Changing the denominator of a fraction so it does not contain a radical. Rationalizing the denominator. Stating the conjugate and using the conjugate to rationalize.
This document discusses combined variation and how to solve problems involving quantities that vary directly and inversely with other variables. It provides examples of translating statements of combined variation into mathematical equations. It also works through an example problem, showing how to solve for an unknown variable value when the quantities it varies with are given. The document concludes by instructing the reader to practice additional combined variation problems from their workbook.
The document summarizes how to subtract polynomials. It explains that to subtract polynomials, one changes the sign of all terms in the subtrahend, changes the operation to addition, and then proceeds to add the polynomials by aligning like terms and combining coefficients. It provides examples of subtracting various polynomials, as well as exercises for students to practice subtracting polynomials.
This document provides information about linear equations in two variables. It defines a linear equation as one that can be written in the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not equal to 0. It discusses using the rectangular coordinate system to graph linear equations by plotting the x- and y-intercepts. It also describes how to determine if an ordered pair is a solution to a linear equation by substituting the x- and y-values into the equation. Finally, it briefly outlines common methods for solving systems of linear equations, including elimination, substitution, and cross-multiplication.
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.
To subtract polynomials, you keep the sign of the first term, change subtraction to addition, and flip the sign of the second term. You then apply this process to every term in the polynomials. The document provides an example rule, two practice problems to try, and the answers to check your work.
Absolute value functions have a V-shape and model situations involving distance or edges. The graph can be transformed by changing the slope (a), shifting the vertex horizontally (h), or shifting the vertex vertically (k). To graph, identify the vertex and axis of symmetry, then use the slope to sketch the right side and symmetry to complete the left. Writing the equation involves identifying the vertex (h, k) and slope (a).
The document discusses linear equations in two variables. It defines a linear equation as one that can be written in the standard form Ax + By = C, where A, B, and C are real numbers and A and B cannot both be zero. Examples are provided of determining if equations are linear and identifying the A, B, and C components if they are linear. The document also discusses using ordered pairs as solutions to linear equations and finding multiple solutions to a given linear equation.
This document discusses combined variation and how to solve problems involving quantities that vary directly and inversely with other variables. It provides examples of translating statements of combined variation into mathematical equations. It also works through an example problem, showing how to solve for an unknown variable value when the quantities it varies with are given. The document concludes by instructing the reader to practice additional combined variation problems from their workbook.
The document summarizes how to subtract polynomials. It explains that to subtract polynomials, one changes the sign of all terms in the subtrahend, changes the operation to addition, and then proceeds to add the polynomials by aligning like terms and combining coefficients. It provides examples of subtracting various polynomials, as well as exercises for students to practice subtracting polynomials.
This document provides information about linear equations in two variables. It defines a linear equation as one that can be written in the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not equal to 0. It discusses using the rectangular coordinate system to graph linear equations by plotting the x- and y-intercepts. It also describes how to determine if an ordered pair is a solution to a linear equation by substituting the x- and y-values into the equation. Finally, it briefly outlines common methods for solving systems of linear equations, including elimination, substitution, and cross-multiplication.
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.
To subtract polynomials, you keep the sign of the first term, change subtraction to addition, and flip the sign of the second term. You then apply this process to every term in the polynomials. The document provides an example rule, two practice problems to try, and the answers to check your work.
Absolute value functions have a V-shape and model situations involving distance or edges. The graph can be transformed by changing the slope (a), shifting the vertex horizontally (h), or shifting the vertex vertically (k). To graph, identify the vertex and axis of symmetry, then use the slope to sketch the right side and symmetry to complete the left. Writing the equation involves identifying the vertex (h, k) and slope (a).
The document discusses linear equations in two variables. It defines a linear equation as one that can be written in the standard form Ax + By = C, where A, B, and C are real numbers and A and B cannot both be zero. Examples are provided of determining if equations are linear and identifying the A, B, and C components if they are linear. The document also discusses using ordered pairs as solutions to linear equations and finding multiple solutions to a given linear equation.
