acute triangle problems

In this blog we will see how to solve acute triangle problems,

Example 2:

solve the example how to Identify the type of triangles?

The angles are

(a) 30° - 40° - 80°,

(b) 75° - 55° - 70°,

(c) 40° - 59° - 80°,this is an example of acute triangle problems

Solution:

(a) 30° - 40° - 80°,

following triangle is an acute triangle. all of the angles is below 90°.

(b) 75° - 55° - 70°,

following triangle is an acute triangle. all of the angles is below 90°.

(c) 40° - 59° - 80°,

following triangle is an acute triangle. all of the angles is below 90°.In the next blog we will learn about what is diameter of a circle, and standard form.

Hope you like the above example of acute triangle problems,please leave your comments if you have any doubts.

how to divide numbers

In this blog we will see an example of how to divide numbers,

How to divide, Division is the arithmetic operation one among 4 arithmetic operations and it is the inverse of multiplication.a divided by b equals c, written: a/b = c Its dented by (÷) or / Where: a is called the dividend, b the divisor c the quotient

Properties
1. Helps to solve many mathematical problems.
2. Concept of division is almost use in all parts of mathematics like derivatives, limits etc.
3. Division of matrices can be denoted as A/B = AB - 1
4. Division by zero is not defined.
5. Division by 1 will give answer dividend

How to divide

Example: How to divide 3 by 6?

Given: 3 divided by 6
Mode of operations: Division
3/6=1/2.

In the coming blog we will learn about how to divide fractions and statistics.

Hope you like the above example of how to divide numbers,please leave your comments if you have any doubts.

how to factor trinomials

In this blog we will learn about how to factor trinomials,we can understand this with the help of an example,

Factor trinomial calculator Method 1:

If the coefficient of x² is one. That is a=1.

x²+bx+c=(x-r₁)(x-r₂), In this r₁ and r₂ are the roots of the trinomial equation

(x - r₁) and (x - r₂) are the factors of the trinomial.

Example Problems:

The following problem will help you understand the factoring trinomial calculator method 1.

Example 1:

Find the factors of the following trinomial. x²- 10 x +16

Solution:

16 (product)

/ \

- 8 - 2

\ /

-10 (sum)

x²- 10 x +16 = x² - 2x - 8x +16

= x ( x-2 ) - 8( x-2 )

= ( x - 8 ) ( x - 2 )

So the factors of the given trinomial is (x-8) and (x-2).In the next blog we will learn about monomials and area of cirlce.

Hope you like the above example of how to factor trinomials,please leave your comments if you have any doubts.

Bar Graphs

Let us now learn about bar graphs,A bar chart or bar graph is a chart which represents blocks or some pic that depicts bars,these bars may even be plotted horizontally.Bar charts are used for plotting discrete (or 'discontinuous') information i.e. information which has discrete values and is not continuous. Some examples of discontinuous information include 'shoe size' or 'eye color', for which you would use a bar chart. In contrast, some examples of continuous information would be 'height' or 'weight'. A bar chart is useful in case you are trying to record sure information whether it is continuous or not continuous information.Let us now look at a bar graph examples,In the next blog we will learn about surd.
Hope you like the above example of Bar Graphs,please leave your comments if you have any doubts.

trigonometric identity

In arithmetic, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables (see Identity (arithmetic)). Geometrically, these are identities involving definite functions of one or more angles. These are different from triangle identities, which are identities involving both angles and side lengths of a triangle. Only the former are covered in this editorial.This is a simple explanation of a trigonometric identity.
These identities are useful whenever expressions involving trigonometric functions require to be simplified.Now let us see decimal division.
In math decimal division , the basic & the standard division type is Long division.Using long division they can divide numbers with complex or multi-complex digit numbers.In the next blog we will learn about fractions.Hope you like the above example of trigonometric identity,please leave your comments if you have any doubts.

Linear programming examples

Let us now learn about Linear programming examples,solve the following linear programming problem graphically. Minimize z = 200x +500 y

subject to the constraints given as x + 2y ≥ 50

3x + 4y ≤ 90

x ≥ 0, y ≥ 0

Solution:

In the figure, the feasible region OABC is bounded. It is indicated as the shaded region in the following figure. This is the feasible region which is determined by the system of constraints given. Therefore, to find out the maximum value of z, we can use corner point method.

The corner point coordinates of O, A, B and C are (0, 5), (4, 3) and (0, 6) respectively. The next step is to calculate z value at each corner point.The standard form of the linear programming problem is used to develop the procedure for solving a general linear programming problems.

