Logic Sentences

Introduction to logic sentences

       In mathematical logic, a sentence is a predicate logic and a well formed formula with no free variables. A sentence is viewed by some as expressing a proposition. It makes an the assertion, potentially concerning any structure of L. This assertion has a fixed truth value with respect to the structure. In contrast, the truth value of a formula (with free variables) may be indeterminate with respect to any structure. As the free variables of an formula can range over several values (which could be members of a universe, relations or functions), its truth value may vary. And now let us see about the  logic sentences.(Sources – Wikipedia).


Basic Concept of Logic sentences:


      Logic is a set of sentences in a proper language. The logic sentences forms a  theory are called its theorems. Logic involved in statements or propositions

Five Terms Propositional in  logic sentences

Not
Or
And
If… then
If  and only if

Some Operations in Logic sentences:


Negation (˜p): The proposition is true means then  they can change into negative and vice versa.

Disjunction (pvq): The  two of the propositions are negative then the result is false or else true.

Conjunction (p^q): The  two of the propositions are right means then the result is true or else false.

Conditional (p→q): The Truth of the proposition ‘p’ is enough to truth of proposition ‘q’.

Bi-conditional (p↔q): ‘p’ is enough condition for ‘q’. ‘q’ is required for ‘p’. if not ‘q’ not ‘p’. Not ‘p’ unless ‘q’. Not ‘p’ without ‘q’.


Example problems:


Example 1:

A, B, can represent the  Logical sentences.  They represent some  definite propositions.

For example:

  A = "My shirt is white"

  B = "The sun is Hot"

 Now we get the final result are:

(A -> B)

But, if I were to dye my shirt  for white on a Hot day, then the

Sentence (A -> B) would become negative.

 Now the a logical sentence, such as:

  (A -> B)

 as discuss in above is true under some situation, and false under

other situation.

 By distinguish, the logical argument:
A |- B

 is *always* invalid.


Example 2:

What is the conjunction equation for the following statements?

     P: Peter reading story book.

     Q: Jenny reading newspaper.   

Solution:

     Given statement is as follows,

         P: Peter reading story book.

        Q: Jenny reading newspaper.   

    Conjunction is a ‘and’ declaration. The symbol of ‘and’ condition is ^.

    We can write the above statement in the following format.

      " Peter reading story book adn Jenny reading newspaper".   

     So logical equation = P ^ Q.

Example 3

Write the logical form for the following statement.

"Jenifer likes apples or oranges".

Solution:

      Let P:Jenifer likes apples

             Q:Jenifer likes oranges.

      The 'or' condition represents the disjunction.

       So logical form=PvQ.

Example 4

What is the conditional form for the following statements?

  "If we go to the college early, then we can enter the class room without punishment".

Solution:

     Given statement is as follows,

          P: If we go to the college early

         Q: then we enter the class room without punishment.

    Conditional is an ‘if-then’ declaration. The symbol of ‘if-then’ condition is ‘→’.

      So logical equation = P → Q.

Example 5

What is the logic form for the following statements?

 "Alex drives a bike or car".

Solution:

     Let P: Alex drives a bike.

          Q: Alex drives a car.

     The given declaration is ‘or’. The notation of ‘or’ is v.

     Therefore the logical form=PvQ.


Practice problems:


Question 1:

What is the conjunction form of the following statements?

     “ Peter has bicycle and bike”.

Question 2:

Write the logic form for the following statement?

    “Jessie likes to play tennis or badminton”.

Question 3:

What is the logic form for the following statement?

  "If u go to school then u will learn the english".

Answers:

1. Conjunction= P^Q

2. Disjunction =PvQ

3. Form =P→Q

These logic design questions are used to learn about the concepts.

What Is Numeric

Introduction to Numeric :

The term numeric can be referred to as numbers especially the characters from 0 to 9.It is a concept derived from 0 and the units. It can be represented as a quantity or it is related to the susceptible of all measurement. It is having the power of apparently denoting or naming .Numerical values are symbols as shown below

Numerals are  0,1,2,3,4,5,6,7,8,9.

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Analysis on Numeric:


Any number is a concept. ‘One’ is a number expressed in name and we use ‘1’ as numeral or symbol to denote it. Different types of symbols were used in various parts of the world to denote the numerals in past days. Number Pattern is defined as a list of numbers which would follow a certain rule.

Numerical pattern revolves all around the numeric values. None of these languages has a separate number system, hence these letters were instead also attributed a number. So we have to learn some knowledge on number pattern.

Some of the different types of number patterns are as follows:

Arithmetic sequence

Geometric sequence

Fibonacci sequence

Overview of Numeric type:

Types of numeric include following types,

Integer numeric

Approximate or floating-point numeric

Exact numeric

Basic operations of the numeric data types:

Minimum:

It is used to yield numerically smallest of the value. The general form is given as Min[x1, x2].

Example:

Minimum of particular numbers Min [3, 10]

Ans: 3

Maximum:

It is used to yield numerically biggest of the value. The general form is given as Max[x1, x2].

Example:

Minimum of particular numbers Max [87,140]

Ans: 140

Total:

The total type of data which is used to provides the whole value or sum of a particular list

Example:

Total [{A, B, C, D}]

Ans: A+B+C+D.

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Example problems:


Problem 1:

Find the minimum value for the given data 1, 8 using numeric data type.

Solution:

Minimum = Min [1, 8]

= 1

Problem 2:

Find the maximum value for the given data set [121, 28] using numeric data type.

