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Algebra is a branch of mathematics that uses letters and symbols to represent numbers and quantities in expressions and equations. Key terms in algebra include variables, which can represent different numbers; replacement sets, which define the possible values a variable can take; and constants, which always represent the same number. Algebraic expressions combine variables, constants, and operation symbols using grouping symbols and relationship symbols to represent a mathematical relationship between quantities.

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Multiplication of algebraic expressions

Algebra is the study of mathematical symbols and rules for calculating those symbols, which allows numbers to be represented by variables. An algebraic expression combines constants and variables using operations like addition, subtraction, multiplication and division. Expressions can be monomials with one term, binomials with two terms, or trinomials with three terms. To multiply algebraic expressions, the signs and coefficients are multiplied, and the variables are multiplied using exponent rules.

Evaluating Algebraic Expressions

This document discusses expressions and equations. It defines an expression as not containing an equal sign, while equations do. There are two types of expressions: numerical expressions containing only numbers, and algebraic expressions containing numbers, symbols, and variables. A variable represents an unknown value and can be any letter. The document provides examples of evaluating algebraic expressions by substituting numbers for variables.

Algebraic expressions and terms

The document defines key terms used in algebraic expressions:
1) A variable represents an unknown value and can be letters or symbols like "B" in the expression "12 + B".
2) An algebraic expression uses variables with numbers and operations like "a + 2" or "3m + 6n - 6".
3) A coefficient is the number multiplied by a variable, like 6 is the coefficient of m in the expression "6m + 5".
4) A term refers to a number, variable, or their combination using multiplication or division, like "a" and "2" are terms in "a + 2".
5) A constant is a number that cannot change

Algebraic expressions

The document defines key terms in algebra including variables, expressions, constants, coefficients, terms, and evaluating expressions. It provides examples of writing algebraic expressions from word phrases and evaluating expressions. Tables are included showing how to complete expressions when given values for variables.

Angles

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Inclusions of the file attachment:
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* Soft copy of the WHOLE ppt slides with effects
ACCEPTING COMMISSIONED POWERPOINT SLIDES
ACCEPTING COMMISSIONED POWERPOINT SLIDES
ACCEPTING COMMISSIONED POWERPOINT SLIDES
EMAIL queenyedda@gmail.com
- - - - - - - - - - - - -
- Definition of Angles
- Parts of Angles
- Protractor
- Kinds of Angles
- Measuring Angles
The Assignment on the last slide is for them to have a background on the next lesson.

Rational numbers in the number line

1) Rational numbers are numbers that can be written as a quotient of two integers, such as a/b where b does not equal 0. They include integers as well as fractions and terminating or repeating decimals.
2) The document provides examples of rational numbers and asks students to determine if examples are rational numbers and to plot them on a number line.
3) Students are given practice locating rational numbers on a number line, such as -5/3, and asked to plot multiple rational numbers on a single number line.

INTRODUCTION TO ALGEBRA

This document provides an overview of the key concepts in the language of algebra. It defines algebra as the branch of mathematics involving expressions with variables. Algebraic expressions combine numbers and variables using letters, symbols, and operation symbols. The language of algebra consists of numerals, variables to represent unknown numbers, constants, and operational symbols to express addition, subtraction, multiplication, and division of expressions. It also defines important terminology like terms, expressions, coefficients and evaluates sample expressions.

Variable and Algebraic Expressions

1. The document provides examples and explanations for evaluating algebraic expressions by substituting values for variables.
2. It gives examples of evaluating expressions involving addition, subtraction, multiplication, division, and order of operations.
3. Students are asked to evaluate expressions for given variable values to check their understanding.

Multiplication of algebraic expressions

Algebra is the study of mathematical symbols and rules for calculating those symbols, which allows numbers to be represented by variables. An algebraic expression combines constants and variables using operations like addition, subtraction, multiplication and division. Expressions can be monomials with one term, binomials with two terms, or trinomials with three terms. To multiply algebraic expressions, the signs and coefficients are multiplied, and the variables are multiplied using exponent rules.

Evaluating Algebraic Expressions

This document discusses expressions and equations. It defines an expression as not containing an equal sign, while equations do. There are two types of expressions: numerical expressions containing only numbers, and algebraic expressions containing numbers, symbols, and variables. A variable represents an unknown value and can be any letter. The document provides examples of evaluating algebraic expressions by substituting numbers for variables.

Algebraic expressions and terms

The document defines key terms used in algebraic expressions:
1) A variable represents an unknown value and can be letters or symbols like "B" in the expression "12 + B".
2) An algebraic expression uses variables with numbers and operations like "a + 2" or "3m + 6n - 6".
3) A coefficient is the number multiplied by a variable, like 6 is the coefficient of m in the expression "6m + 5".
4) A term refers to a number, variable, or their combination using multiplication or division, like "a" and "2" are terms in "a + 2".
5) A constant is a number that cannot change

Algebraic expressions

The document defines key terms in algebra including variables, expressions, constants, coefficients, terms, and evaluating expressions. It provides examples of writing algebraic expressions from word phrases and evaluating expressions. Tables are included showing how to complete expressions when given values for variables.

Angles

This preview may not appear the same on the actual version of the PPT slides.
Some formats may change due to font and size settings available on the audience's device.
To get/buy a soft copy, please send a request to queenyedda@gmail.com
Inclusions of the file attachment:
* Fonts used
* Soft copy of the WHOLE ppt slides with effects
ACCEPTING COMMISSIONED POWERPOINT SLIDES
ACCEPTING COMMISSIONED POWERPOINT SLIDES
ACCEPTING COMMISSIONED POWERPOINT SLIDES
EMAIL queenyedda@gmail.com
- - - - - - - - - - - - -
- Definition of Angles
- Parts of Angles
- Protractor
- Kinds of Angles
- Measuring Angles
The Assignment on the last slide is for them to have a background on the next lesson.

Rational numbers in the number line

1) Rational numbers are numbers that can be written as a quotient of two integers, such as a/b where b does not equal 0. They include integers as well as fractions and terminating or repeating decimals.
2) The document provides examples of rational numbers and asks students to determine if examples are rational numbers and to plot them on a number line.
3) Students are given practice locating rational numbers on a number line, such as -5/3, and asked to plot multiple rational numbers on a single number line.