A general LPP is of the form
Max (or min) Z = c₁x₁ + c₂x₂ + … +c_nx_n
x₁, x₂, ....x_n are called decision variable.In the next blog we will learn about statistics,hope you like the above example of Linear programming examples,please leave your comments if you have any doubts.

maths symbols

Maths symbols is a very commonly heard and commonly used phrase, math symbol denoting the “and” is ^. For example p ^ q, we have used in logic truth tables. It is one of the logical operator and it can be denoted as AND or &. Also we are using in the fuzzy logic and contradictory to their functions.

Now let us learn about line plot:

The definition of Line Plot is,it is a frequency of data and it is known as graph, this shows frequency the length of the number line. It is said to be very easy and fastest way to organize the data.In the next blog let us learn about parallelogram definition.

Hope you like the above example of maths symbols. Please leave your comments if you have any doubts.

8th grade math problems

We have discussed about 8th grade math problems in the previous blogs,in this grade we usually cover topics like Pre-Algebra, Algebra I, or Geometry.We can see one example of a 8th grade math problem given below,

Solve: 16(s – 4) – 26s - 21 = 9(s + 8)

Solution:

Given expression is,

16(s – 4) – 26s - 21 = 9(s + 8)

Multiplying the integer terms

16s - 64 – 26s - 21 = 9s + 72

Grouping the above terms

-10s - 85 = 9s + 72

Add 8 on both sides

-10s + 85 – 85 = 9s + 72 + 85

Grouping the above terms

-10s = 9s + 157

Subtract 9s by on both sides

-10s – 9s = 9s + 157 – 9s

Grouping the above terms

-19s = 157

Divide -4 on both sides

s = -157/19

Answer: s = -157/19.Usually we face many signs while solving problems like multiplication signs,divide symbol,

In the coming blogs we will learn about types of lines, hope you like the example of 8th grade math problems,please leave your comments if you have abny doubts.

equivalent fractions calculator

Let us learn about equivalent fractions calculator Equivalent fractions calculator is a fraction which may look different but it values will be same when we reduce.To simplifying a fraction here both numerator and denominator must be divided by the same number. In a equivalent fractions calculator we have to canceling down or reducing the fraction.

Let us now discuss about integrated algebra, Integrated algebra help introduces the student to help the fundamental concepts of integrated algebra. Topics in integrated algebra help consists of the following types of faces and equations: linear, rational, and radical. Other topics covered include exponents, functions and factoring.

In the coming blogs we will learn about fraction simplifier,hope you like the above example of equivalent fractions calculator,please leave your comments if you have any doubts.

Inverse Variation

Let us learn about inverse variation in this blog,in algebra,the two main types of variation are direct variation and inverse variation.Inverse variation: If x and y are variables, then y is inversely proportional to x, that is one of the variables is reciprocal of the other such that there is a constant k exists. (k is not equal to zero).Now we know what are variations next blog we will learn about define standard deviation,and the exact definition.Hope you like the above example of inverse variation.Please leave ur comments if you have any doubts.

Linear Algebra Tutorial

We have learnt a lot about Linear algebra,one other way to learn about this is to get linear algebra tutorial,there are many ways to learn about the various topics that mathematics and algebra has to offer,hands on equations and various other number problems.Hope you like the example of linear algebra tutorial,please leave your comments if you have any doubts.

Division Algorithm

Division Algorithm:In this blog we will learn about division algorithm,the division algorithm is the theorem that accurately expresses the output of the division process of integers. The theorem has integers as the quotient q and remainder r that are exist and it has the unique a and divisor d, with d ≠ 0.That was an example of a division algorithm, these are some of the answer key math.in math, answer keys are provided for the set of problems in order to refer whether the solution we obtained is correct or not.Hope you like the above example of division algorithm,please leave your comments if you have any doubts.

What are rational numbers

In this blog let us see What are rational numbers:Any number which can be expressed in the form a/b is called as a rational number where a and b are non zero integers. Since b can be any integer, it can even be 1. So all the integers are rational numbers.Now let us see what is a whole number.The normal integer is called as whole number. It is refer the positive integer. Each whole number proceeds with all operations.Hope you like the above example of What are rational numbers.Please leave your comments, if you have any doubts.

What is Trigonometry

What is Trigonometry:Let us learn about what is Trigonometry,Trigonometry (from Greek trigōnon "triangle" + metron "measure") is a branch of mathematics that studies triangles, particularly right triangles.Trigonometry deals with relationships between the sides and the angles of triangles, and with trigonometric functions, which describe those relationships and angles in general, and the motion of waves such as sound and light waves.Once we understand the meaning of Trigonometry we can also learn about trigonometric equations.Hope you like the above example of What is Trigonometry.Please leave your comments, if you have any doubts.