Solution:

Maximum = Max [121, 28]

= 121

Problems 3:

Find the total for the following values, A, B, C using numeric data type.

Solution:

Total [{A, B, C}] = A+B+C.

Problems 4:

Find the total for the following values, 2, 3, 4, 5 using numeric data type.

Solution:

Total [{2, 3, 4, 5}] = 2+3+4+5 = 14

Study Velocity

Introduction to study velocity:-

• The study velocity of an object in an interval of time is the distance traveled by the object divided by the interval of time. the instantaneous speed is the limit of the standard speed as the duration of the time interval approaches zero.

• But study the distance(d) and the time taken(t) is given, the speed can be calculated using the following formula:

Velocity (V) = Distance / Time taken

• During this article to study velocity given distance, we are going to study some of the problems concerned in solving the study velocity if the distance is given.

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Example problems for study velocity:-


1) Solve the Velocity of an object which travels 244 meters in 18 seconds.

Solution:-

Distance = 244 m

Time = 18 sec

Velocity = Distance / Time taken

= 244 / 18

= 13.55 m/sec.

2) Solve the Velocity of an object which travels 320 meters in 20 seconds.

Solution:-

Distance = 320 m

Time = 20 sec

Velocity = Distance / Time taken

= 320 / 20

= 16 m/sec.

3) Solve the Velocity of an object which travels 458 meters in 42 seconds.

Solution:-

Distance = 458 m

Time = 42 sec

Velocity = Distance / Time taken

= 458 / 42

= 10.90 m/sec.

4) Solve the Velocity of an object which travels 322 meters in 34 seconds.

Solution:-

Distance = 322 m

Time = 34 sec

Velocity = Distance / Time taken

= 322 / 34

= 9.47 m/sec.

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Practice problems to study velocity:-


1) Solve the Velocity of an object which travels 315 meters in 13 seconds.

Answer: 24.23 m/s

2) Find the Velocity of an object which travels 252 meters in 18 seconds.

Answer: 14 m/s

3) Find the Velocity of an object which travels 186 meters in 8 seconds.

Answer: 23.25 m/s

4) Find the Velocity of an object which travels 112 meters in 4 seconds.

Answer: 28 m/s.

Vertices in Math

Introduction to Vertices in math
Vertex usually way a bend otherwise an end point wherever lines are congregate. Such as a square include four corners, each one is called a vertex. The plural formation of vertex is described as the vertices. For example the square contains four vertices. Vertices also a triangle would contain 3 vertices.


Vertices in math


Vertices in graph

Within math, a graph is a theoretical illustration of a position of things wherever a few pair of the things is related by links. The interrelated things are stand for by arithmetical concept called vertices, also the links to attach a few pairs of vertices be call edges. Usually, a graph is described within illustrative appearance like a place of points used for the vertices, connected through lines or else arc designed for the edges.

The ends might be directed otherwise undirected. for instance, condition the vertices symbolize people on a party, also here be an edge with two people but they vibrate hands, after to this be an undirected diagram, since condition person 1 vibrate hand through person 2, after that person 2 to vibrate hands through person 1.

In graph the vertices are as well describe points.


Vertices in angles

Vertices are measurement of angles. An angle is finished through the relating of two waves.

To relation be calling the vertex.

Angles are able to as well happen on the joint of two lines.

After to the point of joint is a vertex. These points are significant within the creation of an angle as well as also within the identification of an angle. Condition the vertex is on Point D, also it be the simply angle on Point D, the angle be able to be name Angle D.

Vertices are division of polygons. Every point of relationship is a vertex.

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Example 1: Solve the coordinates of the following equation

y=x^2+18x+20

Solution:

y=x^2+18x+20

dy/dx = 2x + 18

At vertex dy/dx = 0

2x + 18 = 0

x = -9

Therefore, y = (-9) ^2 + 18(-9) + 20 = 81- 162 + 20 = -56

Vertex contain co-ordinates (-9, -56)

Example 2: Solve the coordinates of the following equation

y=x^2+6x+2

Solution:

y=x^2+6x+2

dy/dx = 2x +6

At vertex dy/dx = 0

2x +6 = 0

x = -3

Therefore, y = (-3) ^2 + 6(-3) + 2 = 9- 18 + 2 = -7

Vertex contain co-ordinates (-3, -7)

Math Help Gateways

Introduction to math help gateways:

Math help gateways are websites that help students to learn math. Tutor vista is one of the best website which act as a gateway and help students in solving their homework problems and clear their doubts. This article for math help gateways covers the solving algebraic equation with step by step. After viewing this article student understand the concept and prepared well from math help gateways.


Math help gateways:


Example 1:

Find the value of the expression 12x+7 , if x= 4

Solution:

Substitute x = 4 in the given expression 12x + 7

12x + 7 = 12(4) + 7

= 48+ 7

X  = 55

Here the value of the expression is 55.

Example 2:

Solve: 2x - 2 = 38

Solution:

Given, 2x - 2 = 38

2x = 38 + 2

2x = 40

x = `40/2`

or    x = 20

Example 3:

Solve the following system:

x + y = 14 - (1)

4x - y = 11 - (2)

Solution:

Solve the (1) equation

y =14 -x

substitute in (2)equation

4x - (14 - x)=11

4x - 14 + x=11

5x=25

x=5

substitute value of x in (1)equation

5 + y=14

y=9

The solution is, (5, 9).

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Math help gateways:


Example 4:

One seventh of a certain number is 17. find out certain number.

