This powerpoint presentation discusses or talks about the topic or lesson: Rational Exponents. It also discusses and explains the rules, concepts, steps and examples of Rational Exponents.
The document discusses rules for simplifying radical expressions. It states the square root and multiplication rules, which are that the square root of a squared term is the term itself, and that the square root of a product is the product of the square roots. Examples are provided to demonstrate applying these rules to simplify radical expressions by extracting square factors from the radicand. The division rule for radicals is also stated.
- The document discusses how computers use negative exponents to process fractions and percentages during photo processing, which allows apps like Photoshop to shrink photos.
- It explains that negative exponents represent fractions, with the item with the negative exponent moving to the denominator when written as a fraction. This allows computers to perform mathematical operations involving fractions.
- Examples are provided of how negative exponents simplify to fractions through the rule of a-m = 1/am, with the item in the exponent moving between the numerator and denominator.
This document provides instructions on how to solve radical equations. It begins by defining a radical equation and radicand. It then explains the main steps to solve radical equations: isolate the radical to one side, raise both sides to the same power, and simplify. Several examples are worked through to demonstrate this process. The document emphasizes checking solutions, as raising both sides to an even power can result in extraneous solutions. TI instructions and additional practice problems are also included.
This document discusses dividing radicals and rationalizing radicals. It provides examples of rationalizing radicals by applying the law of radicals to make the denominator free of radicals. Examples of dividing radicals with the same index are also shown. The steps for dividing radicals are to divide the radicands and rationalize if needed to remove radicals from the denominator. An activity is included where students work in groups to solve radical expressions and present their work.
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 defines and explains the rectangular coordinate system. It begins by introducing Rene Descartes as the "Father of Modern Mathematics" who developed the Cartesian plane. The Cartesian plane is composed of two perpendicular number lines that intersect at the origin (0,0) and divide the plane into four quadrants. Each point on the plane is identified by an ordered pair (x,y) denoting its distance from the x-axis and y-axis. The sign of the x and y values determines which quadrant a point falls into. Examples are provided to identify points and their corresponding quadrants.
This document provides an overview of radical functions including:
- Definitions of nth roots and the principal nth root
- Converting between rational exponents and radical form
- Laws of radicals for addition, subtraction, multiplication, and division
- Simplifying radicals by removing factors from the radicand or reducing indices
- Rationalizing denominators containing radicals by using conjugates
1. The document discusses linear pairs of angles and how to determine if two angles form a linear pair.
2. It provides examples of drawing angles and labeling common and uncommon sides to identify linear pairs. Properties of linear pairs are explained, including that angles in a linear pair are supplementary.
3. Analyze statements about linear pairs and determine if they are always, sometimes, or never true. Solve word problems involving finding missing angle measures in linear pairs.
The document discusses rules for simplifying radical expressions. It states the square root and multiplication rules, which are that the square root of a squared term is the term itself, and that the square root of a product is the product of the square roots. Examples are provided to demonstrate applying these rules to simplify radical expressions by extracting square factors from the radicand. The division rule for radicals is also stated.
- The document discusses how computers use negative exponents to process fractions and percentages during photo processing, which allows apps like Photoshop to shrink photos.
- It explains that negative exponents represent fractions, with the item with the negative exponent moving to the denominator when written as a fraction. This allows computers to perform mathematical operations involving fractions.
- Examples are provided of how negative exponents simplify to fractions through the rule of a-m = 1/am, with the item in the exponent moving between the numerator and denominator.
This document provides instructions on how to solve radical equations. It begins by defining a radical equation and radicand. It then explains the main steps to solve radical equations: isolate the radical to one side, raise both sides to the same power, and simplify. Several examples are worked through to demonstrate this process. The document emphasizes checking solutions, as raising both sides to an even power can result in extraneous solutions. TI instructions and additional practice problems are also included.