Area of a Rectangle Formula

Area of a Rectangle Formula:Let us learn about the Area of a Rectangle Formula.Rectangle is a four sided plane surface area whose opposite sides are equal point and parallel point and every angle is a right angle. Area of the rectangle can be found by multiplied the base and height. Area of rectangle = length x breadth.To find the area of a region for enclosed plane figure, we have to draw a figure and write an appropriate formula. Then substitute the given values, and calculate the required area.Now we can understand the meaning of triangle rectangle.Rectangular is one type of polygon,whereas Triangle It has tree sides.The sum interior angle of equilateral triangle is 180 degree each angle is 60 degree.Hope you like the above example of Area of a Rectangle Formula.Please leave your comments, if you have any doubts.

Perpendicular bisector

In geometry, two lines or planes (or a line and a plane), are considered perpendicular (ororthogonal) to each other if they form congruent adjacent angles (a T-shape).

Perpendicular Definition: Perpendicular means "at right angles". A line meeting another at a right angle, or 90° is said to be perpendicular to it. It is possible to draw a perpendicular to a line without any measurement using just a compass and straightedge using techniques developed thousands of years ago by the Greeks.

In general, 'to bisect' something means to cut it into two equal parts. The 'bisector' is the thing doing the cutting. With a perpendicular bisector, the bisector always crosses the line segment at right angles (90°).We also use many calculators to solve many problems at times.One of these many calculators is hypotenuse calculator. Hope you like the above example of Perpendicular Bisector. Please leave your comments, if you have any doubts.

Formula for circumference of a circle

Formula for circumference of a circle:Let us learn the Formula for circumference of a circle, The formula to find the Circumference Cof a circle is

C=2*Pi*r

Which means Circumference of a circle is 2 times the value of pi times r

Where, r = radius of a circle and

Pi=3.142 which is a constant value.We can learn about the perimeter of a circle,in the blogs that we will publish in the future.Hope you like the above example of Formula for circumference of a circle.Please leave your comments, if you have any doubts.

6 sided shape

6 sided shape:One of the most common examples of a 6 sided shape is our very own "DICE".A die (plural dice, from Old French dé, from Latin datum "something given is a small polyhedral object, usually cubic, used for generating random numbers or other symbols. This makes dice suitable as gambling devices, especially for craps or sic bo, or for use in non-gambling tabletop games.A traditional die is a cube (often with corners slightly rounded), marked on each of its six faces with a different number of circular patches or pits called pips. us next learn about the 7 sided polygon,In geometry a polygon (pronounced /ˈpɒlɪɡɒn/) is traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners. An n-gon is a polygon with n sides. The interior of the polygon is sometimes called its body. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions.Hope you like the above example of 6 sided shape.Please leave your comments, if you have any doubts.

Area of the Quadrilateral

Area of the Quadrilateral: In quadrilateral the opposite sides are equal lengths; the opposite angles are equal; or that the diagonals bisect each other.In ABCD quadrilateral diagonal is a straight line joining two alter AC and DB are the diagonals.Areas of quadrilateral is measured in terms of square units such as square inches,squarefeet or square meters.Now let us look at area of a quadrilateral problems.area of a quadrilateral problems, Areas of quadrilaterals = √{(s-a)(s-b)(s-c)(s-d) -1/4(ac+bd+pq)(ac+bd-pq)}, where a,b,c and d are the four sides of the quadrilateral, p and q are diagonals, and s = (a+b+c+d)/2.Let us now calculate the area of a quadrilateral.


You can achieve the same result with this formula:

Areas of a quadrilateral Problem = √{(s-a)(s-b)(s-c)(s-d)-abcd(cos square theta)}

where theta = 1/2 (sum of two opposite angles)

Another method:

The area of quadrilateral ABCD = 1/2Area of ABD +1/2 area of BDC

= ½ x base x altitude + ½ x base x altitude

= 1/2d ( h1 + h2)

Hope you like the above example of Area of the Quadrilateral.Please leave your comments, if you have any doubts.

Least Common Multiple

Least Common Multiple:In arithmetic number of theory is the least common multiple or lowest common multiple (LCM) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple of both of a and of b. Since it was a multiple, it can be divided by a and b without a reminder. If either a or b is 0, so that number is no such positive integer, then LCM(a, b) is defined to be zero.Let us understand the L.C.M with an example.Example 1:Find lowest common multiple for the number 24 and 34.

On finding the LCM we have to find the prime factors for the given number.

