This document discusses different methods for proving that triangles are congruent: SSS, SAS, ASA, AAS, and HL. It defines congruent polygons as having the same size and shape, meaning all corresponding sides are the same length and all corresponding angles have the same measure. The order of letters in a congruence statement indicates which angles or sides are being shown as congruent to prove the triangles are congruent.
Sistema de ecuaciones lineales (suma o resta)racsosc
Este documento explica cómo resolver sistemas de ecuaciones de primer grado utilizando el método de suma o resta. Se presentan cinco ejemplos resueltos paso a paso, mostrando cómo eliminar una variable mediante la suma o resta de las ecuaciones, y luego sustituir el valor obtenido en la otra ecuación para encontrar la solución al sistema.
1) The document defines and provides examples of different types of angles including adjacent angles, complementary angles, supplementary angles, vertical angles, and angles formed when parallel lines are cut by a transversal.
2) It then provides practice problems involving calculating missing angles using properties such as angles summing to 90, 180 degrees, and the interior angles of triangles summing to 180 degrees.
3) The final problems involve identifying congruent, supplementary, and corresponding angles related to two parallel lines cut by a transversal.
Solving System of Equations by SubstitutionTwinkiebear7
1) The document discusses solving systems of equations using substitution. It provides 5 steps for solving a system by substitution: 1) solve one equation for a variable, 2) substitute into the other equation, 3) solve the new equation, 4) plug back in to find the other variable, and 5) check the solution.
2) It then works through examples, showing that substitution is easiest when one equation is already solved for a variable. It also notes that if the final step results in a false statement, there are no solutions, and if true, there are infinitely many solutions.
Distance Formula - PPT Presentation.pptxDenielleAmoma
This document discusses coordinate geometry and the distance formula. It provides examples of using the distance formula to calculate the distance between points in the coordinate plane and to prove geometric properties, such as showing a triangle is isosceles or that four points form a square. It derives the distance formula and explains its components and how to apply it to find distances. Examples are provided to illustrate its use in solving geometry problems using algebraic methods in the coordinate plane.
This document provides instructions on how to solve radical equations. It begins by defining a radical equation and radicand. It then explains the main steps to solve radical equations: isolate the radical to one side, raise both sides to the same power, and simplify. Several examples are worked through to demonstrate this process. The document emphasizes checking solutions, as raising both sides to an even power can result in extraneous solutions. TI instructions and additional practice problems are also included.
This document discusses different methods for proving that triangles are congruent: SSS, SAS, ASA, AAS, and HL. It defines congruent polygons as having the same size and shape, meaning all corresponding sides are the same length and all corresponding angles have the same measure. The order of letters in a congruence statement indicates which angles or sides are being shown as congruent to prove the triangles are congruent.
Sistema de ecuaciones lineales (suma o resta)racsosc
Este documento explica cómo resolver sistemas de ecuaciones de primer grado utilizando el método de suma o resta. Se presentan cinco ejemplos resueltos paso a paso, mostrando cómo eliminar una variable mediante la suma o resta de las ecuaciones, y luego sustituir el valor obtenido en la otra ecuación para encontrar la solución al sistema.
1) The document defines and provides examples of different types of angles including adjacent angles, complementary angles, supplementary angles, vertical angles, and angles formed when parallel lines are cut by a transversal.
2) It then provides practice problems involving calculating missing angles using properties such as angles summing to 90, 180 degrees, and the interior angles of triangles summing to 180 degrees.
3) The final problems involve identifying congruent, supplementary, and corresponding angles related to two parallel lines cut by a transversal.
Solving System of Equations by SubstitutionTwinkiebear7
1) The document discusses solving systems of equations using substitution. It provides 5 steps for solving a system by substitution: 1) solve one equation for a variable, 2) substitute into the other equation, 3) solve the new equation, 4) plug back in to find the other variable, and 5) check the solution.
2) It then works through examples, showing that substitution is easiest when one equation is already solved for a variable. It also notes that if the final step results in a false statement, there are no solutions, and if true, there are infinitely many solutions.
Distance Formula - PPT Presentation.pptxDenielleAmoma
This document discusses coordinate geometry and the distance formula. It provides examples of using the distance formula to calculate the distance between points in the coordinate plane and to prove geometric properties, such as showing a triangle is isosceles or that four points form a square. It derives the distance formula and explains its components and how to apply it to find distances. Examples are provided to illustrate its use in solving geometry problems using algebraic methods in the coordinate plane.
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.
Trigonometry deals with relationships between sides and angles in right triangles. The three main trigonometric functions are sine, cosine, and tangent, which provide ratios of sides of a right triangle based on a given angle. A scientific calculator can be used to find trigonometric ratios for any angle, as well as to calculate missing angles or sides of a right triangle when two pieces of information are known.