This document discusses dividing radicals and rationalizing radicals. It provides examples of rationalizing radicals by applying the law of radicals to make the denominator free of radicals. Examples of dividing radicals with the same index are also shown. The steps for dividing radicals are to divide the radicands and rationalize if needed to remove radicals from the denominator. An activity is included where students work in groups to solve radical expressions and present their work.
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 defines and explains the rectangular coordinate system. It begins by introducing Rene Descartes as the "Father of Modern Mathematics" who developed the Cartesian plane. The Cartesian plane is composed of two perpendicular number lines that intersect at the origin (0,0) and divide the plane into four quadrants. Each point on the plane is identified by an ordered pair (x,y) denoting its distance from the x-axis and y-axis. The sign of the x and y values determines which quadrant a point falls into. Examples are provided to identify points and their corresponding quadrants.
This document provides an overview of radical functions including:
- Definitions of nth roots and the principal nth root
- Converting between rational exponents and radical form
- Laws of radicals for addition, subtraction, multiplication, and division
- Simplifying radicals by removing factors from the radicand or reducing indices
- Rationalizing denominators containing radicals by using conjugates
1. The document discusses linear pairs of angles and how to determine if two angles form a linear pair.
2. It provides examples of drawing angles and labeling common and uncommon sides to identify linear pairs. Properties of linear pairs are explained, including that angles in a linear pair are supplementary.
3. Analyze statements about linear pairs and determine if they are always, sometimes, or never true. Solve word problems involving finding missing angle measures in linear pairs.
This document discusses the three cases of multiplying radicals:
1) Same indices - the indices are multiplied but the radicands are multiplied, e.g. 3√4 * 4√4 = 12√4
2) Different indices but same radicand - the indices are added but the radicand is multiplied, e.g. 5√2 * 5√3 = 5√6
3) Totally different indices and radicands - the indices and radicands are multiplied separately, e.g. 4√3 * 5√2 = 20√6
Examples and practice problems are provided to illustrate each case.
Radical expressions include a root and can be simplified by removing the root or reducing the radicand when possible. Simplifying radical expressions makes it easier to solve equations by grouping like terms and removing radicals. The document provides an example of simplifying a radical expression and explains that radical expressions contain a root and can be made simpler by removing roots or reducing numerical values within the root.
Rational exponents can be written in three different forms. To evaluate or simplify expressions with rational exponents:
- Use properties of exponents like power-to-a-power, product-to-a-power, and quotient-to-a-power laws
- Simplify to remove negative exponents, fractional exponents in the denominator, or complex fractions
- Write expressions with rational exponents as radicals and simplify if possible in 1-2 sentences
solving quadratic equations using quadratic formulamaricel mas
The document discusses how to use the quadratic formula to solve quadratic equations. It provides the formula: x = (-b ± √(b2 - 4ac)) / 2a. It then works through examples of writing quadratic equations in standard form (ax2 + bx + c = 0) and using the formula to solve them. Specifically, it solves the equations: 1) 1x2 + 3x - 27 = 0, 2) 2x2 + 7x + 5 = 0, 3) x2 - 2x = 8, and 4) x2 - 7x = 10. It concludes by providing 3 additional equations to solve using the quadratic formula.
The document discusses simplifying radical expressions. It defines key terms like the radical sign and radicand. It provides two methods for simplifying radicals: using the product property to rewrite with the largest perfect square factor or making a factor tree to pull out factors. Examples are provided to demonstrate simplifying radicals of various forms, including those with variables and higher root expressions. The document also contains practice problems for simplifying radical expressions.
This document discusses solving systems of linear inequalities. It begins with examples of graphing two-inequality systems by shading the regions defined by each inequality boundary and finding the overlapping solution region. It also covers checking solutions by testing points. Applications include painting plates within cost and number limits and geometry shapes defined by inequalities. The document emphasizes representing "greater than" or "less than" situations with systems of inequalities and using graphing to find the solution region.
The document provides steps for dividing out common factors and factoring rational expressions:
1) Identify common factors in the numerator and denominator and divide them out.
2) Factor the numerator and denominator by identifying common factors in each expression.
3) Divide the factored numerator and denominator, simplifying the expression.