INTRODUCTION TO ALGEBRA

This document provides an overview of the key concepts in the language of algebra. It defines algebra as the branch of mathematics involving expressions with variables. Algebraic expressions combine numbers and variables using letters, symbols, and operation symbols. The language of algebra consists of numerals, variables to represent unknown numbers, constants, and operational symbols to express addition, subtraction, multiplication, and division of expressions. It also defines important terminology like terms, expressions, coefficients and evaluates sample expressions.

Variable and Algebraic Expressions

1. The document provides examples and explanations for evaluating algebraic expressions by substituting values for variables.
2. It gives examples of evaluating expressions involving addition, subtraction, multiplication, division, and order of operations.
3. Students are asked to evaluate expressions for given variable values to check their understanding.

Algebraic expressions

1. An algebraic expression is a combination of numbers, variables, and operation symbols. It can be classified as a monomial, binomial, or trinomial based on the number of terms.
2. Like terms contain the same variables raised to the same powers, while unlike terms do not. Multiplication of algebraic expressions follows rules such as the product of like signs being positive and unlike signs being negative.
3. There are special product identities for multiplying binomials and factoring algebraic expressions through grouping and finding greatest common factors. Division of algebraic expressions also follows rules regarding the signs of the quotient.

Integers and Absolute Value

This document discusses integers and absolute value. It defines integers as positive and negative whole numbers and explains how to graph and order integers on a number line. It also defines absolute value as the distance from zero and how to evaluate the absolute value of integers, including that the absolute value of a number can never be negative. Examples are provided for graphing, ordering, and finding opposites and absolute values of integers.

Algebra Expressions and Equations

This document provides an introduction to expressions and equations in Algebra I. It explains that expressions do not contain equals signs, while equations do. Students will practice writing verbal expressions and equations from algebraic forms, and vice versa. They will learn key words associated with addition, subtraction, multiplication, division, powers, and the equals sign. The homework is to complete worksheet 1-1 and bring a picture for a class board.

Translating Expressions

The document provides examples and explanations for translating word problems and phrases into algebraic expressions. It gives examples such as "18 less than a number" being translated to "x - 18" and "the product of a number and 5" being "5n". It also provides word problems like writing an expression for the total cost of admission plus rides at a county fair. The document teaches learners how to identify keywords that indicate mathematical operations when translating word phrases into algebraic notation.

Introduction to algebra

Algebra uses letters and symbols to represent values and their relationships, especially for solving equations. An algebraic expression combines these letters and symbols. An example expression is 8x^2. Expressions contain constants, variables, and exponents. Constants represent exact values like numbers. Variables stand for unknown values, often letters. Exponents written above a variable show how many times it is used in the expression.

Adding Polynomials

This document defines polynomials and describes how to perform operations on them such as addition and subtraction. It provides examples of adding and subtracting monomials and polynomials. Monomials are terms with variables and coefficients, and polynomials are the sum of monomials. Like terms refer to monomials with the same variables and exponents that can be combined. To add polynomials, like terms are lined up and their coefficients are summed. To subtract polynomials, the operation is changed to addition by using the keep-change-change method and then like terms are combined.

Square and square roots

This document provides an overview of squaring numbers and finding square roots. It discusses key concepts such as:
- Squaring a number means multiplying a number by itself
- Perfect squares are numbers that can be written as the square of a whole number
- The square root of a number is another number that, when multiplied by itself, equals the original number
- Examples are provided of finding the square of numbers and the square roots of perfect squares.

algebraic expression

This document provides an overview of algebraic expressions and identities. It defines terms, factors, coefficients, monomials, binomials, polynomials, like and unlike terms. It explains how to perform addition, subtraction, multiplication, and division of algebraic expressions. It also defines what an identity is and how to apply identities.

Trapezoids

This document defines and describes properties of trapezoids and isosceles trapezoids. It defines a trapezoid as a quadrilateral with one set of parallel sides, called bases, and defines an isosceles trapezoid as having two congruent legs. The key properties outlined are that the leg angles are supplementary, base angles and diagonals of an isosceles trapezoid are congruent, and the midsegment of a trapezoid connects the midpoints of the legs and is parallel to the bases. Several example problems are provided to demonstrate applying these properties.

Geometry presentation

Geometry is the branch of mathematics concerned with properties of points, lines, angles, curves, surfaces and solids. It involves visualizing shapes, sizes, patterns and positions. The presentation introduced basic concepts like different types of lines, rays and angles. It also discussed plane figures from kindergarten to 8th grade, including classifying shapes by number of sides. Space figures like cubes and pyramids were demonstrated by having students construct 3D models. The concepts of tessellation, symmetry, and line of symmetry were explained.

Adding and subtracting polynomials

Adding and subtracting polynomials involves combining like terms. Like terms are terms that have the same variables and the same exponents. To add polynomials, terms are grouped by their like terms and the coefficients are combined by adding them. To subtract polynomials, the process is the same as adding the opposite of the second polynomial. The opposite of each term is found by changing its sign. Then the like terms are combined in the same way as when adding.

Quadratic inequality

This document discusses solving quadratic inequalities. It provides examples of single-variable quadratic inequalities and explains how to find the solution set by first setting the inequality equal to an equation, solving for the roots, and then testing values within the intervals formed by the roots. The document also introduces quadratic inequalities with two variables and how to represent them. It defines a quadratic inequality and explains the process of solving them by relating it back to solving a quadratic equation.

Simplifying algebraic expressions

1. The document provides instruction on simplifying algebraic expressions. It gives examples of identifying like terms and combining like terms by adding or subtracting coefficients.
2. Examples are provided to simplify expressions and write expressions for perimeter of triangles. Students are asked to justify steps using properties of algebra.
3. A quiz assesses identifying like terms, simplifying expressions, and writing expressions for perimeters of figures.