The document provides an overview of quadratic functions including definitions of key terms like quadratic function, parabola, quadratic equation, and vertex form. It discusses how to graph quadratic functions, solve quadratic equations using methods like the quadratic formula, and find the maximums and minimums of quadratic functions. It includes examples of using these techniques to solve word problems involving quadratic applications. The document aims to teach students about the basic concepts of quadratic functions.
The document discusses quadratic functions and their graphs. It defines quadratic functions as functions of the form f(x)=ax^2+bx+c, where a is not equal to 0. The graph of a quadratic function is a parabola with certain characteristics: it is symmetrical about an axis of symmetry and has a vertex which is either a maximum or minimum point. The axis of symmetry is the line x=0 for functions of the form f(x)=ax^2 and the vertex is at (0,0). For functions of the form f(x)=ax^2+k, the graph is a translation of f(x)=ax^2, so the vertex is (0,k) and the
The document describes a problem involving combined variation, where the variable z varies jointly as w and x, and inversely as y. It gives the equation of variation as z = kwx/y, where k is the constant of variation. It solves for k when z = 100, w = 4, x = 5, and y = 15, finding that k = 75. Therefore, the equation of combined variation is z = 75wx/y. It then uses this to solve for z when w = 1, x = 5, and y = 3, finding that z = 125.
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.
The document discusses assigning numeric values to letters of the alphabet and using those values to calculate the numeric value of words. It provides examples of calculating values for names like "MARY" and words like "EQUALITY." It then discusses algebraic expressions, including defining them, steps for evaluation, and examples of evaluating expressions when variables are replaced with numeric values. The document ends with assignments on adding polynomials.
1. Absolute-value functions can be transformed through translations, reflections, stretches, and compressions. Translations move the graph up/down or left/right and change the vertex. Reflections flip the graph across an axis. Stretches and compressions make the graph wider/narrower or taller/shorter.
2. Examples show how to write the rule for a transformed absolute-value function g(x) based on an original function f(x). The transformations can be vertical/horizontal shifts, reflections, or vertical/horizontal stretches/compressions.
3. Graphs confirm that the transformations are applied as expected to f(x), resulting in the graph of g(x) with the
This document provides guidance on identifying and factoring perfect square trinomials in algebra. It begins with a definition of a perfect square trinomial as a trinomial that results from squaring a binomial. Examples are provided to illustrate this. Several activity cards are then presented to help students practice determining if an expression is a perfect square trinomial, completing the terms, factoring, and more. An enrichment card adds an assessment with multiple choice questions. Key steps for factoring a perfect square trinomial are outlined, such as taking the square root of the first and last terms. An answer card provides the solutions to the activities. Sources are listed at the end.
The document defines direct variation and provides examples of how to determine if a relationship is direct variation. It explains that direct variation can be represented by an equation in the form of y=kx, where k is the constant of variation. It gives examples of determining the constant of variation from tables of x and y values and using the constant to find unknown values. It also provides examples of solving word problems using direct variation.
This document introduces function notation and how to evaluate functions. It explains that f(x) represents the output of the function f for a given input x. Examples show different functions defined using this notation, such as f(x) = 2x + 1. The document also demonstrates how to evaluate functions for given x-values, find x-values for which a function is a certain amount, and graph functions using this notation. It compares translating and shifting graphs of functions.
The document discusses how the time it takes for water to boil, m, varies inversely with temperature, t. Specifically, it states that as temperature, t, increases, the time to boil, m, decreases. It provides the formula m = k/t, where k is a constant of variation. As one variable (temperature) increases, the other (time to boil) decreases.
This powerpoint presentation discusses or talks about the topic or lesson Functions. It also discusses and explains the rules, steps and examples of Quadratic Functions.
