Help on acute angle

Names of angles:
In this lesson let me help you on acute angle. An angle is the formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide with the other (“Measuring angles").

Name of Angles Types:
1) Acute angle.
2) Right angle.
3) Obtuse angle.
4) Straight angle.
5) Reflex angle.
6) Adjacent angles.
7) Vertical angles.
8) Complementary angles.

This could also help us on factor by grouping.

Acute Angle:
An acute angle is any angle whose measure is less than 90 degree.








I hope this exaplanation is very easy for you to understand. Keep reading may be in the next session let me help you on Fractions Calculator

Introduction to Circumference Formula

Introduction to Circumference Formula:

In this section let me help you on formula for circumference of a circle.The distance around the circle is Circumference. In a circle, the distance from center to any point of a circle is called radius. And the line which touches two points of the circle and passes through the center is known as Diameter of a circle

Formula to Find the Circumference of a Circle

The formula to find the Circumference of a Circle with Diameter is

C=Pi*d

Which means the circumference of a circle is pi times the diameter.

Where, d=Diameter of a circle and

Pi=3.142 which is a constant value.This could also help us on Pythagorean identities.

How to use a Protractor?

Introduction- how to use a protractor to measure angles:

In this lesson let me help you on how to use a protractor?In geometry, a protractor is a circular or semicircular tool for measuring an angle or a circle. The units of measurement utilized are usually degrees.

Some protractors are simple half-discs; these have existed since ancient times. More advanced protractors, such as the Bevel Protractor have one or two swinging arms, which can be used to help measure the angle.
Concept- How to Use a Protractor to Measure Angles:

The two most common units of angular measurement are the angle and the radian. This could also help us on radius of curvature

The angle (°) is the unit familiar to lay people. One angle (1°) is [1 / 360] of a full circle. This means that 90o represents a quarter circle,180° represents a half circle,270° represents three-quarters of a circle, and 360° represents a full circle.

Definition on Polygon

Introduction to polygon

In this section let me help you on polygon definition.

Definition of Polygon:

A polygon is a closed plane figure formed by three or more sides. It has equal number of sides and vertices. Word Polygon is basically from Latin - Greek polugōnon means figure with many angles. In simple words, a closed two dimensional figure having three or more straight sides is a polygon. Exactly two sides meet at every vertex.

Example: Below is the figure of four sided polygon:

A polygon with all sides equal and all interior angles equal is called as Regular polygon, otherwise it is irregular. Specific polygons are named according to the number of sides, such as triangle, pentagon, etc.. this can also help us on vertices definition

Internal angles :-

A regular polygon is a polygon which has all the sides equal and all the angles equal. Regular polygons may be convex or Complex polygon. A regular n-sided polygon has rotational symmetry of order n. All vertices of a regular polygon lie on a common circle (the circumscribed circle), i.e., they are concyclic points.Also, a regular polygon can have an inscribed circle or incircle.

Note on Prime Factorization Calculator

Introduction to prime factorization calculator

Dear readers let me help you on prime factorization calculator.A prime number is a natural number that can be only divided by 2 numbers: 1 and itself. For example 1, 3, 5, 11, 13, 17 etc. Numbers that are divisible by other numbers are no prime numbers such as 4 (4=2*2), 6 (6=2*3), and 4 (8=2*4).

A prime factor is a prime number by which a given number is divisible. For example the prime factors of 6 are 2 and 3. Prime factorization is the process of finding a list of prime factors for a number.To write in short each factor which is repeated can be written in exponent form

Example:

Prime factorization of a few numbers is shown below: This will also help us on interval notation

24 =2 x 2 x 2 x 3= 23 x 3

72= 2 x 2 x 2 x 3 x 3 = 23 x 32

98=2 x 7 x 7= 2 x 72

A prime factorization calculator is a calculator which takes a number as an input and gives the list of prime factorization as its output.

There are various methods of finding prime factorization manually. The most commonly used are;Short Division Method and Factoral trees method.

Note on adding radicals

Introduction to learn adding radicals:

Adding Radicals are defined as the terms which are having the root. The roots present in the radicals are having either square root or cubic root or any other root. There are three terms present in the expression of radicals. One of them is radical symbol, another one is index and another one is called as the radicand. Example: 3√9 is known as the radical expression.

Explanation for Learn Adding Radicals

The explanation for learn adding radical are given in the following,This will also help us on Online pre algebra equations
* The expression of radicals consists of the number terms and the variables terms.
* Most of the arithmetic operations are done in the expression of radicals.
* If suppose the expression of radicals are having the square roots then we have to raise the power of even to the number.
* If suppose the expression of radicals are having the cubic roots then we have to raise the power of odd to the number.

Linear Equations in Two Variables

Linear Equation in two variables -
Linear Equations in Two Variables is a course that discusses about equations limited to linear equations in one variable. Linear equations which have two variables are common, and the solution involves extending some of the procedures which have already been introduced. A linear equation of two variables is of the form ax + by = c, where a is not equal to 0 and b is not equal to 0

Solution of the linear Equation -
Below are the sample solution of the linear Equation thus will also help us on how to graph linear equations
Problem - Find four different solutions of the equation x + 2y = 6.