Classifying Polynomials

The document defines key concepts for classifying algebraic expressions, including:
- Monomials have one term, binomials have two terms, and trinomials have three terms.
- The degree of a polynomial with one variable is the highest exponent, and with multiple variables it is the highest sum of exponents.
- A polynomial can be classified by the number of terms and its degree. The leading coefficient is the coefficient of the highest degree term.

Absolute values

- The document discusses solving absolute value equations and inequalities.
- Absolute value equations will have two solutions, which are found by setting the expression inside the absolute value signs equal to the positive and negative of the right side of the equation.
- Absolute value inequalities require graphing the solutions on a number line. If the sign is >, the solutions are to the right. If <, the solutions are to the left.
- A multi-step example of solving an absolute value inequality is worked through.

Inequalities

This document discusses inequalities and the rules for solving them. It defines inequalities as math problems containing less than, greater than, less than or equal to, and greater than or equal to symbols. It explains that a solution to an inequality is a number that makes the inequality a true statement when substituted for the variable. It outlines three rules for manipulating inequalities: 1) adding or subtracting the same quantity to both sides, 2) multiplying or dividing both sides by a positive number, and 3) reversing the inequality sign when multiplying or dividing by a negative number. It emphasizes that the solution to an inequality should always be expressed as an interval.

POLYNOMIALS

The document discusses polynomials and polynomial functions. It defines a polynomial as a sum of monomials, with a monomial being a variable or the product of a variable and real numbers with whole number exponents. It classifies polynomials by degree and number of terms, with examples of common types like linear, quadratic, and cubic polynomials. It also defines a polynomial function as a function represented by a polynomial, and discusses finding sums, differences, and writing polynomials in standard form.

Absolute value

This document discusses integers and absolute values. It defines integers as numbers to the left and right of zero, with negative integers being less than zero and positive integers being greater than zero. Absolute value is defined as the distance a number is from zero on the number line. Examples demonstrate graphing integers on a number line and performing calculations with absolute values.

Polynomials Mathematics Grade 7

The document defines terms related to polynomials such as numerical coefficient, literal coefficient, degree, similar terms, monomial, binomial, trinomial, multinomial. It also defines the different kinds of polynomials according to the number of terms and degree such as constant, linear, quadratic, cubic, quartic, quintic polynomials. It provides examples of determining the degree, kind according to number of terms, leading term, leading coefficient of a polynomial and writing it in standard form.

Parts of a circle

The document defines a circle as a closed curve where all points are equidistant from the center. It lists and describes the main parts of a circle, including the radius, diameter, chord, tangent line, secant line, central angle, and inscribed angle. The radius is the line from the center to the circumference, the diameter passes through the center and is twice the length of the radius, and a chord connects two points on the circle.

Week 2 (Algebraivc Expressions and Polynomials).pptx

This document defines key concepts in algebra including constants, variables, algebraic expressions, polynomials, and the degree of polynomials. It explains that constants represent fixed values while variables represent unknown numbers. Algebraic expressions use variables, numbers, and operations. Polynomials are expressions with no negative exponents or fractions containing terms with variables and their powers. The degree of a polynomial refers to the highest power of its terms, with monomials having one term, binomials two terms, and trinomials three terms. The document provides examples and exercises to illustrate these algebraic concepts.

thelanguageofalgebra-191009022844 (2).pptx

This document provides an overview of the key concepts in the language of algebra. It discusses that algebra involves expressions with variables, and algebraic expressions combine numbers with variables using letters and operation symbols. The language of algebra contains numerals, variables to represent unknown numbers, constants, and operational symbols to represent addition, subtraction, multiplication, and division. It provides examples of translating word phrases to algebraic expressions and defines terms like algebraic terms, expressions, coefficients and evaluating expressions by substitution.

Algebraic expressions

1. An algebraic expression is a combination of numbers, variables, and operation symbols. It can be classified as a monomial, binomial, or trinomial based on the number of terms.
2. Like terms contain the same variables raised to the same powers, while unlike terms do not. Multiplication of algebraic expressions follows rules such as the product of like signs being positive and unlike signs being negative.
3. There are special product identities for multiplying binomials and factoring algebraic expressions through grouping and finding greatest common factors. Division of algebraic expressions also follows rules regarding the signs of the quotient.

Integers and Absolute Value

This document discusses integers and absolute value. It defines integers as positive and negative whole numbers and explains how to graph and order integers on a number line. It also defines absolute value as the distance from zero and how to evaluate the absolute value of integers, including that the absolute value of a number can never be negative. Examples are provided for graphing, ordering, and finding opposites and absolute values of integers.

Algebra Expressions and Equations

This document provides an introduction to expressions and equations in Algebra I. It explains that expressions do not contain equals signs, while equations do. Students will practice writing verbal expressions and equations from algebraic forms, and vice versa. They will learn key words associated with addition, subtraction, multiplication, division, powers, and the equals sign. The homework is to complete worksheet 1-1 and bring a picture for a class board.

Translating Expressions

The document provides examples and explanations for translating word problems and phrases into algebraic expressions. It gives examples such as "18 less than a number" being translated to "x - 18" and "the product of a number and 5" being "5n". It also provides word problems like writing an expression for the total cost of admission plus rides at a county fair. The document teaches learners how to identify keywords that indicate mathematical operations when translating word phrases into algebraic notation.

Introduction to algebra

Algebra uses letters and symbols to represent values and their relationships, especially for solving equations. An algebraic expression combines these letters and symbols. An example expression is 8x^2. Expressions contain constants, variables, and exponents. Constants represent exact values like numbers. Variables stand for unknown values, often letters. Exponents written above a variable show how many times it is used in the expression.

Adding Polynomials

This document defines polynomials and describes how to perform operations on them such as addition and subtraction. It provides examples of adding and subtracting monomials and polynomials. Monomials are terms with variables and coefficients, and polynomials are the sum of monomials. Like terms refer to monomials with the same variables and exponents that can be combined. To add polynomials, like terms are lined up and their coefficients are summed. To subtract polynomials, the operation is changed to addition by using the keep-change-change method and then like terms are combined.

