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.

Having problem with Numerical Differentiation keep reading my upcoming posts, i will try to help you.

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.

Is this topic cbse board syllabus hard for you? Watch out for my coming posts.

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.

Please express your views of this topic Math Place Value by commenting on blog.

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.

I have recently faced lot of problem while learning cbse board syllabus, But thank to online resources of math which helped me to learn myself easily on net.

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.

I like to share this Hyperbola Vertices with you all through my article.

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).

I have recently faced lot of problem while learning Business Math Formulas, But thank to online resources of math which helped me to learn myself easily on net.

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.

Understanding long division polynomials is always challenging for me but thanks to all math help websites to help me out.

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

Is this topic multiplying integers hard for you? Watch out for my coming posts.

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.

Please express your views of this topic Finding Roots of Polynomials by commenting on blog.

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.

Is this topic Calculate Percentage Formula hard for you? Watch out for my coming posts.

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

Understanding how to solve algebra problems is always challenging for me but thanks to all math help websites to help me out.

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.

Please express your views of this topic quadratic formula discriminant by commenting on blog.

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 +......

Understanding exponential math problems is always challenging for me but thanks to all math help websites to help me out.

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.

Is this topic Sum of Squares Formula hard for you? Watch out for my coming posts.

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

I have recently faced lot of problem while learning solve my math word problem, But thank to online resources of math which helped me to learn myself easily on net.

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.

I have recently faced lot of problem while learning Interest Problems, But thank to online resources of math which helped me to learn myself easily on net.

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.

Having problem with Derivative Product Rule keep reading my upcoming posts, i will try to help you.

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 .

Please express your views of this topic need help with math problems for free by commenting on blog.

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.

Having problem with Interquartile Range Definition keep reading my upcoming posts, i will try to help you.

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
------

Please express your views of this topic help with math word problems for free by commenting on blog.

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.

Understanding Graphing Quadratic Functions in Standard Form is always challenging for me but thanks to all math help websites to help me out.

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 “%”.

Please express your views of this topic Fraction on a Number Line by commenting on blog.

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.

Is this topic Dividing Whole Numbers and Fractions hard for you? Watch out for my coming posts.

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.

Understanding How to Calculate Molar Mass is always challenging for me but thanks to all math help websites to help me out.

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

Fact Family Math

Introduction to fact family math:

The fact family in math is nothing but the math equations or the numbers which can be operated and related within the operations such as addition, subtraction, division and multiplication. Using these operations the related numbers can be calculated. The fact family math can be learned easily with the help of the basic operations. Now we are going to see the fact family math with some examples. Understanding Vector Addition Problems is always challenging for me but thanks to all math help websites to help me out.


About fact family math:


The fact family math can be understands easily by following the basic operations. Let us learn the fact family math with some examples.

Example:

Write the fact family math for the numbers such as 5, 7 and 12.

Solution:

We know these numbers are related as the fact family and can be given as follows,

The number 7 and 5 added to give 12.

7 + 5 = 12

If we add the number 5 to 7 then also it will be 12.

5 + 7 = 12

The number 5 can be obtained by subtracting the number 12 and 7

12 – 7 = 5

The number 7 can be obtained by subtracting the numbers 12 and 5.

12 – 5 = 7

Thus, the given numbers can be obtained by using the operations. These can be called as the fact family because certain numbers can be obtained by repeating the numbers with different operations.

Having problem with Normal Distribution Calculator keep reading my upcoming posts, i will try to help you.

Example for fact family math:

Find the family fact of the numbers such as 5 and 6 using multiplication and division?

Solution:

The family fact math numbers can be determined by using the multiplication and division numbers such as follows,

5 * 6 = 30

If we multiply 5 and 6 we get 30.

If we multiply the number 6 with number 5 again we get 30 only.

6 * 5 = 30.

The number 6 or 5 can be obtained again by dividing the numbers 30 by 5 to get 6.

` 30/5` = 6.

Now the number 5 can be obtained by dividing the numbers 30 by 6

`30/6` = 5.

The above are the facts of the numbers 5 and 6.

