O documento apresenta várias equações matemáticas com símbolos de igualdade e desigualdade relacionando números e medidas de área. As equações definem relações entre diferentes variáveis numéricas e unidades de medida.
To find the distance between points G(-5, -8) and H(3,7) use the distance formula. Also use the distance formula to find the distance between points L(15, 37) and M(42, 73). The distance formula is used to calculate the distance between the points (-19, -16) and (-3, 14).
This document contains a series of numbers and letters arranged in a graphical format with some numbers assigned to the variables x. It shows the values 7 assigned to x in several locations and the value -3 assigned to x in one location. The document also includes four line items labeled 1 through 4 at the bottom.
The document provides 4 examples proving properties of angles and triangles related to congruent complements and supplements. Each example gives angle or side relationships that are then used through reasoning to prove corresponding, alternate interior, or same side interior angles are congruent. The examples demonstrate properties such as if two angles are complementary then their complements are congruent, and if two angles are supplementary then their supplements are congruent.
The document provides instructions for completing proofs, stating that each proof should have one slide listing the givens and what is to be proved, followed by a second slide with the completed proof. Readers are encouraged to attempt each proof before viewing the provided answer.
Lsn 11-3 Proving a Quadrilateral is a ParallelogramKate Nowak
The document discusses a new product launch for a company. It outlines key details of the product, including its features and target customers. It also provides a timeline for rolling out marketing and launching the product nationally over the next year.
This geometry exam review covers topics that will be on the final exam. It includes true/false questions, multiple choice, matching, and free response problems involving geometry concepts like triangles, circles, polygons, and three-dimensional shapes. Calculators may be used but the exam may have non-calculator sections, so students should prepare with and without calculators. The review is due before the scheduled final exam date.
This document appears to be a geometry/trigonometry final exam consisting of multiple choice questions testing concepts related to geometric shapes, their properties, theorems about congruent triangles, angle relationships, and coordinate geometry. The exam contains 66 multiple choice questions and provides diagrams when necessary to illustrate the questions being asked.
To prove that a quadrilateral is a rectangle or rhombus, you must first prove that it is a parallelogram by showing that both pairs of opposite sides are parallel and congruent. Then, you need only one additional condition - either that the diagonals are congruent (rectangle) or that one angle is a right angle (rectangle), or that the diagonals are the same length (rhombus) or that one pair of consecutive sides are congruent (rhombus). The document provides an example proof of showing a quadrilateral is a rectangle.
To find the distance between points G(-5, -8) and H(3,7) use the distance formula. Also use the distance formula to find the distance between points L(15, 37) and M(42, 73). The distance formula is used to calculate the distance between the points (-19, -16) and (-3, 14).
This document contains a series of numbers and letters arranged in a graphical format with some numbers assigned to the variables x. It shows the values 7 assigned to x in several locations and the value -3 assigned to x in one location. The document also includes four line items labeled 1 through 4 at the bottom.
The document provides 4 examples proving properties of angles and triangles related to congruent complements and supplements. Each example gives angle or side relationships that are then used through reasoning to prove corresponding, alternate interior, or same side interior angles are congruent. The examples demonstrate properties such as if two angles are complementary then their complements are congruent, and if two angles are supplementary then their supplements are congruent.
The document provides instructions for completing proofs, stating that each proof should have one slide listing the givens and what is to be proved, followed by a second slide with the completed proof. Readers are encouraged to attempt each proof before viewing the provided answer.
Lsn 11-3 Proving a Quadrilateral is a ParallelogramKate Nowak
The document discusses a new product launch for a company. It outlines key details of the product, including its features and target customers. It also provides a timeline for rolling out marketing and launching the product nationally over the next year.
This geometry exam review covers topics that will be on the final exam. It includes true/false questions, multiple choice, matching, and free response problems involving geometry concepts like triangles, circles, polygons, and three-dimensional shapes. Calculators may be used but the exam may have non-calculator sections, so students should prepare with and without calculators. The review is due before the scheduled final exam date.
This document appears to be a geometry/trigonometry final exam consisting of multiple choice questions testing concepts related to geometric shapes, their properties, theorems about congruent triangles, angle relationships, and coordinate geometry. The exam contains 66 multiple choice questions and provides diagrams when necessary to illustrate the questions being asked.
To prove that a quadrilateral is a rectangle or rhombus, you must first prove that it is a parallelogram by showing that both pairs of opposite sides are parallel and congruent. Then, you need only one additional condition - either that the diagonals are congruent (rectangle) or that one angle is a right angle (rectangle), or that the diagonals are the same length (rhombus) or that one pair of consecutive sides are congruent (rhombus). The document provides an example proof of showing a quadrilateral is a rectangle.