Square and square roots

This document provides an overview of squaring numbers and finding square roots. It discusses key concepts such as:
- Squaring a number means multiplying a number by itself
- Perfect squares are numbers that can be written as the square of a whole number
- The square root of a number is another number that, when multiplied by itself, equals the original number
- Examples are provided of finding the square of numbers and the square roots of perfect squares.

algebraic expression

This document provides an overview of algebraic expressions and identities. It defines terms, factors, coefficients, monomials, binomials, polynomials, like and unlike terms. It explains how to perform addition, subtraction, multiplication, and division of algebraic expressions. It also defines what an identity is and how to apply identities.

Trapezoids

This document defines and describes properties of trapezoids and isosceles trapezoids. It defines a trapezoid as a quadrilateral with one set of parallel sides, called bases, and defines an isosceles trapezoid as having two congruent legs. The key properties outlined are that the leg angles are supplementary, base angles and diagonals of an isosceles trapezoid are congruent, and the midsegment of a trapezoid connects the midpoints of the legs and is parallel to the bases. Several example problems are provided to demonstrate applying these properties.

Geometry presentation

Geometry is the branch of mathematics concerned with properties of points, lines, angles, curves, surfaces and solids. It involves visualizing shapes, sizes, patterns and positions. The presentation introduced basic concepts like different types of lines, rays and angles. It also discussed plane figures from kindergarten to 8th grade, including classifying shapes by number of sides. Space figures like cubes and pyramids were demonstrated by having students construct 3D models. The concepts of tessellation, symmetry, and line of symmetry were explained.

Adding and subtracting polynomials

Adding and subtracting polynomials involves combining like terms. Like terms are terms that have the same variables and the same exponents. To add polynomials, terms are grouped by their like terms and the coefficients are combined by adding them. To subtract polynomials, the process is the same as adding the opposite of the second polynomial. The opposite of each term is found by changing its sign. Then the like terms are combined in the same way as when adding.

Quadratic inequality

This document discusses solving quadratic inequalities. It provides examples of single-variable quadratic inequalities and explains how to find the solution set by first setting the inequality equal to an equation, solving for the roots, and then testing values within the intervals formed by the roots. The document also introduces quadratic inequalities with two variables and how to represent them. It defines a quadratic inequality and explains the process of solving them by relating it back to solving a quadratic equation.

Simplifying algebraic expressions

1. The document provides instruction on simplifying algebraic expressions. It gives examples of identifying like terms and combining like terms by adding or subtracting coefficients.
2. Examples are provided to simplify expressions and write expressions for perimeter of triangles. Students are asked to justify steps using properties of algebra.
3. A quiz assesses identifying like terms, simplifying expressions, and writing expressions for perimeters of figures.

Classifying Polynomials

The document defines key concepts for classifying algebraic expressions, including:
- Monomials have one term, binomials have two terms, and trinomials have three terms.
- The degree of a polynomial with one variable is the highest exponent, and with multiple variables it is the highest sum of exponents.
- A polynomial can be classified by the number of terms and its degree. The leading coefficient is the coefficient of the highest degree term.

Absolute values

- The document discusses solving absolute value equations and inequalities.
- Absolute value equations will have two solutions, which are found by setting the expression inside the absolute value signs equal to the positive and negative of the right side of the equation.
- Absolute value inequalities require graphing the solutions on a number line. If the sign is >, the solutions are to the right. If <, the solutions are to the left.
- A multi-step example of solving an absolute value inequality is worked through.

Inequalities

This document discusses inequalities and the rules for solving them. It defines inequalities as math problems containing less than, greater than, less than or equal to, and greater than or equal to symbols. It explains that a solution to an inequality is a number that makes the inequality a true statement when substituted for the variable. It outlines three rules for manipulating inequalities: 1) adding or subtracting the same quantity to both sides, 2) multiplying or dividing both sides by a positive number, and 3) reversing the inequality sign when multiplying or dividing by a negative number. It emphasizes that the solution to an inequality should always be expressed as an interval.

POLYNOMIALS

The document discusses polynomials and polynomial functions. It defines a polynomial as a sum of monomials, with a monomial being a variable or the product of a variable and real numbers with whole number exponents. It classifies polynomials by degree and number of terms, with examples of common types like linear, quadratic, and cubic polynomials. It also defines a polynomial function as a function represented by a polynomial, and discusses finding sums, differences, and writing polynomials in standard form.

Absolute value

This document discusses integers and absolute values. It defines integers as numbers to the left and right of zero, with negative integers being less than zero and positive integers being greater than zero. Absolute value is defined as the distance a number is from zero on the number line. Examples demonstrate graphing integers on a number line and performing calculations with absolute values.

Polynomials Mathematics Grade 7

The document defines terms related to polynomials such as numerical coefficient, literal coefficient, degree, similar terms, monomial, binomial, trinomial, multinomial. It also defines the different kinds of polynomials according to the number of terms and degree such as constant, linear, quadratic, cubic, quartic, quintic polynomials. It provides examples of determining the degree, kind according to number of terms, leading term, leading coefficient of a polynomial and writing it in standard form.

Parts of a circle

The document defines a circle as a closed curve where all points are equidistant from the center. It lists and describes the main parts of a circle, including the radius, diameter, chord, tangent line, secant line, central angle, and inscribed angle. The radius is the line from the center to the circumference, the diameter passes through the center and is twice the length of the radius, and a chord connects two points on the circle.