Solution:

let the unknown value be x. one seventh of x is `( 1/7 ) * x`

so,  `( 1/7 ) * x` = 17

x = 17 * 7

x = 119

the number is  119.

Example 5:

If four times of a number is equal to 10. Then find what exactly the number is?

Solution:

let us assume the unknown number as " X "

Given   4 * X = 10.

Move left side term to right

Then          X = `10/4`

The unknown number x is

X = 2.5

Example 6:

Given :

12x - 2(7x-10x+2)+x.

Solution:

First simplify those brackets. So we multiply (7x-10x+2) with 2

So, 14x - 20x + 4

It can be written as 12x - 14x + 20x - 4 + x.

add the like terms

So,answer is (19x - 4)

Math Words A to Z

Introduction to math words a to z:

Understanding the concept of math is critical in this modern world today.  Math is used every day by all, from lay persons to degree professionals. Situations in which math is used differ from merely complementary a checkbook or calculating the sum of change due from a store transaction all the way to creating blueprints for an office building or house and the construction of those buildings. Understanding how to solve math is an easy way. Math words a to z has a mathematical terms from a to z.


Some mathematical terms from a to m– math words a to z.


Adjacent angles `–` adjacent angles are angles which are adjacent o each other and it shares a common vertex.

`Addition of vectors` – It is adding two vectors and the result is known as resultant vector.

Bisect – Bisection is dividing the given figure into two parts which are equal to each other.

Center – Center is a middle part of a geometric figure.

Cuboid – Cuboid is a rectangular box.

Decahedron – Decahedron is a three dimensional figure in which it has twelve faces.

Edge – An edge is a line segment between two vertices.

Finite – Limited number of elements.

Geometric sequence – Geometric sequence is a sequence of numbers in which second number is the multiplication of first number and any other constant and it goes on.

Horizontal axis – x axis is a horizontal axis because it is horizontal

Infinite – Unlimited number of elements

Identity matrix – Identity matrix is a square matrix in which all the diagonal elements are equal to 1 and the non diagonal elements are equal to zero.

Joint proportional – It is same as Joint variation.

Kite – It is geometric figure with four sides.

Linear equation – An equation which has only one degree.

Mass – Mass is a weight of an object.

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Some mathematical terms from n to z– math words a to z.


Number line – a line which has numbers from –infinity to +infinity.

Opposite angles – Angles which are opposite to each other.

Polynomial – Polynomial is a term in which it has a combination of variables, constants and exponents.

Quadrangle – Quadrilateral can also be say as quadrangle.

Rate of change – A change in y coordinate the change in x coordinate.

Secant – A straight line which cuts two or more points on a curve.

Tangent – Tangent is a straight line which touches a point on a circle.

Unequal – Two or more quantities are not equal to each other.

Variable – It is a letter used to refer unknown values.

Width – one of the side of a rectangle.

X – Intercept – value of x when y=0

Y-intercept – value of y when x=0

Zero product – A product of two or more expressions is equal to zero.

These are the some math words a to z.

Examples Integers Math

Introduction for examples integers in math:

The integers are formed by the natural numbers including 0 (0, 1, 2, 3, ...) together with the negatives of the non-zero natural numbers (-1, -2, -3, ...). Viewed as subset of the real numbers, they are numbers that can be written without a fractional or decimal component, and fall within the set {... -2, -1, 0, 1, 2, ...}. For example, 65, 7, and -756 are integers; 1.6 and 1½ are not integers. The set of all integers is often denoted by a boldface Z, which stands for Zahlen

-Source Wikipedia


Number Line for examples integers in math :


The number line is shown with the integers in ascending order from left to right:

|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|

-5    -4   -3   -2   -1    0    1    2    3    4    5

The integers on right sided to the 0 is positive integers and the integers on left side to the 0 is negative integers


Absolute Values for examples integers in math :


The absolute value of a number n is written as |n|. The absolute value of the numbers always be positive

Examples:

|44| = 44

|0| = 0

|-44| = 44


Rules for examples integers in math:


Addition rule:

Positive + Positive = Positive:

Negative + Negative = Negative:

In the addition of a negative and a positive number we have to subtract and place the largers number's sign.

Subtraction rules:

Negative - Positive = Negative

Positive - Negative = Positive + Positive = Positive

Negative - Negative = Negative + Positive

In the subtraction of a negative and a positive number we have to subtract and place the largers number's sign

Multiplication rules:

Positive x Positive = Positive

Negative x Negative = Positive

Negative x Positive = Negative

Positive x Negative = Negative

Division rules:

Positive ÷ Positive = Positive

Negative ÷ Negative = Positive

Negative ÷ Positive = Negative

Positive ÷ Negative = Negative

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Example problems for integers in math:


Addition Operation:

5 + 5 =10

5 + (-6) = 5 - 6 = -1

-6 + 5 = -1

Subtraction Operation:

5 - 5 = 0

6 - 5 = 1

5 - (-6) = 5 + 6 =11

-6 - (-6) = -6 + 6 = 0

Multiplication Operation:

6 *  6 = 36

-6 *  -6 = 36

-6 *  -6 = -36

6 *  -6 = -36

Division Operation:

6`-:` 6 = 1

-6 `-:` -6 = 1

-6`-:` 6 = -1

6 `-:` -6 = -1

Lines and Angles Math

Introduction to lines and angles math:

In math geometry the lines and angles are important tools. If any object in ideal, that is called as line and it is represented as straight curve. The angle is related with line that is the cross-section of two-line is create the angle and that intersection point is called as vertex. Here we see about types of line and angle in math.


