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Below are examples of basic math problems that can be solved.

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Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 × b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

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Below are examples of Pre-Algebra math problems that can be solved.

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Below are examples of Algebra math problems that can be solved.

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Below are examples of Precalculus math problems that can be solved.

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Below are examples of Calculus math problems that can be solved.

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Below are examples of Statistics problems that can be solved.

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Below are examples of Finite Math problems that can be solved.

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Example 1 - Find the inverse of the 2x2 matrix below :

Matrix Algebra

A matrix is a rectangular array of numbers, symbols, and expressions arranged in rows and columns.The size of a matrix is defined by the number of rows and columns in it. If a matrix contains m rows and n columns then it is said to be a matric of m x n size.

A matrix with the same number of rows and columns is called a square matrix .

While performing addition or subtraction, add/subtract each element in the first matrix with the corresponding element in the second matrix. Addition and subtraction can be only performed between the matrices of the same size and the resultant matrix is also of the same size .

While Multiplying two matrices the elements of rows in the first matrix are multiplied with the corresponding columns in the second matrix. The first element of the first matrix is multiplied with each element of first column of the second matrix , the summation becomes the first entry of the resultant column, in the same way, we can find the product of two matrices.

Multiplication can be performed between the two matrices only if the no. of columns in the first matrix is equal to the no. of rows in the second matrix. If the dimensions of the first matrix are AxB and the dimensions of the second matrix are BxC then the resultant matrix would be AxC.

An identity matrix is a diagonal matrix in which all the diagonal elements are 1 and all the remaining elements are 0.

Calculus is a branch of mathematics that studies continuous change,it is basically used to study or work with very small quantities. Calculus is used to gain more understanding of the nature of space, time and motion.

The two main branches of Calculus are:

The equation representing the relationship between the quantity that continuously varying concerning in another quantity.

Eg. f(x)=dy/dx is a differential equation.

Order of differential equation: Order of the highest order derivative present in the differential equation.

Degree of Differential equation: The power of highest order derivative is the degree of differential equation.

Integral Calculus : Integral calculus integrates small pieces to find the whole.Integrals are of two types: 1. Definite Integral 2. Indefinite Integral. Integration is the process of finding the antiderivative. Eg. x n dx = x n+1 /n+1 + c C is called the integration constant.

Linear System

A Linear system is nothing but the collection of linear equations involving the same set of variables. The solution of a linear system is the values of variables that satisfy all the linear equations. You have to enter the coefficients of variables in a matrix and constants in another matrix, our calculator will deliver the results you were looking for.

All the linear equations in a linear system have same set of variables of order one and each equation forms a straight line on the graphs.

Quadratic Equations

Any equation with degree 2 is a quadratic equation . A quadratic equation is in the form of ax 2 +bx+c=0 , the solution of a quadratic equation is given by, x = ( -b ± √ b 2 -4ac ) / 2a .

These solutions can be given in the form of real numbers or complex numbers.

Visualization

Visualization is used to represent the given equations on the graphs or 2d plane.A linear equation always forms a straight line on the graph whereas a quadratic equation with real solutions forms a curve.

Simplification

To solve an equation it is important to simplify it to write it in the simplest form.Different methods for simplifying an expression are:

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Math is the study of numbers, space, and structure.

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Mathematical equations can often be confusing, but there are ways to make them clearer. By using simple language and breaking the equation down into smaller pieces, you can help your reader understand what the equation is trying to say.

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Equivalent math meaning

In math, equivalent is different from equal. Equal means same in all aspects, whereas equivalent means similar but not identical. For example, 2 is said to be equal to 2 but equivalent to 1 + 1.

Equivalent expressions

Equivalence relation

Clear up math problems

When it comes to math, it's important to be able to clarify tasks in order to complete them effectively.

Enhance your educational performance

No matter what math challenge you're facing, remember to stay calm and think things through clearly. With a bit of effort, you'll be able to overcome any obstacle!

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Equivalent Definition (Illustrated Mathematics Dictionary)

Equivalent definitions of mathematical structures

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