Alg 2 lesson 5-6
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A radical expression is simplified if it has no perfect powers or fractions under the radical, and no radicals in the denominator. Simplified expressions have no perfect powers under the radical, no fractions under the radical, and no radicals in the denominator. Not simplified expressions can have perfect powers under the radical, fractions under the radical, or radicals in the denominator.
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Alg2 lesson 5-6
This document discusses how to simplify radical expressions. It states that a radical expression is simplified if it has no perfect powers under the radical, no fractions under the radical, and no radicals in the denominator. It provides examples of simplified and non-simplified radical expressions according to these rules.
11.1 and 11.2
This document provides instructions for simplifying radical expressions, including basic operations with radicals, examples of simplifying radical expressions, and homework assignments involving simplifying radicals from pages 713 and 3-21 of the textbook. Students are asked to complete odd numbered problems 3, 7, 9, 17, 19, 23, 25 from page 713 and problems 27 through 53 from page 3-21.
8.4
The document defines key terms related to radical expressions, including radical expressions, radicands, and simplest form. It then outlines several properties of radicals: the product property, which allows multiplying radicals by splitting them into factors; the quotient property, which allows simplifying radicals in fractions; and rationalizing denominators, which removes radicals from denominators. Finally, it provides examples applying these properties to simplify, add, subtract, and multiply radical expressions.
Simplifying Radical Expressions
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.
Personal Entrepreneurial Competencies
This document provides a pre-assessment for identifying characteristics of successful entrepreneurs. It lists 10 characteristics in Column A and their matching definitions in Column B. It then evaluates the personal entrepreneurial competencies (PECs) of an individual in terms of strengths and areas needing development. Finally, it directs the reader to choose characteristics from a provided list that describe their own traits and find ways to align their PECs.
Computer hardware servicing ncii
This document outlines a competency-based curriculum for a Computer Hardware Servicing NC II qualification. It includes 392 hours of training delivered through modules covering basic, common, and core competencies. Basic competencies focus on workplace communication, teamwork, professionalism, and safety. Common competencies include quality standards, computer operation, measurement, technical drawing, hand tools, and electrical wiring. Core competencies center on installing, diagnosing, configuring, and maintaining computer systems and networks. Assessment involves hands-on demonstration, observation, exams, and discussion. The course uses lecture, self-paced learning, and group work delivered by a qualified trainer.
Radical Operations
1) The document discusses various methods for working with radicals, including prime factorization, reducing radicals, adding radicals, multiplying radicals, and working with expressions involving radicals.
2) Key steps for reducing radicals are to prime factorize the radicand, convert to fractional exponent form, distribute the fractional exponent, and simplify.
3) For adding radicals, the radicals must have common radicands, and reducing radicals may be required first.
4) When multiplying radicals, the coefficients are multiplied and the radicands are multiplied, similar to multiplying fractions. Radicals in the result need to be simplified.
7.7 Solving Radical Equations
This document provides steps for solving radical equations:
1) Isolate the radical on one side of the equation by performing inverse operations
2) Raise both sides of the equation to a power equal to the index of the radical to eliminate the radical
3) Solve the remaining polynomial equation
It includes examples of solving simpler radical equations as well as more complex equations involving fractions and multiple radicals. Checking solutions is emphasized as extraneous solutions may occasionally occur. Graphing calculators can also help visualize and find solutions to radical equations.
Recommended
Alg2 lesson 5-6
This document discusses how to simplify radical expressions. It states that a radical expression is simplified if it has no perfect powers under the radical, no fractions under the radical, and no radicals in the denominator. It provides examples of simplified and non-simplified radical expressions according to these rules.
11.1 and 11.2
This document provides instructions for simplifying radical expressions, including basic operations with radicals, examples of simplifying radical expressions, and homework assignments involving simplifying radicals from pages 713 and 3-21 of the textbook. Students are asked to complete odd numbered problems 3, 7, 9, 17, 19, 23, 25 from page 713 and problems 27 through 53 from page 3-21.
8.4
The document defines key terms related to radical expressions, including radical expressions, radicands, and simplest form. It then outlines several properties of radicals: the product property, which allows multiplying radicals by splitting them into factors; the quotient property, which allows simplifying radicals in fractions; and rationalizing denominators, which removes radicals from denominators. Finally, it provides examples applying these properties to simplify, add, subtract, and multiply radical expressions.
Simplifying Radical Expressions
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.
Personal Entrepreneurial Competencies
This document provides a pre-assessment for identifying characteristics of successful entrepreneurs. It lists 10 characteristics in Column A and their matching definitions in Column B. It then evaluates the personal entrepreneurial competencies (PECs) of an individual in terms of strengths and areas needing development. Finally, it directs the reader to choose characteristics from a provided list that describe their own traits and find ways to align their PECs.