Explanation for lines in math


Lines:

If we want to project the real world model in geometry means we can use the lines for straight object representation. This straight object is represented with small height and width and it is infinitely long. The Euclidean math geometry use the line commonly.

Types of lines:

Parallel lines:

The separate two coplanar lines are called as parallel lines that are this line does not intersect with each other. The distance between the two lines are equal and it is represented as | |. The parallel lines are illustrating the two postulates.

Corresponding angles postulate: The angles are same when the transversal is cut the two coplanar lines. So we can say that lines are parallel.

Parallel lines postulate: If the transversal cut the two parallel lines, the same measure angles are present.

Perpendicular lines:

When the angle of 90 degree on two lines that two lines are said to be as perpendicular lines. This perpendicular line is represented as ‘_’. The perpendicular line does not have any postulates but solve some theorems. They are perpendicular lines and slopes theorem, perpendicular to parallel theorem and two perpendiculars theorem.


Explanation for angles in math


Angles:

The above diagram is illustrating the angle by lines. The vertex of angle is A. The meeting line of two lines is called as arms of the angle and the arm points are used for naming the angle. When one angle arm is moved to the other arm is represent the size of an angle.

In math the degree is used for angle size measurement and in geometry the protractor is used. Adjacent angles, complementary angles ad supplementary angles are pairs of angles.

Doing Math Problems

Introduction of doing math problems:

Math is very important term in our day to day life. We have different concepts in math. And commonly formulas are used to solve the complex problems .We have various types of formulas in math. Algebra is the one of the important terms in mathematics. Here we are going to see some example math problems.

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Doing math problems:


Doing simple algebra problem:

Example 1:

g- 43 = 604.

Solution:

Step 1: g - 43 = 604.

Step 2: g - 43+ 43 = 604 + 43. (Add 43on both the sides).

Step 3: g = 647(so, the value of g is 647).

Doing simplification in algebra:

Example 2:

Given:

20x-5(12x-10x+2) +4x.

Solution:

Step 1: First we need to simplify the brackets. So we multiply (12x-10x+2) with 5

Step 2: So,20x-60x+50x-10+4x

Step 3: It can be written as 20x-60x+50x-10+4x

Step 4: So, the answer is 14x-10.

Doing parenthesis problem in math :

Example 3:

Given :

(14/2) * (45-9)

Solution :

Step 1: First we need to simplify the parenthesis ,so

Step 2: We get 14/2 = 7 and (45-9) =36.

Step 3: Here we need to multiply 7*36.

Step 4: So, the answer is 252.


More math problems


Doing inequality problem in math

Example 4:

Solve for 4(a+1) <2a br="">
Solution:

Step 1: It can be written as 4a+4<2a 2a="" both="" br="" on="" sides="" the="" ubtract="">
Step 2:4a+4-2a<2a-2a br="">
Step 3:2a+4<3 4="" both="" br="" on="" sides="" subtract="" the="">
Step 4:2a+4-4<3-4 .="" br="">
Step 5:2a<-1 .so="" a="-1/2.<br">


Doing subtracting algebraic expression in math:

Example 5:

Given:

Subtract 24ab – 10b – 18a from 30ab + 12b + 14a.

Solution:

30ab + 12b + 14a – (24ab – 10b – 18a)

Step1: 30ab + 12b + 14a – 24ab + 10b + 18a

Step2:30ab – 24ab + 12b + 10b + 14a + 18a

Step 3:6ab + 22b + 32a.

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Adding polynomials in math :

Example 6:

(6x+7y) + (2x+1y)

Solution:

Step 1: First we need to clear the parenthesis so, 6x+7y+2x+1y.

Step 2: Now we need to combine the like terms, so 6x+2x+7y+1y.

Step 3: Here we need to add the like terms, so 8x+8y.

Step 4: So the answer is 8(x+y).

Do My Math Problems For Me

Introduction:

Do my math problems for me

Mathematics is a very biggest subject which is very important for our life. Math is not only a subject to know and study but it teaches us what is life is and how does math approaches our life every time. Math problem are very interest to solve. Many different topics of math problem are there to find and solve. Math problem have different sequence of steps, methods, functions every thing. Many chapters are under the math. Now let us do some of the math problem in basics of mathematics like addition subtraction division multiplication etc.

Example math problem:


Find the sum of 5482 + 2451


Solution

5 4 8 2

2 4 5 1 +

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

7 9 3 3

2. Find the difference of 7853 – 3521

Solution

7 8 5 3

3 5 2 1 –

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

4 3 3 2

3. Find the value of x in the equation 5x + 4 = 34

Solution

5x + 4 = 34

Subtract 4 on both sides

5x + 4 – 4 = 34 – 4

5x = 30

Divide 5 on both sides

5x/5 = 30 / 5

X = 6

4 .Use PEMDAS rule to solve the term

(5*5) + 9 – 8 / 2 *2 + 1

Solution

25 + 9 – 8 / 2 * 2 + 1 ------------(Parenthesis first)

25 + 9 – 8 / 4 + 1------------------(No exponents so net multiplication )

25 + 9 – 2 +1 ---------------------(Division)

34-3---------------------------------(Addition)

31

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Do my math problem:


Find the sum of 5487 + 2145

Find the difference of 987 – 123

Find the value of x in this equation 7x -2 = 61

John has 10 pens with him. He gave 3pens to his sister Rosy. Again he gave 2 pens to his friend Jane. Now how many

pens he will have at present.