Direct variation describes the relationship between two quantities where one quantity varies as the other changes proportionally. It can be represented by the equation y = kx, where k is the constant of variation.
Some key points about direct variation:
- The graph of a direct variation will pass through the origin, as there is no y-intercept term.
- To determine if a relationship represents direct variation, calculate the constant of variation k from the data and check if it remains the same for different values.
- Direct variation can be used to find unknown values by setting up a table with the known values and using the direct variation equation y = kx.
This document discusses how to solve equations and inequalities. It covers topics such as: balancing equations, combining like terms, expanding brackets, rearranging formulas to change the subject, representing inequalities on number lines, and solving one-step and two-step inequalities. Examples are provided to demonstrate each concept and practice problems are included for readers to try.
Solving Linear Equations - GRADE 8 MATHEMATICSCoreAces
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
* Complete activities
PRICE: P200 only
This learner's module discusses or talks about the topic of Quadratic Functions. It also discusses what is Quadratic Functions. It also shows how to transform or rewrite the equation f(x)=ax2 + bx + c to f(x)= a(x-h)2 + k. It will also show the different characteristics of Quadratic Functions.
This document discusses linear equations in one variable. It defines linear equations as those involving single variables with the highest power being 1. It presents rules for solving linear equations, including adding, subtracting, multiplying, or dividing the same quantity to both sides. Transposition as a method is explained, where terms change signs when shifted between sides of an equation. Examples of solving linear equations are provided. The document also discusses applying linear equations to word problems by setting up the equation based on the problem and solving for the unknown variable. Several examples of solving word problems involving linear equations are presented.
This document discusses multiplying polynomials. It begins with examples of multiplying monomials by using the properties of exponents. It then covers multiplying a polynomial by a monomial using the distributive property. Examples are provided for multiplying binomials by binomials using both the distributive property and FOIL method. The document concludes by explaining methods for multiplying polynomials with more than two terms, such as using the distributive property multiple times, a rectangle model, or a vertical method similar to multiplying whole numbers.
This document provides guidance on identifying the nature of roots of quadratic equations. It begins by identifying the least mastered skill of identifying the nature of roots. It then reviews the standard form of a quadratic equation and the quadratic formula. The key concept of the discriminant is explained, which determines the number and type of roots. Examples are provided to show how to find the discriminant and use it to describe the nature of roots. Activities are included for students to practice rewriting equations in standard form, finding a, b, c values, calculating discriminants, and determining the nature of roots. An assessment card with example problems is provided to check understanding.
This document discusses polynomial functions and their graphs. It defines polynomial functions as functions of the form P(x) = anxn + an-1xn-1 + ... + a1x + a0, where an is the leading coefficient. The degree of the polynomial determines features of its graph like the maximum number of x-intercepts. The leading coefficient test determines the end behavior of the graph. Key features of polynomial graphs are intercepts, extrema, and end behavior.
This document describes an Algebra 1 lesson plan that uses a Jeopardy-style game to review content from each chapter. The class will be split into two teams competing to answer questions of varying difficulty levels worth different point values. By making algebra review engaging through a familiar game format, the lesson supports universal design principles by accommodating different learning styles and abilities.
To rationalize the denominator of a fraction, multiply the numerator and denominator by the conjugate of the denominator. This eliminates radicals in the denominator by creating rational expressions. Examples demonstrate rationalizing fractions with binomial radical denominators by multiplying the fraction by the conjugate, then simplifying to remove radicals from the denominator. The process of rationalizing allows for further algebraic manipulation and calculation with radical expressions.
The document provides an overview of quadratic functions including definitions of key terms like quadratic function, parabola, quadratic equation, and vertex form. It discusses how to graph quadratic functions, solve quadratic equations using methods like the quadratic formula, and find the maximums and minimums of quadratic functions. It includes examples of using these techniques to solve word problems involving quadratic applications. The document aims to teach students about the basic concepts of quadratic functions.
