Geometric proportion and Laws of Proportion
•
6 likes•9,449 views
This document discusses geometric proportions and the laws of proportions. It defines a proportion as an equality of two ratios, with the ratios written in the form a:b=c:d. It presents the six laws of proportions: 1) the means-extremes product law, 2) the switch means-switch extremes law, 3) the invert-both-sides law, 4) the denominator-addition law, 5) the denominator-subtraction law, and 6) the numerator-denominator sum law. Examples are provided to illustrate how to use each law to solve proportion problems.
Report
Share
Report
Share
Download to read offline
Recommended
trapezoid and its properties
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.
Midline theorem - Mathematics - Geometry
The document explains the midline theorem in geometry. The midline theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. The document provides examples of applying the midline theorem to solve for unknown lengths in various triangles. It also includes a short quiz testing understanding of using the midline theorem.
4 2 rules of radicals
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.
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.
Direct variation power point
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.
Rational Root Theorem
The Rational Root Theorem provides a method to find all possible rational roots of a polynomial with integer coefficients. It states that every rational root must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. Examples are provided to demonstrate finding all possible rational roots using this theorem and then checking them to determine the actual rational roots. Once a rational root is found, synthetic division can be used to find the depressed polynomial which can then be fully factored to obtain all factors of the original polynomial.
Factor Completely Different Types of Polynomials
Polynomials are algebraic expressions that are consist of variables and coefficients. We can perform arithmetic operations such as subtraction, addition, multiplication and division. This presentation is all about factoring completely different types of polynomials. There four types of polynomials to factor that would be discuss in this presentation
Midline Theorem Math 9.pptx
1. The document provides directions for drawing and cutting a triangle, then shading one of the resulting pieces. It defines the midline theorem and has students complete statements about the equal lengths of lines in a bisected triangle.
2. The document tests students on applying the midline theorem by having them calculate unknown line lengths based on given lengths. It also includes true/false questions and word problems about triangles.
3. The final problem asks students to calculate the new perimeter of a triangular farm if an adjacent lot is purchased that doubles the length of two sides of the original triangle.
Recommended
trapezoid and its properties
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.
Midline theorem - Mathematics - Geometry
The document explains the midline theorem in geometry. The midline theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. The document provides examples of applying the midline theorem to solve for unknown lengths in various triangles. It also includes a short quiz testing understanding of using the midline theorem.
4 2 rules of radicals
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.
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.
Direct variation power point
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.
Rational Root Theorem
The Rational Root Theorem provides a method to find all possible rational roots of a polynomial with integer coefficients. It states that every rational root must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. Examples are provided to demonstrate finding all possible rational roots using this theorem and then checking them to determine the actual rational roots. Once a rational root is found, synthetic division can be used to find the depressed polynomial which can then be fully factored to obtain all factors of the original polynomial.
Factor Completely Different Types of Polynomials
Polynomials are algebraic expressions that are consist of variables and coefficients. We can perform arithmetic operations such as subtraction, addition, multiplication and division. This presentation is all about factoring completely different types of polynomials. There four types of polynomials to factor that would be discuss in this presentation
Midline Theorem Math 9.pptx
1. The document provides directions for drawing and cutting a triangle, then shading one of the resulting pieces. It defines the midline theorem and has students complete statements about the equal lengths of lines in a bisected triangle.
2. The document tests students on applying the midline theorem by having them calculate unknown line lengths based on given lengths. It also includes true/false questions and word problems about triangles.
3. The final problem asks students to calculate the new perimeter of a triangular farm if an adjacent lot is purchased that doubles the length of two sides of the original triangle.
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.
Law of sines
The document discusses the Law of Sines, which is a rule used to find unknown angles and sides of triangles when some combination of angles and sides are known. The Law of Sines states that the ratio of any side to its opposite angle is equal to the ratio of any other side to its opposite angle. An example problem demonstrates using the Law of Sines to solve a triangle when two angles and one side are given. Additional resources are provided to learn more about solving triangles with the Law of Sines.
Solving Equations Transformable to Quadratic Equation Including Rational Alge...
Provides examples and solutions on how to solve equations that is transformable to quadratic equation and rational algebraic equations.
Multiplying polynomials
The document describes three methods for multiplying polynomials:
1) The distributive property, which involves multiplying each term of one polynomial with each term of the other.
2) FOIL (First, Outer, Inner, Last), which is a mnemonic for multiplying binomials by multiplying corresponding terms.