This document defines Bernoulli trials and the binomial distribution. A Bernoulli trial is a random experiment with two possible outcomes: success or failure. A sequence of Bernoulli trials involves performing the experiment multiple independent times, keeping the probability of success the same. The binomial distribution calculates the probability of getting a certain number of successes in n Bernoulli trials. It satisfies properties where the experiment is conducted n times independently with a constant success probability p and failure probability of 1-p.
Notes Day 6: Prove that sides are in proportionKate Nowak
This document appears to be an attachment of classwork on corresponding sides of similar triangles. The attachment is a PDF file that likely contains exercises, examples, or instructions related to teaching students about corresponding sides of similar triangles in geometry. In fewer than 3 sentences, the document provides homework or class material on similar triangles and their corresponding sides.
Notes Day 4&5: Prove that Triangles are SimilarKate Nowak
The document discusses three theorems for determining similarity of triangles:
1) The Angle-Angle Similarity (AA) Postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
2) The Side-Angle-Side Similarity (SAS) Theorem states that if an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two angles are proportional, then the triangles are similar.
3) The Side-Side-Side Similarity (SSS) Theorem states that if the corresponding sides of two triangles are proportional, then the triangles are similar.
Similar figures have the same shape but not necessarily the same size. Two polygons are similar if their corresponding angles are congruent and their corresponding sides are proportional. The symbol for similarity is ~. This document provides examples of determining if shapes are similar by checking if corresponding angles are congruent and sides are proportional.
Day 14-4: Probability with Permutations & CombinationsKate Nowak
This document provides examples of using permutations and combinations to calculate probabilities of events occurring. It discusses:
- Calculating the probability of selecting two white and two red balls from an urn containing six white and five red balls by finding the number of ways to choose two white and two red balls, and dividing by the total number of possible outcomes.
- Calculating probabilities for other events involving selecting balls from urns with different ball combinations.
- Calculating probabilities for events involving selecting students for a team from groups with different numbers of boys and girls.
- Calculating the probability of choosing a specific letter from a word by counting the number of ways to choose that letter and dividing by the total letters.
Probability Day 3 - Permutations and CombinationsKate Nowak
The document discusses factorial notation and its definition as the product of all positive integers less than or equal to n. It also covers the fundamental counting principle for combining outcomes, permutations which care about order, combinations which do not care about order, and examples of counting problems involving balls in an urn.
The homework assignment includes problems from two pages in the textbook, with problems 1, 2, 10-14, and 24-27 from pages 42-43, and problems 1-17 odd and 36-40 from pages 534-536.
This document contains a graph with labeled x and y axes ranging from -6 to 6. Within this range are curved lines forming a circle centered at the point (4, 1).
The document provides formulas and examples for calculating slope and midpoints of lines and determining properties of triangles. It includes the slope formula, definitions for lines with the same or opposite reciprocal slopes, the midpoint formula, an example of finding the other endpoint given one endpoint and the midpoint, and an example of proving a triangle is isosceles and right using its vertex coordinates.
The passage discusses the importance of summarization in efficiently conveying key information from lengthy documents. It notes that effective summaries distill the most critical details and events into a brief yet informative recap of the overall topic and narrative. The ability to produce high-quality summaries is a useful skill for professionals across many fields in order to save time and focus on the most pertinent details.
This document contains numerical values for variables a, b, c, and d in two sections about arithmetic and midsegments. In the arithmetic section, the values are 42, 63, 117, and 14 for the first line, and 30, 28.5, 87, and 12 for the second line. In the algebra section, x is given as 6 for the first two lines, but no values are provided for the third line.
This document contains numerical values for variables a, b, c, and d in two sections about arithmetic and midsegments. In the arithmetic section, the values are 42, 63, 117, and 14 for the first line, and 30, 28.5, 87, and 12 for the second line. In the algebra section, x is given as 6 for the first two lines, but no values are provided for the third line.
This document contains 3 trigonometry word problems: 1) Find the length of a segment labeled x in a diagram with a 12 foot side. 2) Given a 46 foot sign on a building, find the height of the building using angles of elevation. 3) Given angles of elevation to a lighthouse from a ship and its distance traveled, find how close the ship is to dangerous rocks near the lighthouse.
The document provides examples of using the Law of Sines and Law of Cosines to solve for missing sides and angles of triangles. It includes 5 multi-step triangle problems worked out using the two trigonometric laws, with the key points being that Law of Sines is used when an angle is given alone, Law of Cosines is used when a side is given alone or one triangle has a right angle, and letter assignments in the Law of Cosines formula can be changed.