The document discusses quadratic functions and their graphs. It defines quadratic functions as functions of the form f(x)=ax^2+bx+c, where a is not equal to 0. The graph of a quadratic function is a parabola with certain characteristics: it is symmetrical about an axis of symmetry and has a vertex which is either a maximum or minimum point. The axis of symmetry is the line x=0 for functions of the form f(x)=ax^2 and the vertex is at (0,0). For functions of the form f(x)=ax^2+k, the graph is a translation of f(x)=ax^2, so the vertex is (0,k) and the
The document describes a problem involving combined variation, where the variable z varies jointly as w and x, and inversely as y. It gives the equation of variation as z = kwx/y, where k is the constant of variation. It solves for k when z = 100, w = 4, x = 5, and y = 15, finding that k = 75. Therefore, the equation of combined variation is z = 75wx/y. It then uses this to solve for z when w = 1, x = 5, and y = 3, finding that z = 125.
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.
The document discusses assigning numeric values to letters of the alphabet and using those values to calculate the numeric value of words. It provides examples of calculating values for names like "MARY" and words like "EQUALITY." It then discusses algebraic expressions, including defining them, steps for evaluation, and examples of evaluating expressions when variables are replaced with numeric values. The document ends with assignments on adding polynomials.
1. Absolute-value functions can be transformed through translations, reflections, stretches, and compressions. Translations move the graph up/down or left/right and change the vertex. Reflections flip the graph across an axis. Stretches and compressions make the graph wider/narrower or taller/shorter.
2. Examples show how to write the rule for a transformed absolute-value function g(x) based on an original function f(x). The transformations can be vertical/horizontal shifts, reflections, or vertical/horizontal stretches/compressions.
3. Graphs confirm that the transformations are applied as expected to f(x), resulting in the graph of g(x) with the
This document provides guidance on identifying and factoring perfect square trinomials in algebra. It begins with a definition of a perfect square trinomial as a trinomial that results from squaring a binomial. Examples are provided to illustrate this. Several activity cards are then presented to help students practice determining if an expression is a perfect square trinomial, completing the terms, factoring, and more. An enrichment card adds an assessment with multiple choice questions. Key steps for factoring a perfect square trinomial are outlined, such as taking the square root of the first and last terms. An answer card provides the solutions to the activities. Sources are listed at the end.
The document defines direct variation and provides examples of how to determine if a relationship is direct variation. It explains that direct variation can be represented by an equation in the form of y=kx, where k is the constant of variation. It gives examples of determining the constant of variation from tables of x and y values and using the constant to find unknown values. It also provides examples of solving word problems using direct variation.
This document introduces function notation and how to evaluate functions. It explains that f(x) represents the output of the function f for a given input x. Examples show different functions defined using this notation, such as f(x) = 2x + 1. The document also demonstrates how to evaluate functions for given x-values, find x-values for which a function is a certain amount, and graph functions using this notation. It compares translating and shifting graphs of functions.
The document discusses how the time it takes for water to boil, m, varies inversely with temperature, t. Specifically, it states that as temperature, t, increases, the time to boil, m, decreases. It provides the formula m = k/t, where k is a constant of variation. As one variable (temperature) increases, the other (time to boil) decreases.
This powerpoint presentation discusses or talks about the topic or lesson Functions. It also discusses and explains the rules, steps and examples of Quadratic Functions.
Direct variation describes the relationship between two quantities where one quantity varies as the other changes proportionally. It can be represented by the equation y = kx, where k is the constant of variation.
Some key points about direct variation:
- The graph of a direct variation will pass through the origin, as there is no y-intercept term.
- To determine if a relationship represents direct variation, calculate the constant of variation k from the data and check if it remains the same for different values.
- Direct variation can be used to find unknown values by setting up a table with the known values and using the direct variation equation y = kx.