Divide 845 by 5

Use PEMDAS rule to solve the term

6+2*3+5-(9/3)

Answers

1.7632

2.864

3.9

4. 5

5. 169

6.14

Algebraic Equations

Algebraic Equations Definition is given as equations that are a sum of number of terms where each term is the multiplication of some constant term and positive integral power of some variables. Algebraic equations can be divided into following categories as:
Linear equations: these include all equations with degree 1 which means the maximum power of variables can be 1 only. For example: x+5=12.

Quadratic equations: these are the equations of degree 2. Graphically these are represented by a U shaped parabola. Mathematically they are represented as: ax2 + bx + c=0 where a  0.
Exponential equations: these are equations where a term includes variable as the power of constant value for example: ex + e =0. Or 2x + x =2 etc.

Logarithmic equations: these equations involves a logarithmic term which is given as: loga x. Here ‘a’ cannot be 1 and a >0, x>0.  Let us see some methods of How to Solve Algebra Equations through some Algebraic Equations Examples now.

1) Linear equations: these equations are very easy to solve. Solution of the equation means to find out the value of variable that satisfies the given equation. Linear equations can be solved by isolating the variable of the equation. For ex:
2x+ 6 = 5.
to isolate x we can move 6 to RHS to get: 2x=5-6 = -1.
now a can be moved to RHS as: x= -1/2.

2) Quadratic equations: there are many methods to solve these equations like factoring, completing the square, quadratic formula and graphing. Here we will be quadratic formula to solve a quadratic equation.
The formula to solve a quadratic equation ax2 + bx + c=0 is given as:
x =
Example: solve 2x2 – 5x +2 =0.
By using above formula we have: a= 2, b =-5 and c =2.
x =

x =
x =
x=
So we get two solutions here as: x=(5+3)/4 and (5-3)/4 or 2, ½.

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3) Exponential equations: to solve these we first isolate exponential term and then take logarithm  at both the sides of equation.
Example: e2x - 3ex+2=0.
This can be written as: (ex-1)(ex-2)=0
Equate both terms of product by zero:
ex - 1=0
ex =1
=> taking logarithm on both sides we get: ln(ex) = ln(1)
=> x (ln(e)) = 0
=>x.1=0. Hence x=0.
ex - 2=0
Similarly solving this we get x=ln(2)=0.69314 approx.

4) Logarithmic Algebra Equation is solved by taking exponential.
Example: ln(x)=3
eln(x) = e3
x=e3.
x=20.085537 approx.

Grade 10th Math

Introduction to grade 10th math:

Mathematics is an essential tool used in throughout the entire world in many areas, like science, medicine, engineering, and social sciences. The 10th grade mathematics covers number system, algebra 1, algebra 11, pre calculus, calculus, statistics, geometry, trigonometry, and advanced trigonometry. In this article we shall discuss about 10th grade math problems and its solutions.

Grade 10th math example problem:


Example 1:

Solving the coefficient of the equation

`(1-(2)/((x-4))) = 8`

Solution:

This equation in the form of rational expression, multiplying the expression by the denominator value (x -4)
(x - 4) (1 - 2 / (x - 4)) = (x - 4)8

Simplifying the equation
(x - 4) - 2 = 8 (x - 4)

Multiplying the factors and arrange the like terms.
x - 6 = 8x - 32

Adding the value -8x to both sides and simplifying the equation

-7x - 6 = - 32

Adding the value + 6 to both sides
-5x = - 25

Solving for x

x = 25 /5.

x=5.

Example 2: Solve the inequality -4 < 2(x+4)-2<18 nbsp="" p="">
Solution:

Given inequalities

-4 < 2(x+4)-2<18 nbsp="" p="">
Multiplying the factor values and arranges the like term

-4<2x nbsp="" p="">-4<2x nbsp="" p="">Subtracting the value 6 on both sides of equation

-4-6<2x nbsp="" p="">-10<2x nbsp="" p="">
Dividing all terms by 2

-5
Conclusion:

The solution consists of all real number the interval (-5, 6)

Example:

A hemispherical bowl of radius 20 cm is contains with soap cream paste. This ice cream paste is made into cylindrical cakes each of radius 2 cm and height 2 cm, how many cakes do we get?

Solution:

Radius of the hemisphere = 20 cm;

Volume of the hemisphere =`3/ 2` `pi` r3 cubic units;

Therefore Volume of the soap paste =`3/2` x `pi ` x 20 x 20 x 20 cm3.

Radius of the cake = 2 cm;

Height of the soap cake = 2 cm;

Volume of the cake =pi x 2 x 2 x 2cm3.

Number of soap cakes = Volume of the soap cream paste / Volume of the cake

=   `(2/3 pi * 20*20*20)/(pi*2*2*2)`

Therefore we get 667 cakes out of the given paste.

Understanding How to Find the Lateral Area is always challenging for me but thanks to all math help websites to help me out.

Grade 10th math practice problem:


Problem 1:

Solving the coefficient of the equation `(1-2/ (x-3)) ` =6

Answer:

x=13/5

Problem 2:

Solve the inequality -2< 2(x+6)-3<17 nbsp="" p="">Answer:

The solution consists of all real number the interval (-6, 4)

Learn Odds in Math

Introduction to learn odds in math:

A number which is not divisible by two is called as odd number in math. This is considered as whole number. The odd numbers are represented in set as { 1, 3, 5, 7, 9,……} and it does not contain multiples of two in math. We can learn the odds by identify the last digit that is if the last digit is 1,3 ,5 ,7 and so on means that number is odd.