Solution - By inspection, x = 2, y = 2 is a solution because for x = 2, y = 2
x + 2y = 2 + 4 = 6
Now, let us choose x = 0. With this value of x, the given equation reduces to 2y = 6 which has the unique solution y = 3. So x = 0, y = 3 is also a solution of x + 2y = 6. Similarly, taking y = 0, the given equation reduces to x = 6. So, x = 6, y = 0 is a solution of x + 2y = 6 as well. Finally, let us take y = 1. The given equation now reduces to x + 2 = 6, whose solution is given by x = 4. Therefore, (4, 1) is also a solution of the given equation. So four of the infinitely many solutions of the given equation are: (2, 2), (0, 3), (6, 0) and (4, 1).

Remark : Note that an easy way of getting a solution is to take x = 0 and get the corresponding value of y. Similarly, we can put y = 0 and obtain the corresponding value of x.

Help on Adding and Subtracting Radicals

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Let me help you in understanding adding and subtracting radicals.

Introduction for adding and subtracting radicals:

Radicals are the inverse operations of an exponent. A radical is an expression that conveys the square roots, cube roots etc.

Solving the Adding and Subtracting Radicals:

Example 1: Adding and subtracting radicals for the following equation: √36+ √25

Solution:

The above radicals can be added by simplification. Since the √36 is 6 and √25 is 5, it can be added easily now.

Now √36+ √25 = 6 + 5 = 11 is the answer.

Now subtraction is also a simple way.

√36 - √25 = 6 - 5 = 1 is the answer.

The radical expression can also solve like the above case. If we have a variable within the root then we can solve the variable online by destruction the root of the variable.

Example 2: solve the adding and subtracting radicals for the following equation: √ x = 6

Solution:

Squaring on equally sides we find (√ x)² = (6)²

x = 36.

Definition of Polygon

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Introduction to polygon:

Definition of Polygon can be explained in this way. A polygon is a closed plane figure formed by three or more sides. It has equal number of sides and vertices. Word Polygon is basically from Latin - Greek polugōnon means figure with many angles. In simple words, a closed two dimensional figure having three or more straight sides is a polygon. Exactly two sides meet at every vertex.

In simple term we can say as A simple closed figure bounded by three or more line segments is called a polygon. The line segments forming the polygon are called its sides. Polygons are named according to the number of sides they possess.

Adjacent sides of a polygon:

If two sides of a polygon have a common end point, then these sides are called the adjacent sides of the polygon

Number of triangles contained in a polygon:

A polygon of n sides can be divided into (n – 2) triangles.

Thus a polygon of 5 sides contains (5-2) = 3 triangles.

Angles of a polygon:

Consider a polygon ABCDE, when one of its side CD is extended, two angles are formed, one inside the polygon and another outside the polygon.

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Coin Word Problems Algebra

As we are studying more on algebra. let me also show you the importance of algebra with coin word problems algebra.

Introduction to Algebra:-

Algebra is the most important branch of the mathematics which concerns the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with the geometry and analysis, topology also the combinatory, and number theory, algebra is one of the main branches of pure mathematics

Algebra coin word problem:-

Let me also help you go through with the sample problems on algebra coin word problems.

Problem-

A Box contains the equal number of nickel, dime and pennies. The coins total $3.36. How many of every kind of coin does the boxhold?

Solution:

While there is the equal number of every kind of coin, here we use only one variable to place for each;

Number of nickels: n

Number of dimes: n
Number of pennies: n

The cost of the coins is the amount of cents for every coin times the number of that kind of coin, so

Cost of nickels: 5n
Cost of dimes: 10n
Cost of pennies: 1n

The sum of value is $ 3.36, so we will add the above set of value and equal to 336 cents, then solve to find the value of n,

5n +10n+1n = 336
16n = 336
n = 21

So there is 21 of every kind of coin the box.

Using Positive Exponents

Positive Exponents

Repeated multiplication can easily be represented by using exponential notation. The exponent is also called as power or index. When we say 3⁵, the base is 3 and the index is 5. The index tells us how many times the base must be multiplied. Here, the base 3 must be multiplied 5 times. That is

3⁵ = 3 × 3 × 3 × 3 × 3

In general, x^m indicates that x is repeatedly multiplied m times.

x^m = x • x • x •……. m times

All the Rules of Exponents apply to the Positive exponents. For any real number a and positive integers m and n

a) a^m × aⁿ = a^m+n

b) a^m ÷ aⁿ = a^m-n

c) (a^m)ⁿ = a^mn

d) (ab)^m = a^mb^m

e) (a/b)^m = a^m/b^m

Simplification of numbers with Positive Exponents

It is important to be able to simplify the arithmetic expressions with positive exponents.

(7³× 7²) / 7 = 7³⁺² / 7

= 7⁵/7

= 7^5-1

= 7⁴

Simplification of variables and Polynomials with Positive Exponents

The Rules of Exponents will work for the Variables and Polynomials as well! We can use the same rules effectively to simplify the polynomials. For example,

(x² × y³)⁴ = (x²)⁴(y³)⁴ Using (ab)^m = a^mb^m

= x⁸y¹² Using (a^m)ⁿ = a^mn

Sometimes we have to use the FOIL method to simplify the polynomial with exponents.

(x² + y³)² = (x² + y³) (x² + y³)

To simplify further we have to use FOIL method.

(x² + y³) (x² + y³) = x² • x² + y³ • x² + x² • y³ + y³ • y³

= x⁴ + 2x²y³ + y⁶ We have used, a^m • aⁿ = a^m+n

Note: (x² + y³)² ≠ (x²)²(y³)²