This document discusses how to solve equations and inequalities. It covers topics such as: balancing equations, combining like terms, expanding brackets, rearranging formulas to change the subject, representing inequalities on number lines, and solving one-step and two-step inequalities. Examples are provided to demonstrate each concept and practice problems are included for readers to try.
Solving Linear Equations - GRADE 8 MATHEMATICSCoreAces
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
* Complete activities
PRICE: P200 only
This learner's module discusses or talks about the topic of Quadratic Functions. It also discusses what is Quadratic Functions. It also shows how to transform or rewrite the equation f(x)=ax2 + bx + c to f(x)= a(x-h)2 + k. It will also show the different characteristics of Quadratic Functions.
This document discusses linear equations in one variable. It defines linear equations as those involving single variables with the highest power being 1. It presents rules for solving linear equations, including adding, subtracting, multiplying, or dividing the same quantity to both sides. Transposition as a method is explained, where terms change signs when shifted between sides of an equation. Examples of solving linear equations are provided. The document also discusses applying linear equations to word problems by setting up the equation based on the problem and solving for the unknown variable. Several examples of solving word problems involving linear equations are presented.
This document discusses multiplying polynomials. It begins with examples of multiplying monomials by using the properties of exponents. It then covers multiplying a polynomial by a monomial using the distributive property. Examples are provided for multiplying binomials by binomials using both the distributive property and FOIL method. The document concludes by explaining methods for multiplying polynomials with more than two terms, such as using the distributive property multiple times, a rectangle model, or a vertical method similar to multiplying whole numbers.
This document provides guidance on identifying the nature of roots of quadratic equations. It begins by identifying the least mastered skill of identifying the nature of roots. It then reviews the standard form of a quadratic equation and the quadratic formula. The key concept of the discriminant is explained, which determines the number and type of roots. Examples are provided to show how to find the discriminant and use it to describe the nature of roots. Activities are included for students to practice rewriting equations in standard form, finding a, b, c values, calculating discriminants, and determining the nature of roots. An assessment card with example problems is provided to check understanding.
This document discusses polynomial functions and their graphs. It defines polynomial functions as functions of the form P(x) = anxn + an-1xn-1 + ... + a1x + a0, where an is the leading coefficient. The degree of the polynomial determines features of its graph like the maximum number of x-intercepts. The leading coefficient test determines the end behavior of the graph. Key features of polynomial graphs are intercepts, extrema, and end behavior.
This document describes an Algebra 1 lesson plan that uses a Jeopardy-style game to review content from each chapter. The class will be split into two teams competing to answer questions of varying difficulty levels worth different point values. By making algebra review engaging through a familiar game format, the lesson supports universal design principles by accommodating different learning styles and abilities.
To rationalize the denominator of a fraction, multiply the numerator and denominator by the conjugate of the denominator. This eliminates radicals in the denominator by creating rational expressions. Examples demonstrate rationalizing fractions with binomial radical denominators by multiplying the fraction by the conjugate, then simplifying to remove radicals from the denominator. The process of rationalizing allows for further algebraic manipulation and calculation with radical expressions.
The document discusses how to rationalize the denominator of a fraction that contains a radical. It explains that to remove the radical from the denominator, one should multiply both the numerator and denominator by the radical term. This preserves the value of the fraction while removing the radical from the denominator, resulting in a rational number.
Semi-detailed Lesson Plan in math IV (k-12 based curriculum) "FINDING THE ARE...Cristy Melloso
This lesson plan aims to teach students how to find the area of a triangle. It reviews prerequisite concepts like finding the area of parallelograms. Example problems are used to introduce and explain the formula for calculating the area of a triangle: A = 1/2 * base * height. Students are divided into groups to practice applying the formula by solving example triangle area problems and finding missing side lengths. The lesson concludes by having students complete a table practicing various triangle area calculation problems.