3) The box method, which involves drawing a box and writing one polynomial above and beside the box, then multiplying corresponding terms. Examples are provided to demonstrate each method.
8 4 Rhombuses, Rectangles, And Squares
This document discusses different types of quadrilaterals (four-sided polygons), including parallelograms, rectangles, rhombuses, and squares. It provides properties to define each shape and instructs how to make a foldable with examples of each quadrilateral type. Key properties include: parallelograms have two pairs of parallel sides; rectangles are parallelograms with four right angles; rhombuses are parallelograms with four congruent sides; squares are rectangles and rhombuses with four right angles and four congruent sides. A Venn diagram compares the properties of these quadrilaterals.
Module 4 Grade 9 Mathematics (RADICALS)
This document summarizes a module on rational exponents and radicals that was presented at a 2014 mid-year inset for secondary mathematics teachers. The module covered lessons on zero, negative integral and rational exponents, radicals, and solving radical equations. It provided examples of simplifying expressions using laws of exponents and radicals. Recommended teaching strategies included problem-solving activities and a group brainstorming activity to discuss critical content areas and difficulties from teacher and student perspectives.
Quadratic inequality
This document discusses solving quadratic inequalities. It provides examples of single-variable quadratic inequalities and explains how to find the solution set by first setting the inequality equal to an equation, solving for the roots, and then testing values within the intervals formed by the roots. The document also introduces quadratic inequalities with two variables and how to represent them. It defines a quadratic inequality and explains the process of solving them by relating it back to solving a quadratic equation.
Trapezoids
This document defines and describes properties of trapezoids and isosceles trapezoids. It defines a trapezoid as a quadrilateral with one set of parallel sides, called bases, and defines an isosceles trapezoid as having two congruent legs. The key properties outlined are that the leg angles are supplementary, base angles and diagonals of an isosceles trapezoid are congruent, and the midsegment of a trapezoid connects the midpoints of the legs and is parallel to the bases. Several example problems are provided to demonstrate applying these properties.
Arithmetic sequence
This document discusses arithmetic sequences and their properties. It defines an arithmetic sequence as a sequence where the difference between consecutive terms is constant. It provides the formula for the nth term of an arithmetic sequence as an = a1 + (n-1)d, where a1 is the first term, n is the term number, and d is the common difference. It gives examples of finding specific terms and summarizing sequences. It also discusses the arithmetic mean and arithmetic sum formulas.
angle of elevation and depression
The document defines and compares angle of elevation and angle of depression. When looking at an object above your position, the angle formed between the line of sight and horizontal is the angle of elevation. When looking below your position, the angle is called the angle of depression. Several examples are given of calculating angles of elevation and depression using trigonometric tangent functions, when the height of the observer or object and the distance between them is known.
Nature of the roots of a quadratic equation
The discriminant of a quadratic equation is represented by b^2 - 4ac. This value determines the nature of the roots. If b^2 - 4ac = 0, then the roots are real and equal. If b^2 - 4ac > 0, then the roots are real but unequal. If b^2 - 4ac < 0, then the roots are imaginary and unequal. The document provides examples of calculating the discriminant and determining the nature of roots for different quadratic equations.
Law of Radicals.pptx
The document discusses laws of radicals including the product law of radicals and quotient law of radicals. It provides examples of applying each law such as 6x ∙ 24x = 3√9x ∙ 3√3x^2 and 75 ÷ 3 = 5√25. The learning targets are to derive the laws of radicals and simplify radical expressions using the laws of radicals. Biblical verses from Hebrews 11:6 and Matthew 6:15 about faith are also included.
Joint and Combined Variation (Mathematics 9)
You already know relationships where one variable varies directly or inversely with another variable.
Now you will look at relationships where one variable varies directly with two or more other variables but does not vary inversely with any other variable.
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.
Factor theorem
The document discusses the factor theorem and how to determine if a polynomial is a factor of another polynomial. It provides examples of using the factor theorem to show that (x + 1) is a factor of 2x^3 + 5x^2 - 3 and that (x - 2) is a factor of x^4 + x^3 - x^2 - x - 18. It also gives an example of finding a polynomial function given its zeros as -2, 1, -1. The document provides exercises for using the factor theorem to determine unknown values in polynomials.
Multiplication of radicals
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.