This document discusses how to solve radical equations by isolating the radical expression, removing the radical sign by raising both sides to the appropriate power, and solving the resulting equation. It provides examples of solving various radical equations step-by-step and checking solutions. Key steps include isolating the radical term, removing the radical, solving the resulting equation, and checking for extraneous roots.
A quadratic inequality is an inequality involving a quadratic expression, such as ax^2 + bx + c < 0. To solve a quadratic inequality, we first find the solutions to the corresponding equation (set the inequality equal to 0) and then test values on either side of those solutions in the original inequality to determine the solutions to the inequality. The solutions to the inequality will be all values of the variable that satisfy the given relationship.
This document discusses operations with radicals. It covers multiplying radicals by combining like terms, dividing radicals by dividing coefficients and radicands when possible and rationalizing denominators to remove radicals, and FOILing with radicals by using the rules for multiplying and adding/subtracting. Examples are provided for simplifying expressions with radicals and for rationalizing denominators when dividing radicals.
Adding and subtracting radical expressionsAlbert Go
The document discusses operations on radicals, including simplifying radicals by identifying the index and radicand, and adding or subtracting radical expressions by combining like terms that have the same index and radicand. It provides examples of simplifying expressions involving addition and subtraction of radicals, emphasizing that unlike indices cannot be combined.
z = kxy
z = -12
z = kxy
z = -84
z = kxy
z = -21
4.
a. Combined means together as a whole.
b. Combined variation is when a quantity varies jointly with respect to the product of two or more variables.
c. The mathematical statement that represents combined variation is a = k(bc) where a varies jointly as b and c multiplied together.
This document provides information about radicals and working with radical expressions. It defines square roots, principal and negative square roots, radicands, perfect squares, cube roots, nth roots, and the product, quotient, and power rules for radicals. It discusses simplifying radical expressions using these rules as well as adding, subtracting, multiplying, and dividing radicals. The document also covers rationalizing denominators, solving radical equations, and using the Pythagorean theorem and distance formula.
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.
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.
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.
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.
A trapezoid is a quadrilateral with two sides parallel and two sides non-parallel, with the parallel sides called the bases and non-parallel sides called the legs. If the legs of a trapezoid are congruent, it is an isosceles trapezoid, and its properties include that the base angles are congruent and the diagonals bisect each other.
This learner's module talks about the topic or lesson Proportional Segments. This also includes the types of Proportional Segments and its corresponding definitions and examples of each Proportional Segment.
A radical expression contains a square root. To add or subtract radical expressions, simplify the expressions by factoring out the root of the radicand or using prime factorization if there is no square root. Only like radicals with the same index can be combined, and the most common index is a square root of 2, but it can also be cube roots or other roots.
This document discusses simplifying radical expressions using the product, quotient, and power rules for radicals. It also covers adding, subtracting, multiplying, and dividing radicals. Rationalizing denominators is explained as well as solving radical equations. Key steps include isolating the radical term, squaring both sides to remove the radical, and checking solutions in the original equation.
The document discusses trigonometric ratios and functions for right triangles. It defines the six trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of the sides of a right triangle with angle A. Reciprocal functions are also defined. The Pythagorean theorem relates the sides of a right triangle. Functions of complementary angles are equivalent to cofunctions of the original angle. Specific values are given for the trig functions of 45, 30, and 60 degrees. Examples are provided to calculate trig functions from right triangles.
This document discusses the three cases of multiplying radicals:
1) Same indices - the indices are multiplied but the radicands are multiplied, e.g. 3√4 * 4√4 = 12√4
2) Different indices but same radicand - the indices are added but the radicand is multiplied, e.g. 5√2 * 5√3 = 5√6
3) Totally different indices and radicands - the indices and radicands are multiplied separately, e.g. 4√3 * 5√2 = 20√6
Examples and practice problems are provided to illustrate each case.