Radical Form in Math

Introduction to radical form in math:

Radicals is a form of symbol which is used in the mathematics. It is shown that the radical  symbol as  root "v". The number inside the radical symbol which is called as the radicand of the radical value, for example if the given value is square root of `sqrtx` . The x is called as the radicand which is the number inside the radical symbol root "v". There are more number of rooting methods available depending upon the value we have. The roots are square root `sqrtx` , cube root `root(3)(x)` , Fourth root `root(4)(x)` this up to nth root `root(n)(x)` . Here we are going to see about the radical form in math in different methods and the solved example problems on it.

Understanding How do you Simplify Radicals is always challenging for me but thanks to all math help websites to help me out.

Radical form in math - Some Properties:

Radicals form - Representations:

Function `a^(1/n)` :

The radical exponent  `a^(1/n) = root(n)(a)`

If n has odd value then,

If a is positive value then the function  `a^(1/n)` is positive.

If a is negative value then the function `a^(1/n)` is negative.

If a is zero value then the function `a^(1/n)` is also zero

If n has even value then,

If a is positive value then the function `a^(1/n)` is positive.

If a is negative value then the function `a^(1/n)` is not a real number.

If a is zero value then the function`a^(1/n)` is also zero

Radical Expression:

`x^(1/n) = root(n)(x)`    it is n root of x value.

Relation between expression and Radical:

`(x^(1/n))^n`   is the relation between the expression and radical .

Radical Exponent of Product:

`root(n)(axxb) = (axxb)^(1/n) = root(n)(a) xx root(n)(b) = a^(1/n) xx b^(1/n) `

Radical for a quotient:

`root(n)(a/b) = (a/b)^(1/n) = root(n)(a)/root(n)(b) = a^(1/n)/b^(1/n)`

Radical of a fraction:

`msqrta^n = a^(n/m) `


Radical form in math - Example Problems:


Radical form in math -  Problem 1:

Solve the radical form for 16.

Solution:

Method 1: Finding the square root of 16 by long division method

_4__
2)16 (
16
0
The value for the `sqrt 16` is 4

Method 2:

`sqrt16` = `sqrt(4^2)`

=` (4^2)^2`

= `(4)^(2/2)`

= 4

Radical form in math - Problem 2:

Solve radical value for 435

Solution:

The root value 435 is nearly equal to the square values between 20 and 21, because 202 = 225 and 212 = 256

Step 1: Divide 435 by 20.

`435 / 20` = 21.75

Step 2: Take average for 21.75 and 20.

` (21.75+20)/2 ` = 20.87500

Step 3: Divide 255 by 16

`435/20.87500 ` =  20.8383234



Step 4: Take average for the 20.8383234 and 20.87500

`( 20.8383234 + 20.87500)/2` =  20.8566617

Step 5: Now check the above result by taking square

20.8566617 2 =  435.000337

This value is more or less equal to 435

If the value is not equal repeat the step 3 and step 4

Is this topic Multiplicative Inverse hard for you? Watch out for my coming posts.

Radical form in math - Example Problems:


Problem 1:

Solve the radical value for 567

Answer: `sqrt 567` = 23.8117618

Problem 2:

Solve the radical val ue for 632

Answer: `sqrt 632` = 25.1396102

Student Problems in Math

Introduction to student problems in math:

Mathematics is the study of magnitude, structure, space, and modify. Mathematicians search for examples, formulate new inferences, and found truth by accurate deduction from correctly chosen theorems and explanation.

Students are allowed to solve the mathematics problems such as homework problems, practice problems and also providing the formulas and definitions. Homework problems are used to develop the knowledge of solving problems themselves. It includes algebra variant, geometry and so on...

I like to share this Volume of a Rectangular Prism Formula with you all through my article.

Example problems for students in math:


Student math problem 1:

A rectangular cabinet is of length 8 m and perimeter 22 m. Find the width of the cabinet.

Solution:

Length of cabinet, l   = 8m

Perimeter of cabinet = 22m

Width of cabinet       =w

Formula for perimeter of rectangle=2*(l + w).

Therefore we can substitute the value of l and p into the above formula,

2(l + w) =22

2(8 + w) = 22

Dividing by the value 2 on both sides,

8+w = 11

Subtracting the value 8 on both sides,

w =3

Therefore, width of rectangular cabinet is 3 m.

Answer: w= 3 m

Student math problem 2:

Solve the following equations using substitution method.

q = 2p

p + 2q = 5

Solution:

Step 1:

Given equations are q = 2p and p + 2q = 5.