Explanation for odd in math


Learn odd in math:

We can learn odd number’s arithmetic operations by using some results. They are,

In addition and subtraction:

If we add the even number and odd number means the resultant value is odd.For example add the numbers 8 + 1 = 9.

If we add the two odd numbers means the resultant value is even. For example add the 5 + 7 = 12.

In multiplication:

If we multiply the even and odd numbers means the resultant value is even. For example multiply the 6 x 7 = 42.

If we multiply the two odd numbers means the resultant value is odd. For example multiply the numbers 3 and 5 and we get the answer as odd value 15.

In other words:

The odd numbers are also called as gnomonic numbers in math. It is in the form as n = 2k + 1. Here integer is k. We can learn odd numbers by using this form. If we want to identify the odd numbers means divide that number by 2 and if we get the remainder, that number is odd.

The odd numbers are generated by using function as `(x(1 + x))/(1 + x)`  = x + 3x2 + 5x3 +......

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Learn odd numbers with example:


Problem 1: Find the odd numbers  from given set

{ 3, 6, 14, 7, 21, 34, 22, 47 }.

Answer:

The odd numbers are { 3, 7, 21, 47 }. Because these numbers are ended with 1,3, 7 and it does not divided by two.

Problem 2: Add and multiply the following odd numbers:

3 + 9 = 12.

53 + 7 = 60.

33 x 5 = 165.

Exercise problem for odd numbers:

Find the odd number from set { 190, 321, 453, 628 }.

Answer: { 321, 453 }.

Definition Reflexive Math

Introduction:

Reflexive is one of the properties in math. It is one of the postulates in equality. Reflexive property means anything equals to itself that is a = a where a is the set of numbers or number. Using reflexive property many geometric proofs were proved. Since it has equality we can find the answer for the given expressions.

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Example problems - Definition reflexive math:

Example 1 - Definition reflexive math:

Use the reflexive property to find the answer for x and the expressions are x+9 and 2x+8.

Solution:

The given expressions are x+9 and 2x+8

We the reflexive property anything equals to same thing

So, the expression can be written as x+9=2x+8

Add –x on both sides in the above equation

X+9+(-x) =2x+8+(-x)

X+9-x = 2x+8-x

9=x+8

Now subtract 8 on both sides

9-8=x+8-8

1=x

The value of x is 1.

Example 2 - Definition reflexive math:

Use the reflexive property to find the answer for y and the expressions are 2y+8 and y+8.

Solution:

The given expressions are 2y+8 and y+8.

We the reflexive property anything equals to same thing

So, the expression can be written as 2y+8 = y+8.

Add –y on both sides in the above equation

2y+8 +(-y)= y+8+(-y)

2y+8-y=y+8-y

y+8=8

Now subtract 8 on both sides

y+8-8=8-8

y=0

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More Example problems - Definition reflexive math:


Example 3 - Definition reflexive math:

Use the reflexive property to find the answer for x and the expressions are 3x+9 and 2x+8.

Solution:

The given expressions are 3x+9 and 2x+8

We the reflexive property anything equals to same thing

So, the expression can be written as 3x+9=2x+8

Add –xx on both sides in the above equation

3x+9+(-2x) =2x+8+(-2x)

3x+9-2x = 2x+8-2x

x+9 =8

Now subtract 9 on both sidesx

x+9-9=8-9

x=-1

The value of x is -1.

Example 4 - Definition reflexive math:

Use the reflexive property to find the answer for y and the expressions are 2y+8 and4y+8.

Solution:

The given expressions are 2y+8 and 4y+8.

We the reflexive property anything equals to same thing

So, the expression can be written as 2y+8 = 4y+8.

Add –2y on both sides in the above equation

2y+8 +(-2y)= 4y+8+(-2y)

8=2y+8

Now subtract 8 on both sides

8-8 =2y+8-8

2y=0

So, y=0.

Maximum Math Terms

Introduction to maximum math terms:
The math term maximum is define different kinds of versions. They are find out the maximum value from given data, determine the maximum distance between two points and the maximum value of set theory function. The greatest value is defined in math as maximum. The integration is used for find out the maximum value in set element.


Explanation for terms maximum in math


Procedures for finding the maximum value in math:

Step 1: Collect the set of data and use the comparison method.

Step 2: The comparison method is arrange the numbers in ascending order.

Step 3: At last find the maximum number from above order of data.

For example take  the set of data as 4, 2, 1, 6, 12, 3, 10. The comparison method is used for data arrangement in ascending order. The elements in ascending order is 1, 2, 3, 4, 6, 10, 12. The greatest value of given set of data is 12.

Maximum in other branch of math terms:

The set operations are used for finding the maximum value in functions. In math the optimization is determine the maxima from set of data and the real valued function is explain the global maximum. The bounded value theorem is essential one for global maximum determination.

In terms maxima, the expression A = { ai }N is explain the maxima for set of elements. The last element of this order is denote the maximum value of set.  The order statistics has different types and this is one type of statistics.

Consider the example as { 1, 5, 8, 4 } and arrange the set of data in ascending order as { 1, 4, 5, 8 }.Finally, the maximum value of set is 8.

Maximum in profit:

The term maximum in profit is how much of profit the company get.

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Examples for maximum in math terms


Problem 1:

Find the maximum value from the set of numbers 8, 4, 1, 20, 15, 9.

Answer:

Arrange the set of numbers in ascending order as 1, 4, 8, 9, 15, 20.

Set’s maximum value is 20.

Problem 2:

Find the maximum profit from P = 6x – 0.04x^2.