Lsn 11-7: Law of Cosines to find an AngleKate Nowak
The document provides 3 examples of using the Law of Cosines to find the measure of an angle given the lengths of 3 sides of a triangle. The first example finds the measure of an acute angle C in a triangle with sides of lengths 5, 12, and 9. The second finds the right angle C in a triangle with sides of lengths 5, 12, and 13. The third finds the measure of an obtuse angle C in a triangle with sides of lengths 5, 12, and 15.
Here are the steps to solve these Law of Sines problems:
1. Given: a = 13, b = 20, A = 75°
Use the Law of Sines: sin(A)/a = sin(B)/b
sin(75°)/13 = sin(B)/20
sin(75°)*20/13 = sin(B)
B = sin-1(0.8) = 67°
2. Given: a = 25, B = 38°
Use the Law of Sines: sin(A)/a = sin(B)/b
sin(38°)/25 = sin(m°)/20
sin(38°)*20/25 = sin
Lsn 11-3 Solving Second Degree Trig EquationsKate Nowak
This document appears to be notes from math lessons covering solving second degree trigonometric equations and examples. It includes solving an equation for theta, and working through an example problem.
The document contains instructions and examples for calculating the area of triangles using various formulas. It asks the reader to find the area of triangles given dimensions and angle measures. It also provides the formula for finding the area of a parallelogram given the base, height, and angle between the base and height.
This document defines Bernoulli trials and the binomial distribution. A Bernoulli trial is a random experiment with two possible outcomes: success or failure. A sequence of Bernoulli trials involves performing the experiment multiple independent times, keeping the probability of success the same. The binomial distribution calculates the probability of getting a certain number of successes in n Bernoulli trials. It satisfies properties where the experiment is conducted n times independently with a constant success probability p and failure probability of 1-p.
Notes Day 6: Prove that sides are in proportionKate Nowak
This document appears to be an attachment of classwork on corresponding sides of similar triangles. The attachment is a PDF file that likely contains exercises, examples, or instructions related to teaching students about corresponding sides of similar triangles in geometry. In fewer than 3 sentences, the document provides homework or class material on similar triangles and their corresponding sides.
Notes Day 4&5: Prove that Triangles are SimilarKate Nowak
The document discusses three theorems for determining similarity of triangles:
1) The Angle-Angle Similarity (AA) Postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
2) The Side-Angle-Side Similarity (SAS) Theorem states that if an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two angles are proportional, then the triangles are similar.
3) The Side-Side-Side Similarity (SSS) Theorem states that if the corresponding sides of two triangles are proportional, then the triangles are similar.
Similar figures have the same shape but not necessarily the same size. Two polygons are similar if their corresponding angles are congruent and their corresponding sides are proportional. The symbol for similarity is ~. This document provides examples of determining if shapes are similar by checking if corresponding angles are congruent and sides are proportional.
Day 14-4: Probability with Permutations & CombinationsKate Nowak
This document provides examples of using permutations and combinations to calculate probabilities of events occurring. It discusses:
- Calculating the probability of selecting two white and two red balls from an urn containing six white and five red balls by finding the number of ways to choose two white and two red balls, and dividing by the total number of possible outcomes.
- Calculating probabilities for other events involving selecting balls from urns with different ball combinations.
- Calculating probabilities for events involving selecting students for a team from groups with different numbers of boys and girls.
- Calculating the probability of choosing a specific letter from a word by counting the number of ways to choose that letter and dividing by the total letters.
Probability Day 3 - Permutations and CombinationsKate Nowak
The document discusses factorial notation and its definition as the product of all positive integers less than or equal to n. It also covers the fundamental counting principle for combining outcomes, permutations which care about order, combinations which do not care about order, and examples of counting problems involving balls in an urn.
The homework assignment includes problems from two pages in the textbook, with problems 1, 2, 10-14, and 24-27 from pages 42-43, and problems 1-17 odd and 36-40 from pages 534-536.
This document contains a graph with labeled x and y axes ranging from -6 to 6. Within this range are curved lines forming a circle centered at the point (4, 1).
The document provides formulas and examples for calculating slope and midpoints of lines and determining properties of triangles. It includes the slope formula, definitions for lines with the same or opposite reciprocal slopes, the midpoint formula, an example of finding the other endpoint given one endpoint and the midpoint, and an example of proving a triangle is isosceles and right using its vertex coordinates.
The passage discusses the importance of summarization in efficiently conveying key information from lengthy documents. It notes that effective summaries distill the most critical details and events into a brief yet informative recap of the overall topic and narrative. The ability to produce high-quality summaries is a useful skill for professionals across many fields in order to save time and focus on the most pertinent details.