The value of q is directly given in the first equation. So, substitute the value of q=2p in the second equation p + 2q = 5 and simplify.

Therefore, p + 2q = 5 becomes p + 2(2p) = 5.

p + 4p = 5

Add 4p and p.

5p = 5

Divide by the value 5 on both the sides to separate p.

p = 1

Step 2:

Substitute the value p = 1 to find the value of q.

Replace the value of p by 1 in the equation q=2p.

q = 2 (1)

q = 2

Step 3:

So, the solution of the given system of equations is (1, 2).

Answer: (1, 2)

I have recently faced lot of problem while learning Regular Polygon Area Formula, But thank to online resources of math which helped me to learn myself easily on net.

Practice problems for students in math:


1.  Solve the following equation using substitution method:

2p + q = 4

4p + 2q = 8

2. Find the area and perimeter of a rectangle whose length is 5 meter and width is 6 meter.

Answer for student problems:

1. Infinite many solutions

2.Area= 30 meter^2 and perimeter= 22 meter

Function in Math

Introduction for function in math:

Before giving the explanation of the function in math, we have to know, what is function in math? The function is nothing but the result of the given argument. The argument is also know as element of the function from the given set. Function is associated with domain and co domain. The element exists in domain which is also exactly one element in co domain.I like to share this Implicit Function with you all through my article.


Pre-requisite for function in math:


Constant and Variable:

The value will not be changed during the mathematical process is called constant. The value will be changed during the mathematical process is called variable.

Interval:

The subset of real number is called interval

Neighborhood:

In a number line the neighborhood of a real number is defined as a open interval of very small length.

Independent / Dependent Variable:

A variable is an independent variable when it has any arbitrary value. A variable is said to be dependent when its value depends on other variables.

Cartesian product:

The Cartesian product of the two sets A and B is denoted by A x B and is denoted as

Let A={ a1,a2,a3} B={b1,b2}

A x B={ (a1,b1),(a1,b2)(a2,b1)(a2,b2)(a3,b1)(a3,b2)}


Explanation of function in math:


A function is a special type of relation. If no two ordered pairs have same first element and different second element, the relation is called function. If two ordered pairs have same first element and different second element, the relation is called not a function. If the element x in the set A is associated with element x in the set B is called image of the function. The set of images is called range of the function. If the range of function in not equal to the co domain, those functions are called mapping.

Understanding Variable and Expressions is always challenging for me but thanks to all math help websites to help me out.

Types of function in math:


1. Identity function:

A function from a set A to the same set A is said to be an identity

2. Inverse of a function:

To define the inverse of a function f i.e. f−1 (read as ‘f inverse’), the

function f must be one-to-one and onto.

3. Constant function:

If the range of a function is a singleton set, the function is called a

constant function.

4. Linear function:

If a function f : R → R is defined in the form f(x) = ax + b then the function

is called a linear function. Here a and b are constants.

5. Polynomial function:

If f : R→R is defined by f(x) = an xn + an − 1 xn − 1+ …+ a1x + a0, where

a0, a1,…, an are real numbers, an≠0 then f is a polynomial function of degree n.

Integers and Math

Introduction to integers and math:
In mathematics, integer is one interesting topics in number representation. Integer has a set of numbers in which there are two difefrent types of integers that are non negative integers and negative integers. Integers have complete entity or unit. No fractional part in integers. Integers perform different arithmetic operations such as addition, subtraction, multiplication and division. Let us solve some example problems in integers and math.

Example for integers:

1254, -5365, 0 etc,

Having problem with Definition for Parallel Lines keep reading my upcoming posts, i will try to help you.

Example problems for integers and math:


Example 1:

Perform arithmetic operation addition for the given two integer numbers

875 + 432

Solution:

Given two integer numbers are

875 + 432

Both are two positive integers so, the result is also a positive numbers

Here we add 875 into 432, and then we get the result

875 + 432

1307

Solution to the given two integers is 1307.

Example 2:

Perform arithmetic operation subtraction for the given two integer numbers

1024 and 827

Solution:

Given two integer numbers are

1024 - 827

Here we subtract 1024 into 827, and then we get the result

1024 - 827

197

Solution to the given two integers is 197.