The document discusses slope and how to calculate it. It defines slope as the steepness of a line or the rate of change between two points. Slope is represented by the letter m. There are three main ways to calculate slope: 1) using the formula m = (y2 - y1) / (x2 - x1) for two points (x1, y1) and (x2, y2); 2) by finding the rise over run when given a graph; 3) by taking the coefficient of x when a line equation is in the form of y = mx + b, where m represents the slope. Examples are provided to demonstrate calculating slope using these different methods.
O documento apresenta questões sobre números primos, perfeitos e congruências numéricas. A questão 1 discute propriedades de números primos e o Lema de Euclides. A questão 2 trata do Teorema de Euclides sobre números perfeitos. A questão 3 prova que o quinto número de Fermat não é primo usando congruências.
Este documento explica los diferentes métodos para resolver ecuaciones de segundo grado, incluyendo ecuaciones incompletas, el método de factorización y la fórmula general. Primero se describen las ecuaciones incompletas donde b o c son iguales a cero y cómo reducirlas a ecuaciones de primer grado. Luego explica el método de factorización para ecuaciones que pueden factorizarse y la fórmula general para cuando no se puede factorizar. Finalmente desea éxito al lector en su prueba.
The document discusses synthetic division, providing 3 examples of dividing polynomials. The first example divides a polynomial by a monic linear divisor. The second divides a polynomial by a non-monic linear divisor. The third divides a polynomial by a monic quadratic divisor. Each example shows the division problem and solution.
This document defines integers and absolute value. Integers include whole numbers and their opposites on the number line, with positive integers above zero and negative integers below zero. Absolute value refers to the distance from zero on the number line, and is represented by bars around an integer, making it a positive number regardless of its original sign. Examples are provided to illustrate integers in contexts like stock prices, elevations, and temperatures.
Evaluating algebraic expressions with substitutioncindywhitebcms
This document defines variables, constants, expressions and provides examples of evaluating expressions for given values of variables. It defines a variable as a quantity that can change and constants as quantities that do not change. Expressions are defined as mathematical phrases involving variables, constants and operations. Several examples are given of evaluating expressions when given values for variables like x, m, p, c, z.
Discriminante de una ecuación de segundo gradoMaría Pizarro
El documento explica cómo calcular el discriminante de una ecuación de segundo grado y cómo determinar la naturaleza de sus soluciones en base al valor del discriminante. El discriminante se obtiene aplicando la fórmula D = b2 - 4ac y su signo indica si las soluciones son reales y distintas (positivo), reales e iguales (cero) o complejas (negativo). Se proveen ejemplos del cálculo del discriminante y su interpretación.
This document discusses writing linear equations in slope-intercept form and point-slope form by given information such as the slope, y-intercept, or two points on the line. It provides examples of finding the equation of a line given its slope and y-intercept, two points, or one point and the slope. The key methods covered are using the slope-intercept form y=mx+b and point-slope form y-y1=m(x-x1).
This document discusses different ways to prove that two triangles are congruent, including:
1) Side-Side-Side (SSS), which proves congruence if all three sides of one triangle are congruent to the corresponding sides of the other triangle.
2) Side-Angle-Side (SAS), which proves congruence if two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle.
3) Angle-Side-Angle (ASA), which proves congruence if two angles and the side between them of one triangle are congruent to the corresponding parts of the other triangle.
The document provides an overview of calculus and analytical geometry presented by Group D. It discusses various topics related to integration including the history and development of integration, the definition and purpose of integration, common integration rules and formulas like integration by parts and integration by partial fractions, and real-life applications of integration in fields like engineering, medicine, and physics. Examples are provided to demonstrate how to use integration techniques like integration by parts and integration by partial fractions to evaluate definite integrals.
This document discusses similarity and congruence of plane figures. It defines similar figures as those where corresponding angles are equal and corresponding side ratios are equal. Examples of similar figures include rectangles where the ratio of length to width is equal. The document provides examples of similar and congruent triangles and quadrilaterals. It also lists key terms and learning objectives related to identifying similar and congruent plane figures based on corresponding side lengths and angles.
Ecuaciones de tercer grado por el metodo ruffini0105790638
El documento describe los pasos para resolver una ecuación de segundo grado dividiendo por números divisibles del término independiente. Primero se identifican los coeficientes de la ecuación original. Luego se divide por números divisibles del término independiente para simplificar la ecuación hasta dejarla como una ecuación de primer grado y finalmente de cero orden, obteniendo la solución final.
This document discusses irrational numbers, which are numbers that cannot be expressed as a ratio of two integers, such as the square root of 2. It provides examples of irrational numbers that arise from calculations involving the sides of geometric shapes, such as the square root of 2 being the length of the diagonal of a unit square. The document also covers operations involving irrational numbers, stating that the product and quotient of irrational numbers are irrational numbers.
