The perfect square numbers are only the positive numbers not having the negative numbers. The positive values are not having perfect square divisors except only one is known as square free.



Formula for perfect square formula :


The regular notation for the perfect square formula is the perfect square of the number n not the n x n that is not the product of the number n.The model of square can be used to number systems.

Explanation of the perfect square formula:

In the arithmetic we have the following perfect squares like,`1^2=1,2^2=4,3^2=9,..`

In this way we can able to make the perfect square in the algebra. It is explained in the following ways, take the expansion of `(a+b)^2`

`(a+b)^2=(a+b)(a+b)=a(a+b)+b(a+b)=a^2 +ab+ba+b^2=a^2+b^2+2ab`

`a^2+b^2+2ab` it is the perfect square formula of the (a+b).

the expansion of `(a-b)^2`

`(a-b)^2=(a-b)(a-b)=a(a-b)-b(a-b)=a^2-ab-ba+b^2=a^2+b^2-2ab`

`a^2+b^2-2ab` it is the perfect square formula of the ( a-b).

Geometrical representation:

Consider the square of a side (a + b) units .

Area of the square `=(side)^2=(a+b)^2`

Area of the square is same as the areas of the four rectangles.so it can be written as,

Area of the square `= a^2+ab+ab+b^2=a^2+2ab+b^2.`

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Example 1 for the perfect square formula:


To solve the following `(x+5)^2`

Solution:

Given,

`(x+5)^2 =(x+5)(x+5)=x(x+5)+5(x+5)=x^2+5x+5x+25=x^2+10x+25.`

The result of the equation is `x^2+10x+25.`

Example 2 for the perfect square formula:

To solve the following `(a+2)^2`

Solution:

Given,

`(a+2)^2 =(a+2)(a+2)=a(a+2)+2(a+2)=a^2+2a+2a+4=a^2+4a+4.`

The result of the equation is` a^2+4a+4.`

Example 3 for the perfect square formula:

To solve the following `(a-2)^2`

Solution:

Given,

`(a-2)^2 =(a-2)(a-2)=a(a-2)-2(a-2)=a^2-2a-2a+4=a^2-4a+4.`

The result of the equation is` a^2-4a+4.`

Learn Basic Mathematics Tutoring

Introduction to learn basic mathematics tutoring

Mathematics is used throughout the world in many fields like, engineering, science, and medicine. Tutoring means receiving instruction or help from tutor. Through tutoring students can get more help. Tutors explain every concept in step by step so that student cans easily learning and understands the concept. In basic math the students can receive first level of math education. In this article we shall learn basic mathematics tutoring example problems. Is this topic 6th grade math test prep hard for you? Watch out for my coming posts.


Learn basic mathematics tutoring example problems


Example:

Express 3678 g in to kilograms

Solution:

1000 g = 1 kg

Hence `3678/1000`

= 3.678 kg

Note:

3678 g = 3000 g + 600 g + 70 g + 8 g

= 3 × 1000 g + 6 × 100 g + 7 × 10 g + 8 g

= 3 × 1 kg + 6 × 1 hg + 7 × 1 dag + 8 g

= 3 kg + 6 hg + 7 dag + 8 g

Example:

Solving the equation 6x – 45 = 2x + 3

Solution:

6x – 45 = 2x + 3

6x = 2x + 3 + 45

6x – 2x = 48

4x = 48

x = 48 x` 1/4`

Therefore x = 12

Example:

A book is bought `$` 120 and sells it profit at a rate of 10% find the selling price of the book.

Solution:

Profit    = 10 % of `$ ` 120

= `10/100` x 120 = 12

Selling price      = cost price + profit

= 120 + 12

The selling price is` $` 132

Example:

The area of the triangle is 1600m2. The triangle base field is 40 m. find the height of the triangle.

Solution:

Given Area of the triangle, A     = 1600m2

Base of the triangle = 40 m

Height of the triangle =?

Area of triangle formula = `1/2 ` b x h

`1/2` x (40) x h =1600

20 x h   = 1600

h          = `1600/20`

Therefore the height of the triangle field = 80 m

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Learn basic mathematics tutoring practice problems


Problem:

Solving the equation 7x – 53 = 2x + 2

Answer:

x = 11

Problem:

The area of the triangle is 1400m2. The triangle base field is 40 m. find the height of the triangle.

Answer:

Height of the triangle field = 80 m

Problem:

A book is bought `$` 180 and sells it profit at a rate of 10% find the selling price of the book.

Answer:

The selling price is` $ ` 198

Prepare for Learn Mathematics

Introduction to prepare for learn mathematics:

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. In this article we shall prepare for learn mathematics problems. (Source: Wikipedia)


Prepare for learn mathematics with example problem


Here we are going to prepare for learn mathematics example problem with detailed solutions.

Example:

A marked of the land price is `$` 7500. The land owner decides to give 6% discount on the original price of the land. What is the selling price of the land?

Solution:

Marked price of the land             =          `$` 7500

Rate of discount                        =          6%

Actual discount amount =          7500x` 6/100`

=          `$` 450

=          7500 – 450

=          `$` 7050

Selling price of the land =          marked price of the land – discount price of the land

=          7500 – 450

=          7050

Therefore the selling price of land is `$` 7050.

Example:

Joes deposited at a bank `$` 9000. The bank paid simple interest on deposit amount and credited yearly at the 6% rate of interest per annum. Find the total money she gets at the end of 5th years.

Solution:

Formula for simple interest = `(PNR)/(100)`

Present amount P = `$` 9000

Rate of interest year r = 6%

Total number of year = 5

A = `(9000*5*6)/(100)`

Interest = 2700

Total amount = Deposit amount + Interest

= `$` 9000 + `$` 2700

= `$` 11700


Prepare for learn mathematics with practice problem


Problem:

A marked of the land price is `$` 2500. The land owner decides to give 7% discount on the original price of the land. What is the selling price of the land?

Answer:

The selling price of land is `$` 2325.

Problem:

Joes deposited at a bank` $` 8000. The bank paid simple interest on deposit amount and credited yearly at the 8% rate of interest per annum. Find the total money she gets at the end of 5th years.

Answer:

`$` 11200