Example 3:

Perform arithmetic operation multiplication for the given two integer numbers

1524 × 1028

Solution:

Given two integer numbers are

1524 × 1028

Both are positive integers so, the result is also a positive numbers

Here we multiply 1524 into 1028, and then we get the result

1524 × 1028

1566672

Solution to the given two integers is 1566672.

Example 4:

Perform arithmetic operation division for the given two integer numbers

6000/ 150

Solution:

Given two integer numbers are

6000 / 150

Both are positive integers so, the result is also a positive numbers

Here we divide 6000 by 150, and then we get the result

6000/ 150

40

Solution to the given two integers is 40.

Example 5:

Perform arithmetic operation addition for the given two integer numbers

- 728 + 206

Solution:

Given two integer numbers are

- 728 + 206

- 728 is negative number and 206 is positive number

Here we add - 728 into 206, and then we get the result

- 728 + 206

- 522

Solution to the given two integers is - 522.

Please express your views of this topic practice problems for algebra 2 by commenting on blog.

Practice problems for integers and math:


Perform arithmetic operation for the given two integers and math are,

i). 3286 + 7025

ii). 5021 – 2856

iii). 481 × 200

iv). 540 / 20

v). – 258 + 625

vi) – 286 × 85

Solution:

i). 10311

ii). 2165

iii). 96200

iv). 27

v) 367

vi) – 24310

Word Problems Second Grade Math

Introduction to word problem:
In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a recursively presented group G is the algorithmic problem of deciding whether two words represent the same element. Although it is common to speak of the word problem for the group G strictly speaking it is a presentation of the group that does or does not have solvable word problem. (Source: Wikipedia)

Please express your views of this topic Linear Equation in Two Variables by commenting on blog.

Example of word problems second grade math


Math second grade word problem: 1

There are 109 boxes in the store. We bought 42 more boxes for the store. How many boxes are there in the store now?

Solution:

In 109 boxes in the store

And then we bought 42 boxes in the store

109 + 42 = 151

Therefore 151 boxes in the store now.

Math second grade word problem: 2

A fruit wholesaler had 128 grapes. He sold 52 grapes. How many grapes did he have left?

Solution:

Wholesaler 128 grapes

Sold 52 grapes

Left grapes =?

So, 128 – 52 = 76

He had totally 76 grapes left.

Math second grade word problem: 3

There are 11 pine apples in each box. How many are there in 8 boxes?

Solution:

In one box = 11 pine apples

In 8 boxes =?

11 * 8 = 88

There are 88 pine apples in 8 boxes.

Math second grade word problem: 4

Andrew bought a sack of 62 kg of flour. He packed the flour equally into 8 bags. How many kilograms of flour in the each bag?

Solution:

In one sack = 62 kg

Then 3 bags =?

64 ÷ 8 = 8

There were 8 kg of flour in each bag.

I have recently faced lot of problem while learning Acceleration Calculator, But thank to online resources of math which helped me to learn myself easily on net.

Practice - word problems second grade math


1. There are 1238 erasers in the store. We bought 53 more erasers for the store. How many erasers are there in the store now?

[Answer: 1291 erasers in the store now]

2. A vegetables seller had 563 potatoes. He sold 154 potatoes. How many potatoes did he have left?

[Answer: He had 162 oranges left]

3. There are 5 pine apples in each box. How many are there in 9 boxes?

[Answer: 45 pine apples in 9 boxes]

4. Arnold bought a sack of 90 kg of flour. He packed the flour equally into 10 bags. How many kilograms of flour in the each bag?

[Answer: 10 kg of flour in each bag]

Matrices in Math

Introduction to matrices in math:

In order to locate the position of a particular element of a matrix. We have to specify  the number of the row and that of  the column in which the element occurs. An element occurring in the ith row and jth column of a matrix A will be called the (i,j)th element of A , to be denoted by aij .

In general ,an m x n matrix A may be written as ,

A     =     `[[a_11,a_12,...,a_1n],[a_21,a_22,...,a_2n],[...,...,...,...],[a_m1,a_m2,...,a_mn]]`

Having problem with Solve Matrix keep reading my upcoming posts, i will try to help you.

Types of matrices:


Row matrix:

Row matrix is a matrix that contain only one row or a row vector.