Radical expressions include a root and can be simplified by removing the root or reducing the radicand when possible. Simplifying radical expressions makes it easier to solve equations by grouping like terms and removing radicals. The document provides an example of simplifying a radical expression and explains that radical expressions contain a root and can be made simpler by removing roots or reducing numerical values within the root.
Rational exponents can be written in three different forms. To evaluate or simplify expressions with rational exponents:
- Use properties of exponents like power-to-a-power, product-to-a-power, and quotient-to-a-power laws
- Simplify to remove negative exponents, fractional exponents in the denominator, or complex fractions
- Write expressions with rational exponents as radicals and simplify if possible in 1-2 sentences
solving quadratic equations using quadratic formulamaricel mas
The document discusses how to use the quadratic formula to solve quadratic equations. It provides the formula: x = (-b ± √(b2 - 4ac)) / 2a. It then works through examples of writing quadratic equations in standard form (ax2 + bx + c = 0) and using the formula to solve them. Specifically, it solves the equations: 1) 1x2 + 3x - 27 = 0, 2) 2x2 + 7x + 5 = 0, 3) x2 - 2x = 8, and 4) x2 - 7x = 10. It concludes by providing 3 additional equations to solve using the quadratic formula.
The document discusses simplifying radical expressions. It defines key terms like the radical sign and radicand. It provides two methods for simplifying radicals: using the product property to rewrite with the largest perfect square factor or making a factor tree to pull out factors. Examples are provided to demonstrate simplifying radicals of various forms, including those with variables and higher root expressions. The document also contains practice problems for simplifying radical expressions.
This document discusses solving systems of linear inequalities. It begins with examples of graphing two-inequality systems by shading the regions defined by each inequality boundary and finding the overlapping solution region. It also covers checking solutions by testing points. Applications include painting plates within cost and number limits and geometry shapes defined by inequalities. The document emphasizes representing "greater than" or "less than" situations with systems of inequalities and using graphing to find the solution region.
The document provides steps for dividing out common factors and factoring rational expressions:
1) Identify common factors in the numerator and denominator and divide them out.
2) Factor the numerator and denominator by identifying common factors in each expression.
3) Divide the factored numerator and denominator, simplifying the expression.
This document discusses how to solve radical equations by isolating the radical expression, removing the radical sign by raising both sides to the appropriate power, and solving the resulting equation. It provides examples of solving various radical equations step-by-step and checking solutions. Key steps include isolating the radical term, removing the radical, solving the resulting equation, and checking for extraneous roots.
A quadratic inequality is an inequality involving a quadratic expression, such as ax^2 + bx + c < 0. To solve a quadratic inequality, we first find the solutions to the corresponding equation (set the inequality equal to 0) and then test values on either side of those solutions in the original inequality to determine the solutions to the inequality. The solutions to the inequality will be all values of the variable that satisfy the given relationship.
This document discusses operations with radicals. It covers multiplying radicals by combining like terms, dividing radicals by dividing coefficients and radicands when possible and rationalizing denominators to remove radicals, and FOILing with radicals by using the rules for multiplying and adding/subtracting. Examples are provided for simplifying expressions with radicals and for rationalizing denominators when dividing radicals.
Adding and subtracting radical expressionsAlbert Go
The document discusses operations on radicals, including simplifying radicals by identifying the index and radicand, and adding or subtracting radical expressions by combining like terms that have the same index and radicand. It provides examples of simplifying expressions involving addition and subtraction of radicals, emphasizing that unlike indices cannot be combined.
z = kxy
z = -12
z = kxy
z = -84
z = kxy
z = -21
4.
a. Combined means together as a whole.
b. Combined variation is when a quantity varies jointly with respect to the product of two or more variables.
c. The mathematical statement that represents combined variation is a = k(bc) where a varies jointly as b and c multiplied together.
This document provides information about radicals and working with radical expressions. It defines square roots, principal and negative square roots, radicands, perfect squares, cube roots, nth roots, and the product, quotient, and power rules for radicals. It discusses simplifying radical expressions using these rules as well as adding, subtracting, multiplying, and dividing radicals. The document also covers rationalizing denominators, solving radical equations, and using the Pythagorean theorem and distance formula.