This lesson plan outlines teaching students how to calculate the area of a triangle. It includes objectives of stating the area formula, drawing triangles, and cooperating in activities. Procedures include reviewing triangles, motivating with an example of cutting paper, deriving and practicing the area formula of 1/2 base x height, and sample problems finding area, base or height when given other values. An evaluation assesses applying the formula to find area, base or height in word problems.
The lesson plan aims to teach students about the elements of a short story using O. Henry's "The Last Leaf". Students will develop their vocabulary by defining words from the story. They will read the story silently and answer comprehension questions about the characters, setting, and events. Finally, students will write a summary of the story and an essay analyzing the friendship between the main characters and reflecting on friendship in their own lives.
Course Descriptions of Language Subject Areas and Goals of Language Teaching
English Elementary
English Secondary
Filipino Elementarya
Filipino Sekondarya
This lesson plan discusses the course descriptions, goals, and objectives of language subjects like English and Filipino. It aims to help students understand the importance of language learning and demonstrate expected competencies in listening, speaking, reading, and writing for each grade level. The teacher leads a discussion where students explain the objectives for different grades in each language subject drawn from the Basic Education Curriculum. The lesson emphasizes that learning the country's languages helps develop communication skills and international competitiveness, making students more successful. For evaluation, students answer short questions about the lesson and write an insight about one language subject area.
MATH Lesson Plan sample for demo teaching preyaleandrina
This is my first made lesson plan ...
i thought before that its hard to make lesson plan but being just resourceful and with the help of different methods and strategies in teaching we can have our guide for highly and better teaching instruction:)..
Detailed Lesson Plan (ENGLISH, MATH, SCIENCE, FILIPINO)Junnie Salud
Thanks everybody! The lesson plans presented were actually outdated and can still be improved. I was also a college student when I did these. There were minor errors but the important thing is, the structure and flow of activities (for an hour-long class) are included here. I appreciate all of your comments! Please like my fan page on facebook search for JUNNIE SALUD.
*The detailed LP for English is from Ms. Juliana Patricia Tenzasas. I just revised it a little.
For questions about education-related matters, you can directly email me at mr_junniesalud@yahoo.com
Changing the denominator of a fraction that contains a radical. Finding the conjugate of a binomial and using the conjugate to rationalize the denominator.
1. This lesson teaches students how to substitute numbers for letters in algebraic expressions.
2. A variable is a symbol used for an unknown number. Substitution is the process of replacing variables with given numbers to simplify expressions and find numerical values.
3. Examples show substituting specific values for variables into expressions, then using arithmetic to simplify and find the solution.
This document contains 10 mathematics questions and their answers related to topics like BODMAS, decimals, fractions, indices, equations, factorizing, and simplifying expressions. The questions cover evaluating expressions, writing numbers in standard form, solving simultaneous equations, factorizing numbers, solving equations involving indices, identifying types of numbers, and finding the value of variables in expressions. The document promotes joining a WhatsApp group for more math, science, and English revision questions.
The document is a daily lesson log from Osmeña National High School in the Philippines. It outlines the objectives, content, procedures, and activities for a 7th grade mathematics lesson on algebraic expressions. The lesson teaches students to translate between verbal phrases and mathematical expressions, identify constants and variables, and evaluate algebraic expressions. Example problems are provided to illustrate key concepts like exponents, addition/subtraction of terms, and substituting values into expressions. The formative assessment asks students to apply these skills by translating phrases, identifying constants/variables, and evaluating expressions with given values.
1. The document discusses concepts related to whole numbers including addition, subtraction, multiplication, and division. It provides definitions, examples, and properties for each operation.
2. Key models for addition and multiplication include set models using counting of objects in sets and measurement models using number lines. Properties like commutativity and distributivity are explained.
3. Subtraction is defined using both a take-away approach and missing addend approach. Division is defined using a missing factor approach and can be thought of as repeated subtraction.