Factoring the difference of two squares
The document discusses factoring the difference of two squares through examples such as (x+5)(x-5)=x^2 - 25. It explains that to factor a difference of two squares, we write the expression as the difference of two terms squared, then group the terms with the same bases and opposite signs inside parentheses. Several practice problems are provided to reinforce this technique for factoring completely the difference of two squares.
Solving Quadratic Equations
Provides example on how to solve quadratic equations using extracting square roots, factoring, completing the square and quadratic formula.
Congruent Triangles
1. Triangles are congruent if all corresponding sides and angles are congruent. They will have the same shape and size but may be mirror images.
2. There are four main postulates and theorems used to prove triangles congruent: SSS (three sides), SAS (two sides and included angle), ASA (two angles and included side), and AAS (two angles and non-included side).
3. Corresponding parts of congruent triangles are also congruent based on the CPCTC theorem. This allows using previously proven congruent parts in future proofs.
GR 8 Math Powerpoint about Polynomial Techniques
-This is a powerpoint inspired by one of Canva displayed presentation.
- This is about Math Polynomials and good for highschoolers presentation for school.
- It consists of 39 pages explaining each of the Polynomial Techniques.
- Good for review or inspired powerpoint.
Digital Logic.pptxghuuhhhhhhuu7ffghhhhhg
Jdjddjdjjfjrjrhhfbrhrjhjjfjrjfrifjhfjdirurfu8fi3hdudoickegdhejdofjrvdjozdkjieofiudjrhciyyfifjjvi9r7ugidof8cdukrkfj2keoekeRecombination in bacterial growth refers to the process by which bacteria exchange genetic material with each other, leading to the formation of new genetic combinations. This process can occur through several mechanisms, including transformation, conjugation, and transduction.
1. Transformation: In transformation, bacteria take up free DNA from their environment and incorporate it into their genome. This DNA may come from lysed bacterial cells or be released into the environment by other means. Once inside the cell, the foreign DNA can recombine with the bacterial chromosome, leading to genetic diversity.
2. Conjugation: Conjugation involves the direct transfer of genetic material from one bacterium to another through physical contact. This transfer typically occurs through a conjugative pilus, a structure that forms a bridge between the donor and recipient cells. During conjugation, a copy of the donor's DNA, often in the form of a plasmid, is transferred to the recipient cell, where it can integrate into the chromosome or exist as a separate genetic element.
3. Transduction: Transduction occurs when bacterial DNA is transferred from one bacterium to another by a bacteriophage (a virus that infects bacteria). During the lytic cycle of viral replication, some bacteriophages may accidentally package bacterial DNA instead of their own genome. When these phages infect other bacteria, they inject this bacterial DNA into the new host, where it can recombine with the recipient chromosome.
Recombination plays a crucial role in bacterial evolution and adaptation by facilitating the exchange of beneficial genetic traits, such as antibiotic resistance or metabolic capabilities. It contributes to the genetic diversity of bacterial populations and can influence their ability to survive and thrive in various environments.In enzymes, a domain refers to a distinct structural and functional unit that contributes to the overall activity of the enzyme. Domains are often modular components within the enzyme's overall structure, each with its own specific role or function. These functions may include substrate binding, catalysis, regulation, or interaction with other molecules. Domains can have specific shapes, surface properties, and active sites tailored to perform particular biochemical tasks within the enzyme's catalytic cycle. Additionally, enzymes can contain multiple domains, which may interact with each other to modulate enzyme activity or to confer versatility in substrate recognition and binding. The organization of domains within an enzyme contributes to its overall efficiency and specificity in catalyzing biochemical reactions.Superscalar architecture is a CPU design paradigm that enables the simultaneous execution of multiple instructions within a single clock cycle. This is achieved by having multiple execution units, allowing t
More Related Content
What's hot
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.
Law of sines
The document discusses the Law of Sines, which is a rule used to find unknown angles and sides of triangles when some combination of angles and sides are known. The Law of Sines states that the ratio of any side to its opposite angle is equal to the ratio of any other side to its opposite angle. An example problem demonstrates using the Law of Sines to solve a triangle when two angles and one side are given. Additional resources are provided to learn more about solving triangles with the Law of Sines.
Solving Equations Transformable to Quadratic Equation Including Rational Alge...
Provides examples and solutions on how to solve equations that is transformable to quadratic equation and rational algebraic equations.
Multiplying polynomials
The document describes three methods for multiplying polynomials:
1) The distributive property, which involves multiplying each term of one polynomial with each term of the other.
2) FOIL (First, Outer, Inner, Last), which is a mnemonic for multiplying binomials by multiplying corresponding terms.