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.
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.
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.
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.
A trapezoid is a quadrilateral with two sides parallel and two sides non-parallel, with the parallel sides called the bases and non-parallel sides called the legs. If the legs of a trapezoid are congruent, it is an isosceles trapezoid, and its properties include that the base angles are congruent and the diagonals bisect each other.
This learner's module talks about the topic or lesson Proportional Segments. This also includes the types of Proportional Segments and its corresponding definitions and examples of each Proportional Segment.
A radical expression contains a square root. To add or subtract radical expressions, simplify the expressions by factoring out the root of the radicand or using prime factorization if there is no square root. Only like radicals with the same index can be combined, and the most common index is a square root of 2, but it can also be cube roots or other roots.
This document discusses simplifying radical expressions using the product, quotient, and power rules for radicals. It also covers adding, subtracting, multiplying, and dividing radicals. Rationalizing denominators is explained as well as solving radical equations. Key steps include isolating the radical term, squaring both sides to remove the radical, and checking solutions in the original equation.
The document discusses trigonometric ratios and functions for right triangles. It defines the six trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of the sides of a right triangle with angle A. Reciprocal functions are also defined. The Pythagorean theorem relates the sides of a right triangle. Functions of complementary angles are equivalent to cofunctions of the original angle. Specific values are given for the trig functions of 45, 30, and 60 degrees. Examples are provided to calculate trig functions from right triangles.
Negative exponents do not represent negative numbers. Any number to the zero power equals one, which can be proven using the division of powers property. Negative exponents can be simplified by raising the number under the exponent to a positive power equal to the negative exponent.
This document provides instruction on using the Law of Sines to solve triangles. It begins with examples of using the Law of Sines to find missing side lengths or angle measures when two angles and a side, or two sides and an angle are known. It also covers cases where an ambiguous triangle could result from given side-side-angle information. The document demonstrates solving for the area of triangles using trigonometric functions. It concludes with practice problems applying the Law of Sines to find missing measurements and the number of possible triangles based on given side lengths and an angle measure.
11X1 T10 07 sum and product of roots (2010)Nigel Simmons
If α and β are the roots of the quadratic equation ax2 + bx + c = 0, then:
(1) The sum of the roots is -b/a;
(2) The product of the roots is c/a;
(3) The roots can be used to form other quadratic equations or to solve for properties of the original quadratic equation.
The document discusses solving linear equations by factoring using an example of determining the number of pizzas ordered. It formulates the problem as the equation 3x + 10 = 34 where x is the number of pizzas. It solves the equation by subtracting 10 from both sides, dividing both sides by 3, and determining that x = 8 pizzas were ordered. The document then provides more details on linear equations, their structure, and their general solution method.
The document discusses the Law of Cosines and Heron's Formula. It begins by explaining that the Law of Cosines can be used to find side lengths and angle measures of a triangle when given side-angle-side or side-side-side information. It then provides examples of using the Law of Cosines to solve for missing values of triangles. It also introduces Heron's Formula, which can be used to find the area of a triangle based on its side lengths. Examples are given of using both the Law of Cosines and Heron's Formula to solve multi-step word problems involving triangles.
The document discusses using factoring to solve equations arising from physics problems involving height, rate, and time. It provides examples of solving equations derived from the physics formula h=rt-16t^2 for height, rate, or time given two of the three variables. Factoring allows setting each factor equal to zero to find the possible solutions, which are then checked in the original equation.
Simplifying expressions with negative and zero exponentsGenny Phillips
The document provides steps for simplifying expressions with negative exponents:
1) Move the base with the negative exponent to the top of the expression, changing the exponent's sign from negative to positive.
2) Remember that anything raised to the zero power is equal to 1.
3) Examples are provided to demonstrate simplifying expressions using these steps.