24 : 2 2 2 3

34 : 2 17

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

LCM : 2 2 2 3 17

Lowest common multiple for the numbers 24 and 34 is 2 * 2 * 2 * 3 * 17 = 408.In this blog a simple explanation is given about math least common multiple-L.C.M.Hope you like the above example of Lower Common Multiple.Please leave your comments, if you have any doubts.

Distance formula

Distance formula:Find the distance between the following pair of points:

A (1,2) and B (4,5).
Suggested answer:

Using the distance formula,

The next important thing that we will learn is Distance Formula Math:
* The distance method can be obtained by generate a triangle and with the Pythagorean Theorem to locate the length of the hypotenuse.
* The hypotenuse of the triangle will be the distance connecting the double points.
* The subscripts refer to the original and next points; it doesn't material which points you call original or next.

Let us now see Formula of Distance :

Distance = [sqrt((y2-y1)^2 + (x2 -x1)^2))]

Here (x1, y1) and (x2, y2) are the end points of the line segment. We need to find the distance the two points.Hope you like the above example of Complex Numbers.Please leave your comments, if you have any doubts.

Sets and relations

Sets and relations:

Introduction about sets and relations:

A group of elements is called a set when the elements in the group are distinct. A characteristic of two objects is called Relation
.
Example of a Set:

• The collection of all natural numbers
• The collection of all equilateral triangles in a plane.

Let us learn more about sets and relations in this chapter.

A relation is a set of ordered pairs(x,y) , where the first component of the ordered pairs are the input values and the second component are the output values.

Set of all Input Values is known as Domain of the given Relation.

Similarly, set of all Output Values is known as Range of the given Relation.

Mathematically,

A relation R defined by ( , {(x,y):x }) ,is the set of ordered pairs of all Input Values (x) and all Output Values(y) such that each element x is related to the corresponding element y.

Here,

x=Domain of the Relation and

y=Range of the Relation

iff no values of x and y is repeated.

x is called Independent variable and y is called Dependent variable because its value depends on the x-value chosen.The most commonly asked question is how do we express a relation,we come across this question very frequently. Relation scan be represented in any of the following forms:-

(i) Roster form

This method is also known as Tabular method. In this method, a set is represented by writing all the elements of the set, separated by commas and are enclosed withinbrackets { }.

For e.g. D = {Sunday, Monday, Tuesday,, Wednesday, Thursday, Saturday}.

Lets take some examples to show the relation in various forms:-

(ii) Set builder form Set builder notation has the form {x : f(x)} (some write {x | f(x)}, using the vertical bar instead of the colon), denoting the set of all individuals in the universe of discourse satisfying the formula f(x), that is, the set whose members are every individual x such that f(x) is true.For e.g. is the set of all positive real numbers.

(iii) By tables

Table representation of the RelationInputOutputa3c2e9
(iv) Arrow diagram :-

(v) By graphs:-

Hope you like the above example of Sets and Relations. .Please leave your comments, if you have any doubts.

Laws of Exponent

Laws of Exponent:

Introduction to Exponents:

Exponent is a math function symbolize by 2 parts ,

is the base.
is the exponent.

The exponent says the number of times the base must be multiplied by it self, Exponent is the part of algebra and they have defined properties, with the help of it we can simplify the given exponent expressions.

Now lets see the laws of exponents.

The laws of exponents are used for combining exponents of numbers. Exponents is a number raised to another number, it is denoted as, a ⁿ, here, n is known as the exponent of the nth power of a.

Pythagoras Theorem

Pythagoras Theorem:

The Pythagoras Theorem is the theorem which is developed by a Greek mathematician named Pythagoras, for finding the sides of any right angle triangle. It is also used to verify the triangle is Right angle triangle or not. According to him, the sum of square of two smaller sides is equal to the square of largest side. It is given by the formulae,

According to Pythagorean Theorem: c² = a² + b².

The longest side of a right angle triangle is always directly across from the 90 degree angle is the hypotenuse. The other two sides are called as legs.

Students may have heard of the Pythagoras Theorem and the problems related to the theorem, but are uncertain about how to solve these kinds of problems or why they would be important in their everyday lives.

To start with, the student should understand that two lines intersect in a point, called a "vertex" and the circular span between the lines is called an angle.A 90 degree angle is the right angle.


Practice Problems on Pythagoras Theorem Learning

Learn to find the missing measure of leg of the right triangle if hypotenuse is 10 cm and right side is 6cm.

The figure is given above for reference.

Hope you like the above example of Pythagoras Theorem.
Please leave your comments, if you have any doubts.