Computer hardware servicing ncii
This document outlines a competency-based curriculum for a Computer Hardware Servicing NC II qualification. It includes 392 hours of training delivered through modules covering basic, common, and core competencies. Basic competencies focus on workplace communication, teamwork, professionalism, and safety. Common competencies include quality standards, computer operation, measurement, technical drawing, hand tools, and electrical wiring. Core competencies center on installing, diagnosing, configuring, and maintaining computer systems and networks. Assessment involves hands-on demonstration, observation, exams, and discussion. The course uses lecture, self-paced learning, and group work delivered by a qualified trainer.
Radical Operations
1) The document discusses various methods for working with radicals, including prime factorization, reducing radicals, adding radicals, multiplying radicals, and working with expressions involving radicals.
2) Key steps for reducing radicals are to prime factorize the radicand, convert to fractional exponent form, distribute the fractional exponent, and simplify.
3) For adding radicals, the radicals must have common radicands, and reducing radicals may be required first.
4) When multiplying radicals, the coefficients are multiplied and the radicands are multiplied, similar to multiplying fractions. Radicals in the result need to be simplified.
7.7 Solving Radical Equations
This document provides steps for solving radical equations:
1) Isolate the radical on one side of the equation by performing inverse operations
2) Raise both sides of the equation to a power equal to the index of the radical to eliminate the radical
3) Solve the remaining polynomial equation
It includes examples of solving simpler radical equations as well as more complex equations involving fractions and multiple radicals. Checking solutions is emphasized as extraneous solutions may occasionally occur. Graphing calculators can also help visualize and find solutions to radical equations.
Module 14 lesson 4 solving radical equations
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.
Rational Exponents
Rational exponents allow radicals to be written as fractional exponents. To write a radical with an index of n as a rational exponent, the index becomes the denominator and the exponent of the radicand becomes the numerator. The rules of exponents still apply to rational exponents. Expressions with rational exponents are simplified by having no negative exponents, no fractional exponents in the denominator, not being a complex fraction, and having the least possible index for any remaining radicals. Examples show how to evaluate, simplify, and perform operations on expressions with rational exponents.
Roots and Radicals
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.
Addition and Subtraction of Radicals
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.
9.2 simplifying square roots
This document discusses simplifying square roots to their simplest form. To be in simplest form, a radical expression cannot have any perfect square factors other than 1 under the radical sign and cannot have any fractions under the radical sign or radicals in denominators.
Simplifying radical expressions, rational exponents, radical equations
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.
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ESD Tools:
1. Anti-static wrist strap
2. Anti-static mat
Hand Tools:
3. Flat head screwdriver
4. Philips head screwdriver
5. Torx screwdriver
6. Hex driver
7. Needle-nose plier
8. Wire cutter
9. Tweezers
10. Part retriever
11. Flashlight
Cleaning Tools:
12. Lint-free cloth
13. Compressed air
14. Cable ties
Diagnostic Tools:
15. Multimeter
16. Loopback Adapter
Computer Hardware Servicing Learning Module v.2.0
This document provides an introduction to the hardware components of a computer system. It identifies and describes the major internal and external hardware components, including the system unit, motherboard, CPU, memory, expansion bus, power supply, hard drive, optical drives, input devices like keyboards and mice, and other adapters. The objectives are to familiarize students with the important computer hardware, their functions, and basic servicing skills. Hands-on activities and exercises are provided to help students develop skills in assembling, installing, and servicing computer hardware.
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Slideshare ppt
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Ratios, proportions, and percents can be used to compare quantities and solve problems. A ratio compares two quantities, like the number of squares to circles. Equal ratios form a proportion, which can be used to solve for unknown values. Percents represent a number out of 100. Common percent calculations include finding a percent of a number and converting between fractions, decimals, and percents. The percent proportion states that the percent equals the part divided by the whole quantity.
1150 day 10
This document covers topics related to repeating decimals, irrational numbers, and square roots. It includes examples of writing repeating decimals as fractions, ordering decimals, finding square roots, and using the Pythagorean theorem. Various math problems are presented along with step-by-step solutions to illustrate these concepts.
1150 day 9
1) Decimals represent numbers using place value with decimal points. To write decimals in expanded form, they are broken into place value terms using positive and negative exponents.
2) Fractions can be converted to decimals using division or by writing the fraction as a ratio of two numbers and setting up a proportion to solve for the decimal.
3) Scientific notation is used to write very large or small numbers in a standard form, such as 3.603 x 107. Operations can be done on decimals by lining up the decimal points or moving them with multiplication/division.
1150 day 8
This document provides an overview of rational numbers including:
- Integers and fractions written in the form a/b where a and b are integers and b ≠ 0
- Equivalent fractions represented by the same number
- Ordering and comparing rational numbers
- Converting between improper fractions and mixed numbers
- Basic operations of addition, subtraction, multiplication, and division of rational numbers
- Word problems involving rational numbers
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The document discusses various aspects of whole number operations including:
1) Place value systems and how numbers are represented in bases other than 10 such as base 5 and base 12.