The document discusses solving quadratic equations using the quadratic formula. It provides the general form of a quadratic equation as ax2 + bx + c = 0 and introduces the quadratic formula as x = (-b ± √(b2 - 4ac))/2a. Several examples of using the quadratic formula to solve quadratic equations are shown step-by-step with explanations of each step. The examples illustrate determining the a, b, and c coefficients and performing the calculations to find the roots of the equations.
This document discusses exponents and powers. It begins with an introduction that explains how exponents are used to write very large numbers in a shorter form. It then defines exponents and bases. Several laws of exponents are covered, including multiplying and dividing powers with the same base, taking powers of powers, and multiplying powers with the same exponent. Examples are provided to illustrate each law and concept. The document appears to be from a textbook on exponents and powers for students.
The document contains examples and explanations of combined and joint variation. It begins with four warm-up problems that demonstrate combined variation, where the dependent variable varies directly with one independent variable and inversely with another. It explains that to find the constant of variation k, one variable is held constant while solving for k. The document then provides an example of finding k and solving a combined variation word problem. It also defines and provides an example of joint variation, where the dependent variable varies directly with two or more independent variables. It explains finding k is done in the same way as in combined variation problems.
This document provides information on solving quadratic equations by finding square roots. It discusses how to solve equations by taking the square root of each side, and that the square root of a positive number has two answers: one positive and one negative. Properties of square roots are presented. Examples are provided on simplifying expressions involving square roots using the product and quotient properties. The document also covers rationalizing the denominator to remove radicals in fractions and solving quadratic equations by taking square roots and isolating the variable. Methods for solving word problems involving falling objects using the quadratic formula are demonstrated.
This document discusses different types of joint variations between quantities. A joint variation occurs when more than two quantities vary together. The document provides examples of direct and inverse joint variations, explaining that if z varies directly as x and y, with k as a constant, then z = kxy. Similarly, if z varies inversely as x and directly as y, with k as a constant, then z = k/xy. Joint variations describe the mathematical relationships between three or more varying quantities.
1. The document discusses solving oblique triangles using the Law of Sines. It provides examples of solving triangles given: (1) two angles and a side (ASA case) and (2) two sides and a non-included angle (SSA case).
2. For the ASA case, it shows how to find the missing angle and sides using the given information. For the SSA case, it notes that SSA is not a unique case and there may be 0, 1, or 2 possible triangles depending on the side lengths.
3. It provides an example of solving a triangle with ASA given and finds the missing angle and sides. It also provides an example of an SSA case where
This powerpoint presentation discusses or talks about the topic or lesson Direct Variations. It also discusses and explains the rules, concepts, steps and examples of Direct Variations.
The document summarizes two laws for solving triangles - the Law of Cosines and the Law of Sines. It also discusses an ambiguous case of the Law of Sines. The Law of Cosines can be used to find a missing side given two sides and the included angle, or to find a missing angle given all three sides. The Law of Sines can be used to find a missing side or angle given two angles and the side opposite one of them. The ambiguous case allows finding a missing angle given two sides and the angle opposite one of them.
Mathematics 9 Lesson 1-A: Solving Quadratic Equations by Completing the SquareJuan Miguel Palero
This powerpoint presentation discusses or talks about the topic or lesson Solving Quadratic Equations using Completing the Square. It also discusses the steps in solving quadratic equations using the method of Completing the Square.
Mathematics 9 Lesson 4-C: Joint and Combined VariationJuan Miguel Palero
This powerpoint presentation discusses or talks about the topic or lesson Joint and Combined Variations. It also discusses and explains the rules, concepts, steps and examples of Joint and Combined Variation
The document explains the Law of Cosines, which is used to find the length of a side or measure of an angle in a triangle when certain other information is known. It provides two examples - one using side, angle, side information to find a missing side length, and another using side, side, side information to find a missing angle measure. Both examples show setting up and solving the Law of Cosines formula to find the unknown value.
It is a powerpoint presentation that deals with the orientation or introduction of the College General Education Subject: Science, Technology and Society. It also includes the topics and assessments to be dealt with.