Answer:

If `(dP)/dx` = 0 then 6 – 0.08x = 0

`(d^2P)/(dx^2)` = -0.08 it has maximum profit.

If x = 200, profit is 400.

Excercise for maximum terms in mat:

1. Find out the maximum from given set of data { 12, 15, 11, 22, 9 }.

Answer: Maximum value of set is 22.

2. Find out the maximum value from set of numbers: 110, 120, 108, 115.

Answer: The minimum value is 120.

Video Tutorials for Math

Introduction about video tutorials for math:

Math is very interesting and complicated subject. We have various types of method and procedures to solve the math question. Tutorial is one of the techniques to improve the student’s knowledge. Students can learn their own speed, and their convenience. Interactive classes can do by a tutor during tutorials. One of the main benefits is, students clarify their doubts frankly as well as immediately. Here we are going to learn about some example problems of tutorials for math.

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Example problems of video tutorials for math:


Example 1:

A train takes to travels 200 miles in 4 hours. How long the train travels in 8 hours?

Solution:

Step 1: We know that the train travel 200 miles. If a train travel 8 hours how many miles the train travel?

Step 2: it’s the direct proportionality.

Step 3: We know that

Hour’s         miles

4               200

8                 x

Step 4: Now we need to solve the value of x using cross multiplication. So, we get 4x= 1600

Step 5: Divide using 4 on both the sides. So, the train travelled 400 miles.

Example 2:

Using these lines. Find the intersecting points?

y = 2y+2

y = x+12

Solution:

Step 1:

y = 2x+2      ------------> ( 1 )

y = x+12      -------------> ( 2 )

Step 2:

We know that the two lines are equal. So, it can be written as ,2x + 2 = x + 12

Step 3:  Here we need to solve the value of x. So, 2x – x = 12 – 2.Therefore, the value of x is 10

Step 4:

Substituting the value of x=10 in equation (1)

y = 2x + 2

= 2 ( 10 ) + 2

= 20 + 2   = 22

y = 22

The two given two lines intersect at a point (10, 22)

This is the example of intersecting lines.

These are the example problems of video tutorials for math .

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One more example of video tutorials for math:


Example 3:

The sum of the least and greatest of 3 consecutive integers is 160. What are the values of the 3 integers?

Solution:

Step 1: Let us assume the integers are x,x+1 and x+2 .

Step 2: And we know that , the least and greatest of the 3 consecutive integer is 160 .

Step 3: So, we can arrange the equation, that is x+(x+2) = 160 .

Step 4: Here we need to solve this equation. So 2x+2 = 160. (Subtract 2 on both the sides)

Step 5: Therefore x= 79. Therefore the least integer is 79.

Step 6: Substitute the x value is x+1, x+2 .

Step 7: Therefore, 79+1 = 80 and 79+2= 81.

Step 8: Therefore, the values of 3 integers are 79, 80 and 81.

These are the examples of video tutorials for math.

Math Skills Practice

Basic Math Definition:

Arithmetic is the one of the Basic mathematics definition. Arithmetic deals with the properties of numbers and ways of combining them through addition (+), subtraction (-), multiplication (*), and division (/) And basic math definition are contain with the arithmetic, Fractions, Decimals, Roots, Exponents, Factorials, Modular and Interval Arithmetic these are the contains with the basic math definition.

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Basic Math Definition Examples:


Arithmetic practice Examples:

Adding Arithmetic Example:

56977 + 21454

56977
+ 21454
---------
78431
---------
Subtracting Arithmetic Example:

782138 – 574121

782138
( - )    574121
----------
208017
----------
Multiplication Arithmetic Example:

875 x 69

875 x 69
-------------
7 8 7 5
5 2 5 0
-------------
6 0 37 5
-------------
Division Arithmetic Example:

45` -: ` 9

9) 45 (5
45
------
0
------

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Fractions practice Examples:


Fraction practice Example 1:

Add Two Fractions  ` 5/6 + 9/8`

Step 1:

For the denominators here, the 6 and 8, a common denominator for both is 24.

Step 2:

With the common denominator, the `5/6` becomes a `20/24 ` and the  `9/8 ` becomes a `27/24`

So, the problem here is to add `20/24` and `27/24`

Step 3:

The two denominators are same adding numerator values then ,we get  `47/24`

Step 4:

The fraction `47/24` is an improper fraction (the numerator is greater than the denominator).
Step 5:

The whole number part of the mixed number is found by dividing the 47 by the 24.

Step 6:

The fractional element of the mixed number is found by using the remainder of the division, which in this case is 23 (47 divided by 24 is 1 remainder 23).

Answer:

`1 23/24`

Reduce the fraction Practice Example:

Reduce the given factor 6/63

Solution:

The fraction `6/63` is not reduced to lowest terms. We can decrease this fraction to lowest terms by dividing both the numerator and denominator by 3.

Greatest Common Factor (GCF) of the numbers 6 and 63. So, this fraction reduced to lowest terms is `2/21`

Answer:  ` 2/21`

Subtracting the Fraction Practice example:

Subtracting the given fraction `8/5` and` 3/5`

Solution:

Step 1:

The given faction denominators (5) are equal.

Step 2:

Therefore the fraction, `5 /5` can be reduced further to 1, because anything over itself (other than zero) is 1.

Step 3:

The fraction 1 is not reduced to lowest terms. We can decrease this fraction to lowest terms by dividing both the numerator and denominator by 5.

Step 4:

Greatest Common Factor (GCF) of the numbers 0 and 5.