Algebraic expressions

Algebraic expressions

Integers and Absolute Value

Integers and Absolute Value

Algebra Expressions and Equations

Algebra Expressions and Equations

Translating Expressions

Translating Expressions

Introduction to algebra

Introduction to algebra

Adding Polynomials

Adding Polynomials

Square and square roots

Square and square roots

algebraic expression

algebraic expression

Trapezoids

Trapezoids

Geometry presentation

Geometry presentation

Adding and subtracting polynomials

Adding and subtracting polynomials

Quadratic inequality

Quadratic inequality

Simplifying algebraic expressions

Simplifying algebraic expressions

Classifying Polynomials

Classifying Polynomials

Absolute values

Absolute values

Inequalities

Inequalities

POLYNOMIALS

POLYNOMIALS

Absolute value

Absolute value

Polynomials Mathematics Grade 7

Polynomials Mathematics Grade 7

Parts of a circle

Parts of a circle

Week 2 (Algebraivc Expressions and Polynomials).pptx

This document defines key concepts in algebra including constants, variables, algebraic expressions, polynomials, and the degree of polynomials. It explains that constants represent fixed values while variables represent unknown numbers. Algebraic expressions use variables, numbers, and operations. Polynomials are expressions with no negative exponents or fractions containing terms with variables and their powers. The degree of a polynomial refers to the highest power of its terms, with monomials having one term, binomials two terms, and trinomials three terms. The document provides examples and exercises to illustrate these algebraic concepts.

thelanguageofalgebra-191009022844 (2).pptx

This document provides an overview of the key concepts in the language of algebra. It discusses that algebra involves expressions with variables, and algebraic expressions combine numbers with variables using letters and operation symbols. The language of algebra contains numerals, variables to represent unknown numbers, constants, and operational symbols to represent addition, subtraction, multiplication, and division. It provides examples of translating word phrases to algebraic expressions and defines terms like algebraic terms, expressions, coefficients and evaluating expressions by substitution.

Algebra I.ppt

An algebraic expression is made up of variables, constants, and algebraic operations. It contains terms and can be represented using unknown variables, constants, and coefficients. There are three main types of algebraic expressions: monomial, binomial, and polynomial. A monomial expression has only one term, while binomial and polynomial expressions have two or more terms.

Combine liketerms

I can simplify expressions with several variables by combining like terms. To do this, I use the distributive property to distribute any coefficients to the terms within parentheses and then combine terms that have the same variables and exponents. For example, 5(3x + 4) = 15x + 20 and 4(7n + 2) + 6 = 28n + 14. It is important that I only combine like terms and do not add or combine terms that have different variables or exponents.

Forming algebraic expressions

This document discusses algebraic expressions. It defines an algebraic expression as an expression involving variables, and notes they originated from Arabic mathematics. It then provides definitions and examples of terms, variables, and how expressions are formed by combining terms using operations. The document asks questions about representing word problems as expressions and evaluating expressions for given variable values. It discusses forming expressions from word problems and evaluating them. Finally, it gives practice problems asking to evaluate expressions for given variable values.

Expresiones algebraicas

1. The document discusses algebraic expressions, factorization, and radicalization. It provides examples of algebraic expressions, addition and subtraction of expressions, and finding the numeric value of an expression.
2. Notable products are introduced as special multiplication expressions between algebraic terms whose results can be easily determined without step-by-step calculation.
3. Factorization is described as expressing an algebraic term as the product of other terms called factors, such as factoring the number 20 into the prime numbers 2, 2, and 5.

Lesson2_MathematicalLanguageAndSymbols _Lesson 2.1_VariablesAndTheLanguageOfS...

Lesson2_MathematicalLanguageAndSymbols _Lesson 2.1_VariablesAndTheLanguageOfSets.pdf
This pdf tackles about the Mathematical Language and Symbols and the Variables and the Language of Sets.
This presentation contains definitions, tables, illustrations as well as examples.
I hope you'll find this helpful.

Grade 7 Mathematics Week 4 2nd Quarter

1. Algebra uses variables, constants, and symbols to represent quantities in mathematical expressions that model real-world situations. Variables represent unknown values, constants represent fixed values, and symbols represent operations.
2. Algebraic expressions are made up of terms separated by plus or minus signs. A term contains variables or constants and can be a single number, variable, or combination. Monomials have one term, binomials have two terms, and trinomials have three terms.
3. The degree of a polynomial indicates the highest exponent of any variable in its terms. For polynomials with one variable, the degree is the highest power of that variable. For polynomials with multiple variables, the degree is the sum of

Sets of numbers

Here are the translations between set notations:
A. The set of integers greater than -5.5
B. {10, 20, 30, 40, ...}
C. {x | x ≤ -2}

Expresiones algebraicas

Suma, Resta, Valor numérico, Multiplicación, División y Productos Notables de Expresiones algebraicas.
Factorización por Productos Notables

Teaching Pal - Algebra in NZ

This document provides definitions and examples related to algebra concepts including variables, algebraic expressions, and writing and evaluating algebraic expressions. It defines a variable as a letter or symbol that represents a number and provides examples of algebraic expressions involving addition, subtraction, and variables. It also shows how to write algebraic expressions to represent word problems and evaluates sample expressions for a given value of the variable.

GRADE 7 Algebraic Expressions PowerPoint

GRADE 7 Algebraic Expressions PowerPoint

Properties of Addition & Multiplication

The document discusses various properties of real numbers including the commutative, associative, identity, inverse, zero, and distributive properties. It also covers topics such as combining like terms, translating word phrases to algebraic expressions, and simplifying algebraic expressions. Examples are provided to illustrate each concept along with explanations of key terms like coefficients, variables, and like terms.

1.3

This document provides an overview of algebraic expressions and how to work with them. It covers the order of operations, writing expressions from word phrases, evaluating expressions, definitions of terms, coefficients, constants, and like terms. It also discusses simplifying expressions by combining like terms. Examples are provided to demonstrate evaluating expressions and simplifying by combining like terms. The homework assigned is to complete selected problems on page 22.

Expresiones algebraicas

An algebraic expression is a combination of letters and numbers linked by operation signs: addition, subtraction, multiplication, division and exponentiation. Algebraic expressions allow us, for example, to find areas and volumes. Some examples given are the circumference of a circle (2πr), the area of a square (s=l2), and the volume of a cube (V=a3). The document then provides examples and explanations of algebraic addition, subtraction, multiplication, division, and factorization.

Maths ppt on algebraic expressions and identites

This document discusses algebraic expressions and identities. It defines expressions as combinations of numbers and variables connected by operation signs. Expressions can be monomials containing one term, binomials containing two terms, or trinomials containing three terms. Terms are separated parts of expressions and factors are the numbers within terms. Coefficients are factors without signs. The document also covers adding, subtracting and multiplying expressions, as well as defining identities as equalities that are true for all variable values. It provides examples of standard identities for the sum and difference of squares and multiplying the sum and difference of two terms.

algebra and its concepts

Algebra is a method of written calculations that helps reason about numbers. Like any skill, algebra requires practice, specifically written practice. Algebra uses letters to represent unknown numbers, allowing arithmetic rules to be applied universally.