Example :

(i) A = [aij]1 × 3 = [1 6 5] is a row matrix of order 1 × 3.

(ii) B = [bij]1 × 2 = [0  1] is a row matrix of order 1 × 2

(iii) C = [cij]1 × 1 = [1] is a row matrix of order 1 × 1

Column matrix:

A colum matrix is a matrix that contain  only one column  or a column vector.

Example :

1)[aij]mxn =`[[2],[4],[6]]` is a column matrices of order 3 x1

2)[aij]mxn =`[[0],[1]]` is a column matrices of order 2 x1

3)[aij]mxn =[45] is column matrices of order 1 x1

Square matrix:

A square  matrix is a matrix in which the elments in rows and columns are equal and a  matrix of order n × n is also known as a square matrix of order n.

Example :

1) `[[4,5],[5,4]]` is the square matces of order 2 x2

2) `[[1,2,3],[4,5,6],[7,8,9]]` is the square matrix of order 3 x3

3) `[[0,1,2,3],[2,1,4,5],[3,4,6,7],[0,6,7,8]]` is the square matrix of order 4 x4.

Diagonal matrix:

Diagonal matrix means  a  square matrix A = [aij]n × n is said to be a diagonal matrix if aij = 0 when i ? j. In a diagonal matrix all the entries except the entries along the main diagonal are zero.

Example :

1) `[[1,0,0],[0,2,0],[0,0,3]]` is the diagonal matrix of order 3 x3

2) `[[3,0],[0,7]]`   is the diagonal matrix of order 2 x2.

Zero matrix or null matrix or void matrix:

All the entries are zero in the given matrix then the matrix is said ti be a zero  matrix .

Example :

A = `[[0,0,0],[0,0,0],[0,0,0]]` is the null matrix  or zero matrix of order 3 x 3

Please express your views of this topic Sample Standard Deviation Calculator by commenting on blog.

Operation on Matrices in math:


Basic operation involved in matrix:

Addition of two matrices in math
Subtraction of matrices in Math
Multiplication of matrices in math.
Let  us discuss about the  operation of matrices in math.

1)Addition of matrices.

Let us consider the two different matrices of order 2 x2

A=`[[3,5],[4,7]]` and B= `[[1,8],[4,7]]`

A+B = `[[3+1,5+8],[4+4,7+7]]`

A+B =`[[4,13],[8,14]]`

Subtraction of two matrices:

Let us consider the two different matrices of order 2 x2

X= `[[4,6],[3,5]]` and Y =`[[5,7],[3,4]]`

X-Y =`[[4-5,6-7],[3-3,5-4]]`

X-Y =`[[-1,-1],[0,1]]`

Multiplication of two matrices:

Let us consider the two different matrices of order 2 x2

P = `[[4,5],[3,2]]` and Q =`[[2,3],[2,1]]`

PQ =`[[4*2 +5*2,4*3+2*1],[3*2+2*2,3*3+2*1]]`

PQ =`[[8+10,12+2],[6+4,9+2]]`

PQ =`[[18,14],[10,11]]`

6th Grade Math Probability

Introduction to 6th grade math Probability:

Probability is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems. (Source: Wikipedia)


Example problems for 6th grade math probability:


Example: 1

Two dice are rolled. A is the event that the sum of the numbers shown on the two dice is 5, and B is the event that at least one of the dice shows up a 3. Are the two events

(i) Mutually exclusive

(ii) Exhaustive? Give the arguments in support of your answer.

Solution:

When two dice are rolled, we have n(s) = (6 x 6) = 36.

Now, A = {(1, 4), (2,3),(4,1),(3,2)} and

B = {(3,1), (3,2), (3,3), (3,4), (3, 5), (3,6), (1,3), (2,3), (4,3), (5,3), (6,3)}

(i) A`nn`B = {(2,3), (3,2)} `!=` `phi` .

(ii) Also, A`uu`B `!=` s

Therefore A and B are not exhaustive events.

Example: 2

Two dices are rolled. Let A, B, C  be the event getting a sum of 2, a sum of 3 and a sum of 4 respectively. Then, show that

(i)    A is a simple event

(ii)   B and C are compound events

(iii)  A and B are mutually exclusive

Solution:

Clearly we have

A  = {(1, 1), B = (1,2),(2,1) and c = (1,3),(3,1),(2,2)}

(i) Since A consists of a single sample point, it is a simple event.