This document provides answer keys for 12 lessons that are part of a mathematics curriculum for 3rd grade students. The lessons cover place value and problem solving using units of measure. Each answer key provides the correct answers for problems, exercises and homework in the corresponding lesson. The lessons involve skills like telling time to the nearest 5 minutes, measuring and comparing weights and volumes, adding and subtracting time intervals, and rounding measurements.
The document is a math test with 16 multiple choice questions covering various math topics such as word problems involving ages, factorials, logarithms, geometry, and other concepts. It tests skills like setting up and solving equations, recognizing patterns in numbers, using properties of shapes, and logical reasoning. The questions range in difficulty from straightforward calculations to multi-step problems requiring conceptual understanding.
1. This module discusses illustrating and graphing linear inequalities in two variables. It contains lessons, activities, and tests to help students learn and apply related concepts.
2. Activities include matching mathematical sentences to inequalities, determining properties of inequalities, and solving a word problem involving a linear inequality in two variables representing the number of face masks and face shields an online seller would need to sell to make at least Php 2,000.
3. A linear inequality in two variables can be written as an expression involving two variables separated by addition or subtraction, with an inequality symbol and a constant on the right side, such as the example given: 35x + 75y ≥ 2,000.
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.
When dividing radicals, only the numbers outside the radicals are divided in the numerator and denominator, and the same for numbers inside radicals. This can sometimes leave a radical in the denominator, which is improper. To fix this, a process called rationalizing the denominator is used to remove radicals from the denominator. Examples are provided of dividing radicals and rationalizing denominators.
This document discusses dividing radicals. It states that when dividing radicals, only the numbers outside the radicals in the numerator are divided by those outside in the denominator, and the same is done for numbers inside the radicals. An example is shown where this leaves a radical in the denominator, which is improper form. The document notes that a process called rationalizing the denominator is used to remove radicals from the denominator.
This document discusses transformations of the square root function y=√x. It includes:
1) Matching equations like y=3√x and y=√x/2 to their graphs by graphing the parent function first.
2) Explaining that a negative sign in front of the square root, like y=-√x, reflects the graph over the x-axis.
3) Having students work in groups to draw transformed square root graphs, identify the transformation, and write the domain and range.
The document discusses adding and subtracting radicals. It reviews collecting like terms and then explains that to add or subtract radicals, you add the coefficients of like terms, which are radicals that have the same index and radicand. Examples are provided to demonstrate adding and subtracting radicals.
This document provides a lesson on adding and subtracting radicals. It first reviews collecting like terms when adding and subtracting expressions. It then explains that to add or subtract radicals, you add the coefficients of like terms, where like terms are radicals with the same index and radicand. Examples are provided to demonstrate adding and subtracting radicals.
The document defines and provides information about common mathematical functions including linear, quadratic, square root, cubic, cube root, absolute value, greatest integer, rational, trigonometric, exponential growth and decay, and logarithmic functions. Tables are included that specify domains, ranges, x-intercepts, and y-intercepts for each function.
The document defines and provides information about common mathematical functions including linear, quadratic, square root, cubic, cube root, absolute value, greatest integer, rational, trigonometric, exponential growth and decay, and logarithmic functions. Tables are included that specify domains, ranges, x-intercepts, and y-intercepts for each function.
1. The project requires students to graph the 13 parent functions and apply transformations to create child functions.
2. Students must complete a parent function foldable with information on all 13 functions and create a poster showing the graphs of each parent function and one example of a child function using a transformation.
3. The poster will be graded based on neatness, completeness of information and transformations, and visual appeal.
1. The document discusses trigonometric ratios and how to use them to solve for missing side lengths and angle measures in right triangles.
2. It provides examples of setting up trig ratios, using the Pythagorean theorem, and using inverse trig functions to find missing angles.
3. The key steps are to label the sides of the right triangle, set up the appropriate trig ratios based on which information is known or missing, and use trig identities or the inverse functions to calculate the missing information.