Matemática expresiones algebraicas

expresiones algebraicas
sumas algebraicas
resta algebraicas
valor numérico de una expresión algebraicas
Multiplicación de expresiones algebraicas
División de expresiones algebraicas
Productos notables de expresiones algebraicas
Factorizacion de productos notables

algebra expression presentation math.ppt

The document discusses the difference between algebraic expressions and equations. An algebraic expression combines variables, numbers, and operations but does not have an equal sign, while an algebraic equation is a statement of equality between two expressions and must have an equal sign. Examples of expressions and equations are provided to illustrate the difference. The reader is then asked to identify phrases and sentences as expressions or equations.

Marh algebra lesson

1. Natural numbers include counting numbers like 1, 2, 3, and continue indefinitely. Whole numbers include natural numbers plus zero. Integers include whole numbers and their opposites.
2. Rational numbers can be written as a fraction, like 1.5 = 3/2. Irrational numbers cannot be written as a fraction, like π.
3. The four basic operations are addition, subtraction, multiplication, and division. Addition and subtraction follow rules about sign and order. Multiplication and division rules depend on the signs of the factors or dividend and divisor.

Week 2 (Algebraivc Expressions and Polynomials).pptx

Week 2 (Algebraivc Expressions and Polynomials).pptx

thelanguageofalgebra-191009022844 (2).pptx

thelanguageofalgebra-191009022844 (2).pptx

Algebra I.ppt

Algebra I.ppt

Combine liketerms

Combine liketerms

Forming algebraic expressions

Forming algebraic expressions

Expresiones algebraicas

Expresiones algebraicas

Lesson2_MathematicalLanguageAndSymbols _Lesson 2.1_VariablesAndTheLanguageOfS...

Lesson2_MathematicalLanguageAndSymbols _Lesson 2.1_VariablesAndTheLanguageOfS...

Grade 7 Mathematics Week 4 2nd Quarter

Grade 7 Mathematics Week 4 2nd Quarter

Sets of numbers

Sets of numbers

Expresiones algebraicas

Expresiones algebraicas

Teaching Pal - Algebra in NZ

Teaching Pal - Algebra in NZ

GRADE 7 Algebraic Expressions PowerPoint

GRADE 7 Algebraic Expressions PowerPoint

Properties of Addition & Multiplication

Properties of Addition & Multiplication

1.3

1.3

Expresiones algebraicas

Expresiones algebraicas

Maths ppt on algebraic expressions and identites

Maths ppt on algebraic expressions and identites

algebra and its concepts

algebra and its concepts

Matemática expresiones algebraicas

Matemática expresiones algebraicas

algebra expression presentation math.ppt

algebra expression presentation math.ppt

Marh algebra lesson

Marh algebra lesson

LF Energy Webinar: Carbon Data Specifications: Mechanisms to Improve Data Acc...

This LF Energy webinar took place June 20, 2024. It featured:
-Alex Thornton, LF Energy
-Hallie Cramer, Google
-Daniel Roesler, UtilityAPI
-Henry Richardson, WattTime
In response to the urgency and scale required to effectively address climate change, open source solutions offer significant potential for driving innovation and progress. Currently, there is a growing demand for standardization and interoperability in energy data and modeling. Open source standards and specifications within the energy sector can also alleviate challenges associated with data fragmentation, transparency, and accessibility. At the same time, it is crucial to consider privacy and security concerns throughout the development of open source platforms.
This webinar will delve into the motivations behind establishing LF Energy’s Carbon Data Specification Consortium. It will provide an overview of the draft specifications and the ongoing progress made by the respective working groups.
Three primary specifications will be discussed:
-Discovery and client registration, emphasizing transparent processes and secure and private access
-Customer data, centering around customer tariffs, bills, energy usage, and full consumption disclosure
-Power systems data, focusing on grid data, inclusive of transmission and distribution networks, generation, intergrid power flows, and market settlement data

Northern Engraving | Modern Metal Trim, Nameplates and Appliance Panels

What began over 115 years ago as a supplier of precision gauges to the automotive industry has evolved into being an industry leader in the manufacture of product branding, automotive cockpit trim and decorative appliance trim. Value-added services include in-house Design, Engineering, Program Management, Test Lab and Tool Shops.

AWS Certified Solutions Architect Associate (SAA-C03)

AWS Certified Solutions Architect Associate (SAA-C03)

AppSec PNW: Android and iOS Application Security with MobSF

Mobile Security Framework - MobSF is a free and open source automated mobile application security testing environment designed to help security engineers, researchers, developers, and penetration testers to identify security vulnerabilities, malicious behaviours and privacy concerns in mobile applications using static and dynamic analysis. It supports all the popular mobile application binaries and source code formats built for Android and iOS devices. In addition to automated security assessment, it also offers an interactive testing environment to build and execute scenario based test/fuzz cases against the application.
This talk covers:
Using MobSF for static analysis of mobile applications.
Interactive dynamic security assessment of Android and iOS applications.
Solving Mobile app CTF challenges.
Reverse engineering and runtime analysis of Mobile malware.
How to shift left and integrate MobSF/mobsfscan SAST and DAST in your build pipeline.