(ii) Since both B and C contain more than one sample point, each one of them is compound event.

(iv) Since A`nn` B =`phi`, A and B are mutually exclusive.

Please express your views of this topic Rules of Probability by commenting on blog.

Practice problems for 6th grade math probability:


1. From a well-shuffled deck of 52 cards, a card is drawn at random. Find the probability that the card drawn is

(i) red and a  king

(ii) Either red or a king

[Answer: (i) 1/26

(ii) 7/13]

2.The odds in favour of occurrence of an event are 5:12. Find the probability of the event.

[Answer: 5/17]

Answer Math Problems For You

Introduction to answer math problems:

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. I like to share this Small Sample Size Statistics with you all through my article.

Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and problems of game theory.

SOURCE: WIKIPEDIA


Examples of answer math problems:


Math problem 1:

Solve the equation 5(-3y - 2) - (y - 3) = -4(4y + 5) + 13

Solution:

Given the equation 5(-3y - 2) - (y - 3) = -4(4y + 5) + 13

First we can multiply the factors for both left hand side and right hand side.

-15y - 10 - y + 3 = -16y - 20 +13

Here we can group the like terms on both sides. Then we get.

-16y - 7 = -16y – 7

Add 16y+7 on both sides. Then we get the final answer.

0=0

Therefore all real numbers are possible solution to the given equation.

Math problem 2:

Solve p: 2p – 4q = 9

Solution:

Given 2p– 4q=9

If we can find p intercept value we set the q=0.

Then we can find the p value.

Substitute the value of q (q=0) into the above equation.

2p– 4(0) =9

2p– 0=9

2p=9

Divide by the value 2 on both sides. Then we get the final answer.

`(2p)/2` =`9/2`

p=`9/2`

Answer: `9/2`

Math problem 3:

Find the area of following figure:

Solution:

Given length= 15 ft and width= 7 ft

We can find the area of rectangle by using the following formula:

Area A= length*width or (l*w)

Substitute the value of l and w into the above formula and then we get the final answer.

Area A= 15*7

= 105 ft2

Answer: 105 ft2

I have recently faced lot of problem while learning Volume Sphere, But thank to online resources of math which helped me to learn myself easily on net.

Practice problems of math:


Problems:

Solve x: 10+5x=50
Solve y: 2y+3x=5
Find the perimeter of square with the side value 5 cm.
Answer key:

x= 8
y=`5/2`
20 cm

Superstar Math Answers

Introduction to superstar answers:

The fundamental concepts of algebra, number, measurement, and geometry. Simple addition, subtraction, multiplication, and conservation are performed in the number. The Superstars program is to provide extra challenge that self- motivated to the students. More number of way to solve any problem. But student wants to know the shortcut methods. This shortcut method is one of the best way to study the math’s and easily understand the concept.


Math superstar answers:


Superstar math problem 1:

Rohit saw 4 cow and 2 dogs outside. How many legs did he see?

Solution:                          4 cow = 16 legs

2 dogs = 8 legs

8 + 16 = 24 legs

Answer:  24 legs

Superstar math problem 2:

Nijam have 5 nickel and 3 pennies, how much money do he have all together?

Solution:                   1 nickel = 5 pennies

So, 5 nickel = 25 pennies

Total = 25 + 3 = 28 pennies

Answer:  28 pennies

Superstar math problem 3:

Reena saw eight triangles, how many sides are there all together on eight triangles?

Solution:                                 1 triangle has 3 sides

8 triangle has 8 × 3 = 24 sides

Answer:  24 sides

Superstar math problem 4:

There are 5 cars and 6 tricycles in the neighbor's garage. How many wheels are there in all? Forget about any "spare tires"!

Solution:             20 wheels on the 5 cars,  and 18 on the 6 tricycles

Total = 20 + 18 = 38

Answer:  38wheels

Superstar math problem 5:

Martin has 16 balls, half of them are red. How many are Red?

Solution:                                  Total balls = 16

Half of ball = `16/2` = 8

Answer: 8 Red balls

Superstar math problem 6:

If the 22th day of the month falls on Thursday, on what day did the 11th fall?