So, this fraction reduced to lowest terms is 1

Answer

The subtracting fraction is 1

Fog and Gof Math Problems

Introduction to fog and gof math problems:
Basically fog and gof math problems are nothing but we have to convert the one function into other function. If the given function is in the form of f(x) mean we have to convert this into f (g (x)) form. If the given function is in the g (x) form then we have to change this into g (f (x)) form.  Let us see some example for these types of problems.


Example for fog and gof math problems


Example 1:

Find the fog and gof for the given math problems. Where f (x) = x and g (x) = 3x + 4

Solution:

First we have to find fog for the given problem.  For that first we have to find the g(x).

Where g (x) = 3x + 4

fog = f (g (x)) = f (3x + 4) = 3x + 4

Likewise we have to find gof for the given math problem.

gof mean first we have to find f(x)

Where f (x) = x

Then gof = g (f (x)) = g (x) = 3x +4

From the above we understand we have to write the output of the one function value into the other function form.

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Example 2:


Find the fog and gof for the given math problems. Where f(x) = 2x + 5 and g(x) = 5x

Solution:

First we have to find fog for the given problem.  For that first we have to find the g(x).

Where g (x) = 5x

fog = f (g (x)) = f (5x) = 2(5x) + 5

= 10x + 5

Likewise

gof mean first we have to find f(x)

Where f (x) = 2x + 5

Then gof = g (f (x)) = g (2x + 5) = 5(2x + 5)

= 10x + 25

If suppose we are having the square or cubic function mean we have to find the square or cubic roots. After that we have to expand the function. From the above there is no square or cubic value. So we just find the function values.

Math Percent Help Now

Introduction to percentage:

In Math subject, a percent (percentage) is one way of expressing a number as a fraction number of 100. It means one per hundred. The percent is using the sign “%”. Example, 69% (to read this number  “sixty-nine percent”) is equal to 69 / 100, otherwise 0.69. So, in this way of math percent help now for us. The percentage sign or symbol is “%”.

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Math Percent help:


The percentages are mostly helpful now, it is used and expressed how large quantity and small quantity is, related to another quantity. It has using two quantities; usually the first quantity represents the part of second quantity. And it should be greater than zero.

Example:

Increase of  `$ 0.15` on a rate of `$1.50 ` an increase by a fraction of 0.15 / 1.50 = 0.1. So, that 0.1 * 100 = 10%, as a percentage expressed as, this is a 10% increase.

And also percentages helps to find and express numbers between zero and one, any dimensionless proportionality can be expressed as a percentage. For example, 129% is 1.29 and -0.29% is -0.0029.


Calculate the percentage:


The concept of performing calculations with percentages is, the percent symbol can be treated as being equivalent to the number constant 1 / 100 = 0.01. , for an example 75% of 400 can be written as (75 / 100) × 400 = 300.

Unit represents:

To find the percentage of a unit represents out of a whole of N units, divide 100% by N. For suppose, if we have 125 apples, and we want to find out what percentage of these 125 apples.

In a single apple represents, 100 / 125 = (100 / 125) % the answer of 0.8%.

So, if you give away one apple, you have given away 0.8% of the apples we had.

Then, if we give away 100 apples, we have given away 100 × 0.8% = 80% of us 125 apples.

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Example problems in math percentage:

Example 1:

What is the answer for 300% of 40?

Solution:

300% × 40 = (300 / 100) × 40 = 120.

Answer is 120.

Example 2:

What is the solution of 15% of 75?

Solution:

15% × 75 = (15 / 100) × 75 = 11.25

Answer is 11.25.

Example 3:

75% of all college students are male. There are 1500 male students. How many (total) students are in the college?

Solution:

1500 = 75% × X, therefore X = (1500 / (75 / 100)) = 2000.

Answer is 2000.

Algebra Game Math

Introduction to algebra games math:

In math, the numerical numbers are learnt by the algebra. Here we will see the simplest games of algebra. It is also used to study the polynomials and the equations etc. In this algebra having the quadratic equation, polynomial, algebraic expressions and algebraic identities. Here we will see about these explanation and example games.


Explanation about the algebra games math


Let us see about algebra games math:

Algebra math problem, the quadratic equation of the variable of A. An equation in the form xa2+yb+c=0.

A polynomial of quantity one is known as a linear polynomial.
Algebraic expressions are a partition of polynomial. It is indicated by a letters and exponent.
Algebraic identities are the form (x+y)^2=x^2+2xy+y^2.

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Some sample practice problem about algebra games math

Let us see about algebra games math:

Example 1:

To change the word of character by the same number to use the arithmetic operations are right.

SEND
MORE
---------
MONEY

Answer: 10652

Example 2:

To change the word of character by the same number to use the arithmetic operations are right.

SEVEN + SEVEN + SIX = TWENTY

Answer: 138214

Example 3:

To change the word of character by the same number to use the arithmetic operations are right.

SINUS
SINUS
KOSINUS
-------------
TANGENS

Answer: 4076175

Example 4:

John last birthday he weighed 125 pounds. After one year later he has put on x pounds. Which appearance gives he weight one year later?

Answer: x 125

Example 5:

If you multiply the square of a number n by 3 and then added 7 to the product, the sum is equal to 55. One of the terms is equals 55, which one is it?

Answer: 3n2 7

Example 6:

To change the word of character by the same number to use the arithmetic operations are right.

(J+O+I+N+T)*(J+O+I+N+T)*(J+O+I+N+T) = JOINT

Answer: 19683