Must Know Postgres Extension for DBA and Developer during Migration

Mydbops Opensource Database Meetup 16
Topic: Must-Know PostgreSQL Extensions for Developers and DBAs During Migration
Speaker: Deepak Mahto, Founder of DataCloudGaze Consulting
Date & Time: 8th June | 10 AM - 1 PM IST
Venue: Bangalore International Centre, Bangalore
Abstract: Discover how PostgreSQL extensions can be your secret weapon! This talk explores how key extensions enhance database capabilities and streamline the migration process for users moving from other relational databases like Oracle.
Key Takeaways:
* Learn about crucial extensions like oracle_fdw, pgtt, and pg_audit that ease migration complexities.
* Gain valuable strategies for implementing these extensions in PostgreSQL to achieve license freedom.
* Discover how these key extensions can empower both developers and DBAs during the migration process.
* Don't miss this chance to gain practical knowledge from an industry expert and stay updated on the latest open-source database trends.
Mydbops Managed Services specializes in taking the pain out of database management while optimizing performance. Since 2015, we have been providing top-notch support and assistance for the top three open-source databases: MySQL, MongoDB, and PostgreSQL.
Our team offers a wide range of services, including assistance, support, consulting, 24/7 operations, and expertise in all relevant technologies. We help organizations improve their database's performance, scalability, efficiency, and availability.
Contact us: info@mydbops.com
Visit: https://www.mydbops.com/
Follow us on LinkedIn: https://in.linkedin.com/company/mydbops
For more details and updates, please follow up the below links.
Meetup Page : https://www.meetup.com/mydbops-databa...
Twitter: https://twitter.com/mydbopsofficial
Blogs: https://www.mydbops.com/blog/
Facebook(Meta): https://www.facebook.com/mydbops/

Christine's Supplier Sourcing Presentaion.pptx

How I source suppliers

Astute Business Solutions | Oracle Cloud Partner |

Your goto partner for Oracle Cloud, PeopleSoft, E-Business Suite, and Ellucian Banner. We are a firm specialized in managed services and consulting.

"$10 thousand per minute of downtime: architecture, queues, streaming and fin...

Direct losses from downtime in 1 minute = $5-$10 thousand dollars. Reputation is priceless.
As part of the talk, we will consider the architectural strategies necessary for the development of highly loaded fintech solutions. We will focus on using queues and streaming to efficiently work and manage large amounts of data in real-time and to minimize latency.
We will focus special attention on the architectural patterns used in the design of the fintech system, microservices and event-driven architecture, which ensure scalability, fault tolerance, and consistency of the entire system.

Mutation Testing for Task-Oriented Chatbots

Conversational agents, or chatbots, are increasingly used to access all sorts of services using natural language. While open-domain chatbots - like ChatGPT - can converse on any topic, task-oriented chatbots - the focus of this paper - are designed for specific tasks, like booking a flight, obtaining customer support, or setting an appointment. Like any other software, task-oriented chatbots need to be properly tested, usually by defining and executing test scenarios (i.e., sequences of user-chatbot interactions). However, there is currently a lack of methods to quantify the completeness and strength of such test scenarios, which can lead to low-quality tests, and hence to buggy chatbots.
To fill this gap, we propose adapting mutation testing (MuT) for task-oriented chatbots. To this end, we introduce a set of mutation operators that emulate faults in chatbot designs, an architecture that enables MuT on chatbots built using heterogeneous technologies, and a practical realisation as an Eclipse plugin. Moreover, we evaluate the applicability, effectiveness and efficiency of our approach on open-source chatbots, with promising results.

"Frontline Battles with DDoS: Best practices and Lessons Learned", Igor Ivaniuk

At this talk we will discuss DDoS protection tools and best practices, discuss network architectures and what AWS has to offer. Also, we will look into one of the largest DDoS attacks on Ukrainian infrastructure that happened in February 2022. We'll see, what techniques helped to keep the web resources available for Ukrainians and how AWS improved DDoS protection for all customers based on Ukraine experience

Apps Break Data

How information systems are built or acquired puts information, which is what they should be about, in a secondary place. Our language adapted accordingly, and we no longer talk about information systems but applications. Applications evolved in a way to break data into diverse fragments, tightly coupled with applications and expensive to integrate. The result is technical debt, which is re-paid by taking even bigger "loans", resulting in an ever-increasing technical debt. Software engineering and procurement practices work in sync with market forces to maintain this trend. This talk demonstrates how natural this situation is. The question is: can something be done to reverse the trend?

Containers & AI - Beauty and the Beast!?!

As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
Keywords: AI, Containeres, Kubernetes, Cloud Native
Event Link: https://meine.doag.org/events/cloudland/2024/agenda/#agendaId.4211

Biomedical Knowledge Graphs for Data Scientists and Bioinformaticians

Dmitrii Kamaev, PhD
Senior Product Owner - QIAGEN

Lee Barnes - Path to Becoming an Effective Test Automation Engineer.pdf

So… you want to become a Test Automation Engineer (or hire and develop one)? While there’s quite a bit of information available about important technical and tool skills to master, there’s not enough discussion around the path to becoming an effective Test Automation Engineer that knows how to add VALUE. In my experience this had led to a proliferation of engineers who are proficient with tools and building frameworks but have skill and knowledge gaps, especially in software testing, that reduce the value they deliver with test automation.
In this talk, Lee will share his lessons learned from over 30 years of working with, and mentoring, hundreds of Test Automation Engineers. Whether you’re looking to get started in test automation or just want to improve your trade, this talk will give you a solid foundation and roadmap for ensuring your test automation efforts continuously add value. This talk is equally valuable for both aspiring Test Automation Engineers and those managing them! All attendees will take away a set of key foundational knowledge and a high-level learning path for leveling up test automation skills and ensuring they add value to their organizations.

The Microsoft 365 Migration Tutorial For Beginner.pptx

This presentation will help you understand the power of Microsoft 365. However, we have mentioned every productivity app included in Office 365. Additionally, we have suggested the migration situation related to Office 365 and how we can help you.
You can also read: https://www.systoolsgroup.com/updates/office-365-tenant-to-tenant-migration-step-by-step-complete-guide/

What is an RPA CoE? Session 1 – CoE Vision

In the first session, we will review the organization's vision and how this has an impact on the COE Structure.
Topics covered:
• The role of a steering committee
• How do the organization’s priorities determine CoE Structure?
Speaker:
Chris Bolin, Senior Intelligent Automation Architect Anika Systems

Demystifying Knowledge Management through Storytelling

The Department of Veteran Affairs (VA) invited Taylor Paschal, Knowledge & Information Management Consultant at Enterprise Knowledge, to speak at a Knowledge Management Lunch and Learn hosted on June 12, 2024. All Office of Administration staff were invited to attend and received professional development credit for participating in the voluntary event.
The objectives of the Lunch and Learn presentation were to:
- Review what KM ‘is’ and ‘isn’t’
- Understand the value of KM and the benefits of engaging
- Define and reflect on your “what’s in it for me?”
- Share actionable ways you can participate in Knowledge - - Capture & Transfer

QR Secure: A Hybrid Approach Using Machine Learning and Security Validation F...