Introduction to the Philosophy of the Human Person - Inductive and Deductive ...Juan Miguel Palero
This is a powerpoint presentation that discusses about one of the core subjects in the k-12 curriculum of the Senior High School: Introduction to the Philosophy of the Human Person. On this presentation, it discusses about the definition and philosophical definition of inductive and deductive reasoning with philosophers who pioneered it.
This is a powerpoint presentation that covers one of the topic of Senior High School: Reading and Writing. For this presentation, it deals with the topic of patterns of idea development. It also discusses a type of pattern of idea development: Cause and Effect. It also includes some activities and tips in patterns of idea development.
This is a powerpoint presentation that is about one of the Senior High School Core Subject: Earth and Life Science. It is composed of the definition, characteristics and processes about rocks.
Komunikasyon at Pananaliksik sa Wika at Kulturang Pilipino - Gamit ng Wika sa...Juan Miguel Palero
Ito ay isang powerpoint presentation na nakatuon sa pagtalakay ng mga teorya na nagpapaliwanag sa konsepto na nakapaloob sa paksang: gamit ng wika sa lipunan.
Personal Development - Sigmund Freud's Theory of Human PsycheJuan Miguel Palero
This is a powerpoint presentation of one of the Senior High School Core Subject: Personal Development. For this powerpoint, this serves as a presentation about the topic of the definition of Sigmund Freud's Theory of the Human Psyche. It also includes the parts of the human psyche.
This document provides an overview of personal development and key concepts in psychology. It discusses developing the whole person through understanding how physiological, cognitive, psychological, spiritual, and social factors influence thoughts, feelings, and behaviors. Important psychologists discussed include Sigmund Freud, who developed concepts of the psyche and life/death drives; Carl Jung, who studied archetypes and extraversion/introversion; William James, who studied emotion; Carl Rogers, who studied self-actualization; and Alfred Adler, who developed individual psychology. The document also defines psychology, areas it concerns like cognition and relationships, distinguishes it from psychiatry which treats mental disorders, and lists branches of psychiatry. Homework assignments are provided to research important psychological concepts.
This is a powerpoint presentation that is about one of the Senior High School Core Subject: Earth and Life Science. It is composed of the definition, characteristics, history and processes involved in basic crystallography.
Introduction to the Philosophy of the Human Person - Definition of Philosophi...Juan Miguel Palero
This is a powerpoint presentation that discusses about one of the core subjects in the k-12 curriculum of the Senior High School: Introduction to the Philosophy of the Human Person. On this presentation, it discusses about the definition and philosophical definition of philosophizing and the philosophers behind it.
This is a powerpoint presentation that discusses about one of the applied subjects in the k-12 curriculum of the Senior High School: Empowerment Technologies. On this powerpoint presentation, it discusses about the definition and elements of Microsoft Word.
Understanding Culture, Society and Politics - Biological EvolutionJuan Miguel Palero
This is a powerpoint presentation of one of the Senior High School Core Subject: Understanding Culture, Society and Politics. For this powerpoint, this serves as a presentation about the topic of the definition and timeline of human biological evolution.
This document defines different types of definitions and outlines the key parts of a definitive writing. An operational definition provides a clear and concise description of a term to specify its meaning. The main parts of a definitive writing include an introduction that hooks the reader and presents terms to define, a body that defines each term through several paragraphs, and a conclusion that restates the main idea and lessons learned.
Introduction to the Philosophy of Human Person - What is the TruthJuan Miguel Palero
This is a powerpoint presentation that discusses about one of the core subjects in the k-12 curriculum of the Senior High School: Introduction to the Philosophy of the Human Person. On this presentation, it discusses about the definition and philosophical definition of truths and axioms.
This is a powerpoint presentation of one of the Senior High School Core Subject: Personal Development. For this powerpoint, this serves as a presentation about the topic of the definition of self in a psychological point of view.
Understanding Culture, Society and Politics - Definition of Anthropology, Pol...Juan Miguel Palero
This is a powerpoint presentation of one of the Senior High School Core Subject: Understanding Culture, Society and Politics. For this powerpoint, this serves as a presentation about the topic of the definition of anthropology, political science and sociology.