This document discusses right triangles on May 12, 2014. It covers right triangles and their properties over multiple pages. The key topic is right triangles and how to understand their characteristics and relationships between sides and angles.
This document discusses the parts of a right triangle, listing the opposite leg, adjacent leg, and hypotenuse multiple times on May 4, 2014. It focuses on the basic geometric terms for the sides of a right triangle.
This document contains a review worksheet with 35 questions covering topics in exponential and logarithmic functions including determining if equations represent exponential growth or decay, graphing functions and their inverses, evaluating logarithmic expressions with and without a calculator, solving exponential equations, and applying exponential and logarithmic concepts to word problems involving population growth, depreciation, radioactive decay, compound interest, and stock price growth.
This document contains a unit review with answers to multiple choice and free response questions about functions, inverses, logarithms, and transformations. There are 35 total problems covering topics like determining if a relationship represents a function, evaluating logarithmic expressions, and describing transformations of graphs. Tables of values are also provided for 4 functions and their inverses.
This document discusses common logarithms and how to evaluate logarithmic expressions with and without a calculator. It provides examples of rewriting exponential expressions as logarithmic expressions by setting them equal to variables and manipulating the equations. It also introduces the change of base formula for evaluating logarithms with bases other than 10.
This document contains 7 word problems about exponential growth and decay models. The problems cover topics like population growth, healthcare costs, radioactive decay, savings accounts, milk consumption, population of Washington D.C., and guppy population growth. For each problem, the student is asked to write an exponential function model, make predictions based on the model, or calculate other related values. The overall goal is to practice applying exponential functions to real-world scenarios involving growth and decay over time.
This document contains an assignment on exponential equations and logarithms. It is divided into four sections: 1) determining whether functions represent exponential growth or decay, 2) describing transformations of exponential functions, 3) graphing exponential functions and stating their domains and ranges, and 4) graphing exponential functions and their inverse logarithmic functions and stating their domains and ranges. There are 14 problems or exercises presented.
This document appears to be a log of activities that took place over two days, April 3rd and 4th, 2014. However, no specific activities or events are described within the document itself, which only repeats the date header five times without providing any additional context or information about what occurred.
This 3 sentence summary provides the high level information from the document. The document appears to be notes from a class titled "U6 day2 1st pd." that was held on April 22, 2014. It includes the title and date repeated 3 times with no other context or details provided.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
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How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
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Article: https://pecb.com/article
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Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
1. lesson 2 1st
March 07, 2014
Lesson 2 - Division and Radicals
I. Review
A. 35
C. 5 7
B. 35
D. 7 5
A. 150
C. 25 6
B. 6 25
D. 5 6
A. 49
C. 7
B. 7 7
D. 7
A. 64
C. 8 8
B. 8
D. 8
II. Rationalizing Denominators
Just like when we solve 5x = 11 and we get
where we must solve:
for x, it will happen
we will get
This answer is correct, but it is considered bad etiquette to leave a
radical in the denominator. So how can we change a number's "look"
without changing its value?
Multiply by the number 1!
But we will use a "magic" number 1 to do this!
3. lesson 2 1st
March 07, 2014
8.
7.
9.
III. Conjugates
Def: A conjugate is when you change the middle sign of a binomial
Ex. The conjugate of a + b is a - b
State the conjugates of:
a. h + k
b.
c.
d.
4. lesson 2 1st
March 07, 2014
What happens if we multply something by its conjugate?
or not?
Pick two, what happens if you multiply a binomial times itself?
Times its conjugate?
a. h + k
b.
c.
d.
Examples:
1.
2.
5. lesson 2 1st
March 07, 2014
3.
IV. Quadratic Formula Review
At times, we would get answers when doing the quadratic formula, as
below, let's practice simplifying them to proper forms:
Think - 1. Simplify Radical
1.
2. Find a GCF
2.
3. Reduce