3) The box method, which involves drawing a box and writing one polynomial above and beside the box, then multiplying corresponding terms. Examples are provided to demonstrate each method.
8 4 Rhombuses, Rectangles, And Squares
This document discusses different types of quadrilaterals (four-sided polygons), including parallelograms, rectangles, rhombuses, and squares. It provides properties to define each shape and instructs how to make a foldable with examples of each quadrilateral type. Key properties include: parallelograms have two pairs of parallel sides; rectangles are parallelograms with four right angles; rhombuses are parallelograms with four congruent sides; squares are rectangles and rhombuses with four right angles and four congruent sides. A Venn diagram compares the properties of these quadrilaterals.
Module 4 Grade 9 Mathematics (RADICALS)
This document summarizes a module on rational exponents and radicals that was presented at a 2014 mid-year inset for secondary mathematics teachers. The module covered lessons on zero, negative integral and rational exponents, radicals, and solving radical equations. It provided examples of simplifying expressions using laws of exponents and radicals. Recommended teaching strategies included problem-solving activities and a group brainstorming activity to discuss critical content areas and difficulties from teacher and student perspectives.
Quadratic inequality
This document discusses solving quadratic inequalities. It provides examples of single-variable quadratic inequalities and explains how to find the solution set by first setting the inequality equal to an equation, solving for the roots, and then testing values within the intervals formed by the roots. The document also introduces quadratic inequalities with two variables and how to represent them. It defines a quadratic inequality and explains the process of solving them by relating it back to solving a quadratic equation.
Trapezoids
This document defines and describes properties of trapezoids and isosceles trapezoids. It defines a trapezoid as a quadrilateral with one set of parallel sides, called bases, and defines an isosceles trapezoid as having two congruent legs. The key properties outlined are that the leg angles are supplementary, base angles and diagonals of an isosceles trapezoid are congruent, and the midsegment of a trapezoid connects the midpoints of the legs and is parallel to the bases. Several example problems are provided to demonstrate applying these properties.
Arithmetic sequence
This document discusses arithmetic sequences and their properties. It defines an arithmetic sequence as a sequence where the difference between consecutive terms is constant. It provides the formula for the nth term of an arithmetic sequence as an = a1 + (n-1)d, where a1 is the first term, n is the term number, and d is the common difference. It gives examples of finding specific terms and summarizing sequences. It also discusses the arithmetic mean and arithmetic sum formulas.
angle of elevation and depression
The document defines and compares angle of elevation and angle of depression. When looking at an object above your position, the angle formed between the line of sight and horizontal is the angle of elevation. When looking below your position, the angle is called the angle of depression. Several examples are given of calculating angles of elevation and depression using trigonometric tangent functions, when the height of the observer or object and the distance between them is known.
Nature of the roots of a quadratic equation
The discriminant of a quadratic equation is represented by b^2 - 4ac. This value determines the nature of the roots. If b^2 - 4ac = 0, then the roots are real and equal. If b^2 - 4ac > 0, then the roots are real but unequal. If b^2 - 4ac < 0, then the roots are imaginary and unequal. The document provides examples of calculating the discriminant and determining the nature of roots for different quadratic equations.
Law of Radicals.pptx
The document discusses laws of radicals including the product law of radicals and quotient law of radicals. It provides examples of applying each law such as 6x ∙ 24x = 3√9x ∙ 3√3x^2 and 75 ÷ 3 = 5√25. The learning targets are to derive the laws of radicals and simplify radical expressions using the laws of radicals. Biblical verses from Hebrews 11:6 and Matthew 6:15 about faith are also included.
Joint and Combined Variation (Mathematics 9)
You already know relationships where one variable varies directly or inversely with another variable.
Now you will look at relationships where one variable varies directly with two or more other variables but does not vary inversely with any other variable.
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.
Factor theorem
The document discusses the factor theorem and how to determine if a polynomial is a factor of another polynomial. It provides examples of using the factor theorem to show that (x + 1) is a factor of 2x^3 + 5x^2 - 3 and that (x - 2) is a factor of x^4 + x^3 - x^2 - x - 18. It also gives an example of finding a polynomial function given its zeros as -2, 1, -1. The document provides exercises for using the factor theorem to determine unknown values in polynomials.
Multiplication of radicals
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.