General Mathematics - Intercepts of Rational FunctionsJuan Miguel Palero
It is a powerpoint presentation that will help the students to enrich their knowledge about Senior High School subject of General Mathematics. It is comprised about Rational functions and its intercepts. It also includes some examples and exercises of the said topic.
This is a powerpoint presentation that is about one of the Senior High School Core Subject: Earth and Life Science. It is composed of the definition and the properties of the different classification of minerals.
Komunikasyon at Pananaliksik sa Wika at Kulturang Pilipino - Register bilang ...Juan Miguel Palero
Ito ay isang powerpoint presentation na nakatuon sa pagtalakay ng mga teorya na nagpapaliwanag sa konsepto na nakapaloob sa register bilang barayti ng wikang Filipino
Minerals are naturally occurring chemical compounds that form in pure crystalline structures within the Earth. They originate as igneous rocks cool and crystallize below the Earth's surface. Minerals have distinct chemical compositions and properties including color, streak, luster, hardness, cleavage, diaphaneity, and magnetism. These properties are determined by a mineral's composition and crystalline structure. Color, for example, is usually caused by electromagnetic radiation interacting with a mineral's electrons. Hardness refers to a mineral's resistance to scratching and is measured using the Mohs scale. Cleavage describes a mineral's tendency to break along planes of weaker atomic bonding.
CapTechTalks Webinar Slides June 2024 Donovan Wright.pptxCapitolTechU
Slides from a Capitol Technology University webinar held June 20, 2024. The webinar featured Dr. Donovan Wright, presenting on the Department of Defense Digital Transformation.
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...TechSoup
Whether you're new to SEO or looking to refine your existing strategies, this webinar will provide you with actionable insights and practical tips to elevate your nonprofit's online presence.
🔥🔥🔥🔥🔥🔥🔥🔥🔥
إضغ بين إيديكم من أقوى الملازم التي صممتها
ملزمة تشريح الجهاز الهيكلي (نظري 3)
💀💀💀💀💀💀💀💀💀💀
تتميز هذهِ الملزمة بعِدة مُميزات :
1- مُترجمة ترجمة تُناسب جميع المستويات
2- تحتوي على 78 رسم توضيحي لكل كلمة موجودة بالملزمة (لكل كلمة !!!!)
#فهم_ماكو_درخ
3- دقة الكتابة والصور عالية جداً جداً جداً
4- هُنالك بعض المعلومات تم توضيحها بشكل تفصيلي جداً (تُعتبر لدى الطالب أو الطالبة بإنها معلومات مُبهمة ومع ذلك تم توضيح هذهِ المعلومات المُبهمة بشكل تفصيلي جداً
5- الملزمة تشرح نفسها ب نفسها بس تكلك تعال اقراني
6- تحتوي الملزمة في اول سلايد على خارطة تتضمن جميع تفرُعات معلومات الجهاز الهيكلي المذكورة في هذهِ الملزمة
واخيراً هذهِ الملزمة حلالٌ عليكم وإتمنى منكم إن تدعولي بالخير والصحة والعافية فقط
كل التوفيق زملائي وزميلاتي ، زميلكم محمد الذهبي 💊💊
🔥🔥🔥🔥🔥🔥🔥🔥🔥
How to Setup Default Value for a Field in Odoo 17Celine George
In Odoo, we can set a default value for a field during the creation of a record for a model. We have many methods in odoo for setting a default value to the field.
Gender and Mental Health - Counselling and Family Therapy Applications and In...PsychoTech Services
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.pptHenry Hollis
The History of NZ 1870-1900.
Making of a Nation.
From the NZ Wars to Liberals,
Richard Seddon, George Grey,
Social Laboratory, New Zealand,
Confiscations, Kotahitanga, Kingitanga, Parliament, Suffrage, Repudiation, Economic Change, Agriculture, Gold Mining, Timber, Flax, Sheep, Dairying,