QR Secure: A Hybrid Approach Using Machine Learning and Security Validation Functions to Prevent Interaction with Malicious QR Codes.
Aim of the Study: The goal of this research was to develop a robust hybrid approach for identifying malicious and insecure URLs derived from QR codes, ensuring safe interactions.
This is achieved through:
Machine Learning Model: Predicts the likelihood of a URL being malicious.
Security Validation Functions: Ensures the derived URL has a valid certificate and proper URL format.
This innovative blend of technology aims to enhance cybersecurity measures and protect users from potential threats hidden within QR codes 🖥 🔒
This study was my first introduction to using ML which has shown me the immense potential of ML in creating more secure digital environments!

"NATO Hackathon Winner: AI-Powered Drug Search", Taras Kloba

This is a session that details how PostgreSQL's features and Azure AI Services can be effectively used to significantly enhance the search functionality in any application.
In this session, we'll share insights on how we used PostgreSQL to facilitate precise searches across multiple fields in our mobile application. The techniques include using LIKE and ILIKE operators and integrating a trigram-based search to handle potential misspellings, thereby increasing the search accuracy.
We'll also discuss how the azure_ai extension on PostgreSQL databases in Azure and Azure AI Services were utilized to create vectors from user input, a feature beneficial when users wish to find specific items based on text prompts. While our application's case study involves a drug search, the techniques and principles shared in this session can be adapted to improve search functionality in a wide range of applications. Join us to learn how PostgreSQL and Azure AI can be harnessed to enhance your application's search capability.

Leveraging the Graph for Clinical Trials and Standards

Katja Glaß
OpenStudyBuilder Community Manager - Katja Glaß Consulting
Marius Conjeaud
Principal Consultant - Neo4j

LF Energy Webinar: Carbon Data Specifications: Mechanisms to Improve Data Acc...

LF Energy Webinar: Carbon Data Specifications: Mechanisms to Improve Data Acc...

Northern Engraving | Modern Metal Trim, Nameplates and Appliance Panels

Northern Engraving | Modern Metal Trim, Nameplates and Appliance Panels

AWS Certified Solutions Architect Associate (SAA-C03)

AWS Certified Solutions Architect Associate (SAA-C03)

AppSec PNW: Android and iOS Application Security with MobSF

AppSec PNW: Android and iOS Application Security with MobSF

Must Know Postgres Extension for DBA and Developer during Migration

Must Know Postgres Extension for DBA and Developer during Migration

Christine's Supplier Sourcing Presentaion.pptx

Christine's Supplier Sourcing Presentaion.pptx

Astute Business Solutions | Oracle Cloud Partner |

Astute Business Solutions | Oracle Cloud Partner |

"$10 thousand per minute of downtime: architecture, queues, streaming and fin...

"$10 thousand per minute of downtime: architecture, queues, streaming and fin...

Mutation Testing for Task-Oriented Chatbots

Mutation Testing for Task-Oriented Chatbots

"Frontline Battles with DDoS: Best practices and Lessons Learned", Igor Ivaniuk

"Frontline Battles with DDoS: Best practices and Lessons Learned", Igor Ivaniuk

Apps Break Data

Apps Break Data

Containers & AI - Beauty and the Beast!?!

Containers & AI - Beauty and the Beast!?!

Biomedical Knowledge Graphs for Data Scientists and Bioinformaticians

Biomedical Knowledge Graphs for Data Scientists and Bioinformaticians

Lee Barnes - Path to Becoming an Effective Test Automation Engineer.pdf

Lee Barnes - Path to Becoming an Effective Test Automation Engineer.pdf

The Microsoft 365 Migration Tutorial For Beginner.pptx

The Microsoft 365 Migration Tutorial For Beginner.pptx

What is an RPA CoE? Session 1 – CoE Vision

What is an RPA CoE? Session 1 – CoE Vision

Demystifying Knowledge Management through Storytelling

Demystifying Knowledge Management through Storytelling

QR Secure: A Hybrid Approach Using Machine Learning and Security Validation F...

QR Secure: A Hybrid Approach Using Machine Learning and Security Validation F...

"NATO Hackathon Winner: AI-Powered Drug Search", Taras Kloba

"NATO Hackathon Winner: AI-Powered Drug Search", Taras Kloba

Leveraging the Graph for Clinical Trials and Standards

Leveraging the Graph for Clinical Trials and Standards

- 3. ALGEBRA
- 4. Find the definition of the following terms: Algebra variable replacement set substitution constant symbols of grouping symbols of relationship algebraic term algebraic expression factors numerical coefficient literal coefficient
- 11. EXAMPLES: 1 1 – { 1 2 – [ 4 – (8 + 9 ) ] – 1 3 } 1 1 – { 1 2 – [ 4 – 1 7 ] – 1 3 } 1 1 – { 1 2 – 1 3 + 1 3 } 1 1 – 1 2 - 1
- 12. SYMBOLS OF RELATIONSHIP ≠ Is not equal to ≤ Is less than or equal to ≥ Is greater than or equal to < Is less than > Is greater than = Equals, is equal to, is
- 13. EXAMPLES: x + 7 < 1 0 x = 1 1 + 7 < 1 0 8 < 1 0 √
- 19. ALGEBRAIC term expression equation 2x, 29 2x + 29 2x + 29 = 50 x, y x - y x - y = -10 a2 , 2b, 5 a2 + 2b - 5 a2 + 2b – 5 = 9
- 21. Page 167, VII: Identifying literal coefficients, no.s 59-63 and page 165, IX: Identifying numerical coefficients, no.s 65-69.