Factoring the difference of two squares
The document discusses factoring the difference of two squares through examples such as (x+5)(x-5)=x^2 - 25. It explains that to factor a difference of two squares, we write the expression as the difference of two terms squared, then group the terms with the same bases and opposite signs inside parentheses. Several practice problems are provided to reinforce this technique for factoring completely the difference of two squares.
Solving Quadratic Equations
Provides example on how to solve quadratic equations using extracting square roots, factoring, completing the square and quadratic formula.
Congruent Triangles
1. Triangles are congruent if all corresponding sides and angles are congruent. They will have the same shape and size but may be mirror images.
2. There are four main postulates and theorems used to prove triangles congruent: SSS (three sides), SAS (two sides and included angle), ASA (two angles and included side), and AAS (two angles and non-included side).
3. Corresponding parts of congruent triangles are also congruent based on the CPCTC theorem. This allows using previously proven congruent parts in future proofs.
What's hot (20)
Solving Equations Transformable to Quadratic Equation Including Rational Alge...
Solving Equations Transformable to Quadratic Equation Including Rational Alge...
Similar to Geometric proportion and Laws of Proportion
GR 8 Math Powerpoint about Polynomial Techniques
-This is a powerpoint inspired by one of Canva displayed presentation.
- This is about Math Polynomials and good for highschoolers presentation for school.
- It consists of 39 pages explaining each of the Polynomial Techniques.
- Good for review or inspired powerpoint.
Digital Logic.pptxghuuhhhhhhuu7ffghhhhhg
Jdjddjdjjfjrjrhhfbrhrjhjjfjrjfrifjhfjdirurfu8fi3hdudoickegdhejdofjrvdjozdkjieofiudjrhciyyfifjjvi9r7ugidof8cdukrkfj2keoekeRecombination in bacterial growth refers to the process by which bacteria exchange genetic material with each other, leading to the formation of new genetic combinations. This process can occur through several mechanisms, including transformation, conjugation, and transduction.
1. Transformation: In transformation, bacteria take up free DNA from their environment and incorporate it into their genome. This DNA may come from lysed bacterial cells or be released into the environment by other means. Once inside the cell, the foreign DNA can recombine with the bacterial chromosome, leading to genetic diversity.
2. Conjugation: Conjugation involves the direct transfer of genetic material from one bacterium to another through physical contact. This transfer typically occurs through a conjugative pilus, a structure that forms a bridge between the donor and recipient cells. During conjugation, a copy of the donor's DNA, often in the form of a plasmid, is transferred to the recipient cell, where it can integrate into the chromosome or exist as a separate genetic element.
3. Transduction: Transduction occurs when bacterial DNA is transferred from one bacterium to another by a bacteriophage (a virus that infects bacteria). During the lytic cycle of viral replication, some bacteriophages may accidentally package bacterial DNA instead of their own genome. When these phages infect other bacteria, they inject this bacterial DNA into the new host, where it can recombine with the recipient chromosome.
Recombination plays a crucial role in bacterial evolution and adaptation by facilitating the exchange of beneficial genetic traits, such as antibiotic resistance or metabolic capabilities. It contributes to the genetic diversity of bacterial populations and can influence their ability to survive and thrive in various environments.In enzymes, a domain refers to a distinct structural and functional unit that contributes to the overall activity of the enzyme. Domains are often modular components within the enzyme's overall structure, each with its own specific role or function. These functions may include substrate binding, catalysis, regulation, or interaction with other molecules. Domains can have specific shapes, surface properties, and active sites tailored to perform particular biochemical tasks within the enzyme's catalytic cycle. Additionally, enzymes can contain multiple domains, which may interact with each other to modulate enzyme activity or to confer versatility in substrate recognition and binding. The organization of domains within an enzyme contributes to its overall efficiency and specificity in catalyzing biochemical reactions.Superscalar architecture is a CPU design paradigm that enables the simultaneous execution of multiple instructions within a single clock cycle. This is achieved by having multiple execution units, allowing t
Franyinex roas.
1. The document discusses algebraic expressions and operations such as addition, subtraction, multiplication, and division of algebraic expressions. It provides examples and step-by-step solutions to problems involving these operations.
2. Key concepts covered include the properties and rules of exponents, signs, and how to perform operations on monomials, polynomials, and algebraic expressions. Special products like the difference and sum of cubes are also explained.
3. Worked examples provide solutions to problems involving adding, subtracting, multiplying, and dividing algebraic monomials and polynomials. Concepts like factoring trinomials using special products are demonstrated through examples.