Solution:   The calendar or make a chart with “Su, M, T, W, Th, F, Sa” at the top and begin numbering

backward putting 24 under Saturday. The date 17th and 10th must be fall on Saturdays and count Forward one

from the 10th.

Answer:  Sunday

Superstar math problem 7:

The sum of 3 consecutive numbers is 555. What are the numbers?

Solution:   We can use guess-check-revise method. Some students know that the numbers they seek are about `1/3`

of the total, and approximate the numbers by dividing 555 by 3. This gives 185, which is the middle number.

Answer:  184, 185, 186

Superstar math problem 8:

How many corners are on 3 triangles and 2 rectangles?

Solution:                                      1 triangle = 3 corners

1 rectangle = 4 corners

So, 3 triangle and 1 rectangle = (3 * 3) + (2 * 4) = 9 + 8 = 17 corners

Answer: 17 corners

Superstar math problem 9:

Together, 12 cars and 6 bikes weigh 1050 pounds. The bikes all weigh the same -- x pounds. Each cars weighs 55 pounds.

What is the  weigh of one bike?

Solution:      First finding the total weight of the 12cars: 12 × 55 = 660 pounds. Then they

will calculate 1050 - 660 = 390 pounds, the weight of the 6 bikes = 390 pounds.

So weight of one bike = ` 390 / 6` = 65 pounds per bike

Answer:  65pounds

Superstar math problem 10:

Find the side of the square if the perimeter of square is 20 m.

Solution:            The perimeter formula for square = 4a

4a = 20

a = ` 20/4` = 5 m

Answer: The side of the square 5m

I Need a Math Function

Introduction to math function:

The mathematical concept of a function expresses the intuitive idea that one quantity (the argument of the function, also known as the input) completely determines another quantity (the value, or the output). A function assigns a unique value to each input of a specified type.(source : wikipedia)

An example, the function f(x) = 5x, which assigns to all real number the real number that is three times as big. In this case, we can write f (3) = 15. Please express your views of this topic Types of Functions by commenting on blog.


Examples problem for math function:


1. Add the two function for given functions, f (x) = 6x + 6 and g (x) = 2x + 5 when x = 4 find f (4) + g (4).

Solution:

Given function is f (x) = 6x + 6 and g (x) = 2x + 5

Add the two functions,

f (x) + g (x) = 6x + 6 + 2x + 5

Combine the terms,

= 6x + 2x + 6 + 5

Add the terms,

= 8x + 11

f (x) + g (x) = 8x + 11

When x = 4,

Find the f (4) + g (4),

f (4) + g (4) = 8x +11

Plug x = 4 in the equation,

= 8 (4) + 11

= 32 + 11

= 43

The solution of f (4) + g (4) is 43.

2. Subtract the two function for given functions, f (x) = 3x + 15 and g (x) = 9x + 5 when x = 3 find f (3) + g (3).

Solution:

Given function is f (x) = 3x + 15 and g (x) = 9x + 5

Subtract the two functions,

f (x) + g (x) = 3x + 15 - 9x - 5

Combine the terms,

= 3x - 9x + 15 - 5

Subtract the terms,

= -6x + 10

f (x) + g (x) = -6x + 10

When x = 3,

Find the f (3) + g (3),

f (3) + g (3) = -6x + 10

Plug x = 3 in the equation,

= -6 (3) + 10

= -18 + 10

= -8

The solution of f (3) + g (3) is -8.

Is this topic Obtuse Angle Images hard for you? Watch out for my coming posts.

More examples problem for math function:


3. Multiply the two function for given functions, f (x) = x + 5 and g (x) = 2x + 2 when x = 5 find f (5) + g (5).

Solution:

Given function is f (x) = x + 5 and g (x) = 2x + 2

Multiply the two functions,

f (x) + g (x) = (x + 5) × (2x + 2)

Multiply the terms,

= 2x2 + 10x + 2x + 10

Combine the terms,

= 2x2 + 12x + 10

f (x) + g (x) = 2x2 + 12x + 10

When x = 5,

Find the f (5) + g (5),

f (5) + g (5) = 2x2 + 12x + 10

Plug x = 8 in the equation,

= 2(52) + 12 (5) + 10

= 50 + 60 + 10

= 120

The solution of f (5) + g (5) is 120.