This document contains numerical values for variables a, b, c, and d in two sections about arithmetic and midsegments. In the arithmetic section, the values are 42, 63, 117, and 14 for the first line, and 30, 28.5, 87, and 12 for the second line. In the algebra section, x is given as 6 for the first two lines, but no values are provided for the third line.
This document contains numerical values for variables a, b, c, and d in two sections about arithmetic and midsegments. In the arithmetic section, the values are 42, 63, 117, and 14 for the first line, and 30, 28.5, 87, and 12 for the second line. In the algebra section, x is given as 6 for the first two lines, but no values are provided for the third line.
This document contains 3 trigonometry word problems: 1) Find the length of a segment labeled x in a diagram with a 12 foot side. 2) Given a 46 foot sign on a building, find the height of the building using angles of elevation. 3) Given angles of elevation to a lighthouse from a ship and its distance traveled, find how close the ship is to dangerous rocks near the lighthouse.
The document provides examples of using the Law of Sines and Law of Cosines to solve for missing sides and angles of triangles. It includes 5 multi-step triangle problems worked out using the two trigonometric laws, with the key points being that Law of Sines is used when an angle is given alone, Law of Cosines is used when a side is given alone or one triangle has a right angle, and letter assignments in the Law of Cosines formula can be changed.
Lsn 11-7: Law of Cosines to find an AngleKate Nowak
The document provides 3 examples of using the Law of Cosines to find the measure of an angle given the lengths of 3 sides of a triangle. The first example finds the measure of an acute angle C in a triangle with sides of lengths 5, 12, and 9. The second finds the right angle C in a triangle with sides of lengths 5, 12, and 13. The third finds the measure of an obtuse angle C in a triangle with sides of lengths 5, 12, and 15.
Here are the steps to solve these Law of Sines problems:
1. Given: a = 13, b = 20, A = 75°
Use the Law of Sines: sin(A)/a = sin(B)/b
sin(75°)/13 = sin(B)/20
sin(75°)*20/13 = sin(B)
B = sin-1(0.8) = 67°
2. Given: a = 25, B = 38°
Use the Law of Sines: sin(A)/a = sin(B)/b
sin(38°)/25 = sin(m°)/20
sin(38°)*20/25 = sin
Lsn 11-3 Solving Second Degree Trig EquationsKate Nowak
This document appears to be notes from math lessons covering solving second degree trigonometric equations and examples. It includes solving an equation for theta, and working through an example problem.
The document contains instructions and examples for calculating the area of triangles using various formulas. It asks the reader to find the area of triangles given dimensions and angle measures. It also provides the formula for finding the area of a parallelogram given the base, height, and angle between the base and height.
Egito antigo resumo - aula de história.pdfsthefanydesr
O Egito Antigo foi formado a partir da mistura de diversos povos, a população era dividida em vários clãs, que se organizavam em comunidades chamadas nomos. Estes funcionavam como se fossem pequenos Estados independentes.
Por volta de 3500 a.C., os nomos se uniram formando dois reinos: o Baixo Egito, ao Norte e o Alto Egito, ao Sul. Posteriormente, em 3200 a.C., os dois reinos foram unificados por Menés, rei do alto Egito, que tornou-se o primeiro faraó, criando a primeira dinastia que deu origem ao Estado egípcio.
Começava um longo período de esplendor da civilização egípcia, também conhecida como a era dos grandes faraós.
O Que é Um Ménage à Trois?
A sociedade contemporânea está passando por grandes mudanças comportamentais no âmbito da sexualidade humana, tendo inversão de valores indescritíveis, que assusta as famílias tradicionais instituídas na Palavra de Deus.
Folheto | Centro de Informação Europeia Jacques Delors (junho/2024)Centro Jacques Delors
Estrutura de apresentação:
- Apresentação do Centro de Informação Europeia Jacques Delors (CIEJD);
- Documentação;
- Informação;
- Atividade editorial;
- Atividades pedagógicas, formativas e conteúdos;
- O CIEJD Digital;
- Contactos.
Para mais informações, consulte o portal Eurocid:
- https://eurocid.mne.gov.pt/quem-somos
Autor: Centro de Informação Europeia Jacques Delors
Fonte: https://infoeuropa.mne.gov.pt/Nyron/Library/Catalog/winlibimg.aspx?doc=48197&img=9267
Versão em inglês [EN] também disponível em:
https://infoeuropa.mne.gov.pt/Nyron/Library/Catalog/winlibimg.aspx?doc=48197&img=9266
Data de conceção: setembro/2019.
Data de atualização: maio-junho 2024.