Algebra
This document provides an overview of 10 cases of algebraic factorization. It begins by defining factorization as finding two or more factors whose product equals the given expression. The 10 cases covered are: 1) common factor, 2) common factor by grouping, 3) perfect square trinomial, 4) difference of squares, 5) perfect square trinomial by addition/subtraction, 6) trinomial in the form x^2 + bx + c, 7) trinomial in the form ax^2 + bx + c, 8) perfect cube of binomials, 9) sum or difference of perfect cubes, and 10) sum or difference of equal powers. Examples are provided for each case along with step-by-step explanations of the
MATHS SYMBOLS - PROPORTIONS - FIRST PROPERTIES - MANY OTHER PROPERTIES
MATHS SYMBOLS - PROPORTIONS - FIRST PROPERTIES - MANY OTHER PROPERTIESIst. Superiore Marini-Gioia - Enzo Exposyto
MATHS SYMBOLS - PROPORTIONS - DEFINITION - FIRST PROPERTIES - CROSS PRODUCTS PROPERTY - EXTREMES SWITCHING PROPERTY - MEANS SWITCHING PROPERTY - UPSIDE-DOWN PROPERTY - DENOMINATOR ADDITION PROPERTY - DENOMINATOR SUBTRACTION PROPERTY - MANY OTHER PROPERTIES - PROOFS - EXAMPLES and CALCULATIONS STEP by STEP - 28 TABLES
Expresiones algebraicas.
1) An algebraic expression is a combination of letters and numbers connected by operation signs such as addition, subtraction, multiplication, division, and exponentiation. It represents one or more mathematical operations or relationships.
2) The basic operations on algebraic expressions are addition, subtraction, multiplication, and division. Addition and subtraction follow the same rules as arithmetic, while multiplication and division have special rules for exponents and require distributing terms.
3) Polynomial expressions can be added, subtracted, multiplied, and divided following specific rules for combining like terms, distributing operations, and applying laws of exponents respectively. The result of each operation is another polynomial expression.
Quant01
The document summarizes key concepts about ratios, proportions, indices, and logarithms. It defines ratios, proportions, and the difference between them. It outlines properties and rules for proportions, including the cross product rule. It also defines indices and logarithms, and lists laws and properties for working with indices and logarithms, such as the laws for multiplying, dividing, and changing bases of logarithms.
Module 1 similarity
This module introduces ratio, proportion, and the Basic Proportionality Theorem. Students will learn about ratios, proportions, and how to use the fundamental law of proportions to solve problems involving similar triangles. The module is designed to help students apply the definition of proportion to find unknown lengths, illustrate and verify the Basic Proportionality Theorem and its converse, and develop skills for solving geometry problems involving triangles. Exercises cover writing and simplifying ratios, setting up and solving proportions, determining if ratios form proportions, and applying the Basic Proportionality Theorem.
Advanced algebra
The document discusses various topics in advanced algebra including inequalities, arithmetic progressions, geometric progressions, harmonic progressions, permutations, combinations, matrices, determinants, and solving systems of linear equations using matrices. Key properties and formulas are provided for each topic. Examples are included to demonstrate solving problems related to each concept.
determinants-160504230830.pdf
Determinants provide a scalar quantity associated with square matrices. There are several properties of determinants, including that the determinant of a matrix does not change if rows or columns are interchanged. The determinant can be expressed as the sum of the products of each element and its corresponding cofactor. Examples show how to evaluate determinants by expanding along rows or columns and applying properties such as identical rows resulting in a determinant of zero.
determinants-160504230830_repaired.pdf
Determinants provide a scalar quantity associated with square matrices. There are several properties of determinants, including that the determinant of a matrix does not change if rows or columns are interchanged. The determinant can be expressed as the sum of the products of each element and its corresponding cofactor. Examples show how to evaluate determinants by expanding along rows or columns and applying properties such as identical rows resulting in a determinant of zero.
NumberTheory.ppt
This document provides an overview of topics in number theory that will be covered in a discrete structures course, including divisibility, greatest common divisors, primes, and modular arithmetic. It introduces basic concepts such as integers dividing other integers, prime numbers, the fundamental theorem of arithmetic, the Euclidean algorithm for finding greatest common divisors, and modular arithmetic involving remainders when dividing integers. Examples are provided to illustrate key definitions and properties related to these foundational number theory topics.