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3) Properties of operations like the commutative, associative, identity, and zero properties of multiplication.
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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.
Rational Exponents
Rational exponents allow radicals to be written as fractional exponents. To write a radical with an index of n as a rational exponent, the index becomes the denominator and the exponent of the radicand becomes the numerator. The rules of exponents still apply to rational exponents. Expressions with rational exponents are simplified by having no negative exponents, no fractional exponents in the denominator, not being a complex fraction, and having the least possible index for any remaining radicals. Examples show how to evaluate, simplify, and perform operations on expressions with rational exponents.
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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.
Addition and Subtraction of Radicals
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.
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This document discusses simplifying square roots to their simplest form. To be in simplest form, a radical expression cannot have any perfect square factors other than 1 under the radical sign and cannot have any fractions under the radical sign or radicals in denominators.
Simplifying radical expressions, rational exponents, radical equations
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.
Computer Hardware-servicing-learning-module
ESD Tools:
1. Anti-static wrist strap
2. Anti-static mat
Hand Tools:
3. Flat head screwdriver
4. Philips head screwdriver
5. Torx screwdriver
6. Hex driver
7. Needle-nose plier
8. Wire cutter
9. Tweezers
10. Part retriever
11. Flashlight
Cleaning Tools:
12. Lint-free cloth
13. Compressed air
14. Cable ties
Diagnostic Tools:
15. Multimeter
16. Loopback Adapter
Computer Hardware Servicing Learning Module v.2.0
This document provides an introduction to the hardware components of a computer system. It identifies and describes the major internal and external hardware components, including the system unit, motherboard, CPU, memory, expansion bus, power supply, hard drive, optical drives, input devices like keyboards and mice, and other adapters. The objectives are to familiarize students with the important computer hardware, their functions, and basic servicing skills. Hands-on activities and exercises are provided to help students develop skills in assembling, installing, and servicing computer hardware.
DepEd TLE Computer Hardware Servicing Curriculum Guide Grade 7-10
The document provides an overview of the Grade 7/8 exploratory course on Information and Communications Technology - Computer Hardware Servicing. The course covers seven key lessons: 1) Personal Entrepreneurial Competencies, 2) Environment and Market concepts, 3) Use of Hand Tools and Equipment, 4) Maintaining tools and equipment, 5) Performing measurements and calculations, 6) Preparing and interpreting technical drawings, and 7) Practicing occupational health and safety procedures. For each lesson, the document outlines the relevant content standards, performance standards, learning competencies, and codes. The overall aim is for students to gain foundational knowledge and skills related to computer hardware servicing as a potential career path.
Slideshare Powerpoint presentation
Art is a creative expression that stimulates the senses or imagination according to Felicity Hampel. Picasso believed that every child is an artist but growing up can stop that creativity. Aristotle defined art as anything requiring a maker and not being able to create itself.
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Miss goodheart created a PowerPoint to test out the Slideshare tool, which was introduced to her by Sharon Tonner on January 20th, 2011.
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Ratios, proportions, and percents can be used to compare quantities and solve problems. A ratio compares two quantities, like the number of squares to circles. Equal ratios form a proportion, which can be used to solve for unknown values. Percents represent a number out of 100. Common percent calculations include finding a percent of a number and converting between fractions, decimals, and percents. The percent proportion states that the percent equals the part divided by the whole quantity.
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This document covers topics related to repeating decimals, irrational numbers, and square roots. It includes examples of writing repeating decimals as fractions, ordering decimals, finding square roots, and using the Pythagorean theorem. Various math problems are presented along with step-by-step solutions to illustrate these concepts.
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1) Decimals represent numbers using place value with decimal points. To write decimals in expanded form, they are broken into place value terms using positive and negative exponents.
2) Fractions can be converted to decimals using division or by writing the fraction as a ratio of two numbers and setting up a proportion to solve for the decimal.
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- Equivalent fractions represented by the same number
- Ordering and comparing rational numbers
- Converting between improper fractions and mixed numbers
- Basic operations of addition, subtraction, multiplication, and division of rational numbers
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2) Algorithms for addition, subtraction, multiplication, and division using various models and representations.
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A business may deal with both sales and purchases occasionally. They buy things from vendors and then sell them to their customers. Such dealings can be confusing at times. Because multiple clients may inquire about the same product at the same time, after purchasing those products, customers must be assigned to them. Odoo has a tool called Reception Report that can be used to complete this assignment. By enabling this, a reception report comes automatically after confirming a receipt, from which we can assign products to orders.
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- 1. A radical expression is simplified if: •It has no perfect powers under the radical •It has no fractions under the radical •It has no radicals in the denominator Simplified: Not Simplified:
- 3. Simplify
- 4. simplify 3
- 5. Simplify •x = •x x = x8 x x8
- 6. Simplify • 3 x2 • 3 x2
- 7. Simplify
- 8. Simplify
- 9. Simplify