Module 1 similarity
This module introduces ratio, proportion, and the Basic Proportionality Theorem. Students will learn about ratios, proportions, and how to use the fundamental law of proportions to solve problems involving triangles. The module is designed to teach students to apply the definition of proportion of segments to find unknown lengths and illustrate and verify the Basic Proportionality Theorem and its Converse. Examples are provided to demonstrate how to express ratios in simplest form, find missing values in proportions, determine if ratios form proportions, and solve problems involving angles and segments in triangles using ratios and proportions.
Quant01. Ratio & Proportion, Indices, Logarithms
Revision Notes for CPT
Chapter: Ratio & Proportion, Indices, Logarithms
Subject: Quantitative Aptitude
Tarea 2 unidad 1 power point
The document discusses various algebraic concepts including:
- Expressions involving numbers, letters and signs known as algebraic expressions.
- Methods for adding, multiplying, and dividing algebraic expressions.
- Factorization, which involves writing a polynomial as a product of factors.
- Functions and their key elements such as domain, range, and rule of correspondence.
GRE - Algebra
This document provides an overview of topics related to algebra, including quadratic equations, inequalities, absolute value, and modulus. It discusses how to form quadratic equations given different conditions on the roots. Methods for finding roots such as splitting the middle term and using the quadratic formula are presented. Properties and techniques for solving different types of inequalities and absolute value equations are outlined. Maximum and minimum values of functions involving modulus are also addressed.
Challenges for coupling approaches for classical linear elasticity and bond-b...
The document presents coupling approaches for combining classical linear elasticity models with non-local peridynamic models for applications in computational mechanics. It describes three coupling methods - matching displacements (MDCM), matching stresses (MSCM), and variable horizon (VHCM). Numerical examples are presented to compare the accuracy of the three methods on manufactured solutions using cubic and quartic polynomials, demonstrating that all methods converge with refinement but VHCM typically has the lowest error.
paper
This document describes a proposed implementation of the Region Connection Calculus (RCC) using constraint handling rules (CHR). It defines the 8 base RCC relations in terms of connectedness relations. The implementation uses CHR to define simplification, propagation, and simpagation rules to represent and reason about RCC constraints. Some key relations like connection, disconnection, and part are defined through corresponding CHR rules based on their definitions in RCC axioms. The implementation aims to simplify constraints into just connections but has some limitations, such as not fully capturing part relations due to inability to define global constraints.
Determinants
This document provides information about determinants of square matrices:
- It defines the determinant of a matrix as a scalar value associated with the matrix. Determinants are computed using minors and cofactors.
- Properties of determinants are described, such as how determinants change with row/column operations or identical rows/columns.
- Examples are provided to demonstrate computing determinants by expanding along rows or columns and using cofactors and minors.
- Applications of determinants include finding the area of triangles and solving systems of linear equations.
Expresiones algebraicas
The document discusses various algebraic expressions and operations including:
1) Finding the numeric value of algebraic expressions by substituting values for variables and simplifying.
2) Adding, subtracting, multiplying, and dividing algebraic expressions using properties like the distributive property.
3) Factoring expressions using factoring by grouping, difference of squares, and perfect square trinomials.
Similar to Geometric proportion and Laws of Proportion (20)
MATHS SYMBOLS - PROPORTIONS - FIRST PROPERTIES - MANY OTHER PROPERTIES
MATHS SYMBOLS - PROPORTIONS - FIRST PROPERTIES - MANY OTHER PROPERTIES
Challenges for coupling approaches for classical linear elasticity and bond-b...
Challenges for coupling approaches for classical linear elasticity and bond-b...
More from Ma. Guadalupe Robles
Human Development: Infancy
Human Development: Infancy
Slides on the characteristics, developmental tasks, and hazards of infants
Michel de Montaigne
Michel de Montaigne was a French Renaissance writer and philosopher. He is known for popularizing the essay as a literary genre through his work Essais, which consisted of his autobiographical writings and explorations of various topics. Montaigne focused on skepticism and humanism, and his work influenced later psychology and education. He held various public offices throughout his career and was respected by both Catholic and Protestant French kings during the Wars of Religion in the late 16th century.
Inscribed Angles
1) An inscribed angle is an angle whose vertex lies on a circle and whose sides contain chords of the circle.
2) The measure of an inscribed angle is equal to one-half the measure of its intercepted arc.
3) If two inscribed angles intercept the same arc or congruent arcs, then the angles are congruent.
The nervous system
The document discusses the nervous system and its main components:
1) The central nervous system (CNS) controls most body functions and consists of the brain and spinal cord. The brain interprets sensory information and controls movement.
2) The peripheral nervous system (PNS) connects the CNS to organs and limbs. It has two divisions - the somatic nervous system which controls voluntary movement, and the autonomic nervous system which controls involuntary functions.
3) Nerve fibers transmit signals in the CNS and PNS. Myelin sheaths surround some fibers and are formed by different cells in each system.
Thomas Gray
Thomas Gray was an English poet born in 1716 in London to Philip and Dorothy Gray. He was educated at Eton College and Peterhouse College, Cambridge. Gray is best known for his poem "Elegy Written in a Country Churchyard" which he began writing in 1742 in a Buckinghamshire churchyard. He had few other publications before his death in 1771. Gray was a pivotal figure that preceded the Romantic literary movement with his focus on emotion in his poetry.
Visible Light
The document discusses the visible light spectrum and unsaturated colors. It notes that red light has the longest wavelength while violet has the shortest. It also defines wavelength as the distance between waves of energy traveling from one point to another, and photon as a tiny particle of light or electromagnetic radiation.
Caritas in Veritate
Pope Benedict XVI's encyclical "Caritas in Veritate" addresses the topics of charity, truth, development, hunger, the environment, migration, sexual tourism, and population issues. The document calls for integrating charity and truth in development work. It also calls for new economic institutions to address hunger, regulating exploitation of resources, respecting migrants' rights, ending sexual tourism, and recognizing factors beyond population increase influence development.
More from Ma. Guadalupe Robles (7)
Recently uploaded
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama UniversityAkanksha trivedi rama nursing college kanpur.
Natural birth techniques are various type such as/ water birth , alexender method, hypnosis, bradley method, lamaze method etcHow to Setup Warehouse & Location in Odoo 17 Inventory
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.
How to Make a Field Mandatory in Odoo 17
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
How to Manage Your Lost Opportunities in Odoo 17 CRM
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
How to Fix the Import Error in the Odoo 17
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Aberdeen
How to Add Chatter in the odoo 17 ERP Module
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS Template 2023-2024 by: Irene S. Rueco
Walmart Business+ and Spark Good for Nonprofits.pdf
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
Hindi varnamala | hindi alphabet PPT.pdf
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...Nguyen Thanh Tu Collection
https://app.box.com/s/y977uz6bpd3af4qsebv7r9b7s21935vdPCOS corelations and management through Ayurveda.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Recently uploaded (20)
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
Pride Month Slides 2024 David Douglas School District
Pride Month Slides 2024 David Douglas School District
How to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRM
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
Geometric proportion and Laws of Proportion
- 2. ratio comparison of two numbers with the same units or different units a:b= a (first number) b (second number)
- 3. proportion equality of two ratios a:b=c:d
- 4. proportion *number in a proportion= TERM a(first term) = c(third term) b(second term) d(fourth term)
- 9. First law of proportion Means-Extremes Product Law of Proportions If a = c , then ad=bc, b d where b≠0, d≠0
- 10. Means-Extremes Product Law of Proportions Example: 4 = 2 x 6
- 11. Means-Extremes Product Law of Proportions Example: 2x = 4(6) 2x = 24
- 12. Means-Extremes Product Law of Proportions Example: 2x = 4(6) 2x = 24 2 2
- 13. Means-Extremes Product Law of Proportions Answer: X=12
- 14. Second law of proportions Switch Means-Switch Extremes law of Proportions If a = c , then a = b and d = c b d c d b a Where a, b, c, and d are nonzero real numbers
- 15. Switch Means-Switch Extremes law of Proportions a:b=c:d a = c b d Switch of Means: a:b=c:d MEANS
- 16. Switch Means-Switch Extremes law of Proportions a:c=b:d a = b c d
- 17. Switch Means-Switch Extremes law of Proportions Switch of Extremes: a:b=c:d EXTREMES d:b= c:a d = c b a
- 18. Third law of proportions Invert-Both-Sides Law of Proportions If a = c , then b = d b d a c Where a, b, c, and d are nonzero real numbers
- 19. fourth law of proportions Denominator-Addition Law of Proportions If a+b = c+d b d Where b≠0, d≠0
- 20. fifth law of proportions Denominator-Substraction Law of Proportions If a-b = c-d b d Where b≠0, d≠0
- 21. Sixth law of proportions Numerator-Denominator Sum Law of Proportions If a = c = e … then, a+c+e = a = c =e b d f b+d+f b d f