Pre-5.1 - trigonometry ratios in right triangle and special right triangles.pptMariOsnolaSan
Right triangle trigonometry is based on ratios of the sides of right triangles. The six trigonometric functions - sine, cosine, tangent, cotangent, secant, and cosecant - are defined by ratios of the opposite, adjacent, and hypotenuse sides. To find a missing angle or side, the appropriate trigonometric ratio is selected based on the known sides and then calculated. There are special right triangle theorems for 45-45-90 and 30-60-90 triangles that allow determining side lengths based on one known side length.
The document discusses linear inequalities in two variables and their graphical representations. It introduces the Cartesian coordinate system developed by Rene Descartes and its importance. It explains how to graph linear inequalities by first drawing the line as an equation, then determining whether to shade above or below the line based on whether a test point satisfies the inequality. Students are assigned to bring graphing paper, coloring materials, and a ruler to class on Monday to graph linear inequalities.
The document provides instructions on how to add and subtract monomials. It defines key terms like coefficient, base, exponent, degree of a monomial, degree of a polynomial, and like terms. It explains that to add monomials, you add the coefficients and keep the base, and to subtract monomials you subtract the coefficients and keep the base. Examples are given of simplifying expressions by combining like terms.
1. The document discusses solving equations involving absolute value, including equations with a single absolute value and equations with two absolute values.
2. To solve an equation with a single absolute value, the equation is isolated so it is in the form |ax + b| = c, then the absolute value is separated into two cases: ax + b = c and ax + b = -c. These two equations are then solved.
3. To solve an equation with two absolute values, the equation is also separated into two cases since the values inside the absolute values could be the same or opposite. Each case is then solved.
Here is the system of inequalities for the cross-country team problem:
Let x = number of water bottles sold to students
Let y = number of water bottles sold to others
x + y ≤ 100 (they have 100 bottles total)
3x + 5y ≥ 400 (they need at least $400)
Graph the regions defined by these inequalities and the overlapping region is the solution.
Trigonometry deals with relationships between sides and angles in right triangles. The three main trigonometric functions are sine, cosine, and tangent, which provide ratios of sides of a right triangle based on a given angle. A scientific calculator can be used to find trigonometric ratios for any angle, as well as to calculate missing angles or sides of a right triangle when two pieces of information are known.
The document discusses slope and how to calculate it. It defines slope as the steepness of a line or the rate of change between two points. Slope is represented by the letter m. There are three main ways to calculate slope: 1) using the formula m = (y2 - y1) / (x2 - x1) for two points (x1, y1) and (x2, y2); 2) by finding the rise over run when given a graph; 3) by taking the coefficient of x when a line equation is in the form of y = mx + b, where m represents the slope. Examples are provided to demonstrate calculating slope using these different methods.
O documento apresenta questões sobre números primos, perfeitos e congruências numéricas. A questão 1 discute propriedades de números primos e o Lema de Euclides. A questão 2 trata do Teorema de Euclides sobre números perfeitos. A questão 3 prova que o quinto número de Fermat não é primo usando congruências.
Este documento explica los diferentes métodos para resolver ecuaciones de segundo grado, incluyendo ecuaciones incompletas, el método de factorización y la fórmula general. Primero se describen las ecuaciones incompletas donde b o c son iguales a cero y cómo reducirlas a ecuaciones de primer grado. Luego explica el método de factorización para ecuaciones que pueden factorizarse y la fórmula general para cuando no se puede factorizar. Finalmente desea éxito al lector en su prueba.
The document discusses synthetic division, providing 3 examples of dividing polynomials. The first example divides a polynomial by a monic linear divisor. The second divides a polynomial by a non-monic linear divisor. The third divides a polynomial by a monic quadratic divisor. Each example shows the division problem and solution.
This document defines integers and absolute value. Integers include whole numbers and their opposites on the number line, with positive integers above zero and negative integers below zero. Absolute value refers to the distance from zero on the number line, and is represented by bars around an integer, making it a positive number regardless of its original sign. Examples are provided to illustrate integers in contexts like stock prices, elevations, and temperatures.
Evaluating algebraic expressions with substitutioncindywhitebcms
This document defines variables, constants, expressions and provides examples of evaluating expressions for given values of variables. It defines a variable as a quantity that can change and constants as quantities that do not change. Expressions are defined as mathematical phrases involving variables, constants and operations. Several examples are given of evaluating expressions when given values for variables like x, m, p, c, z.
Discriminante de una ecuación de segundo gradoMaría Pizarro
El documento explica cómo calcular el discriminante de una ecuación de segundo grado y cómo determinar la naturaleza de sus soluciones en base al valor del discriminante. El discriminante se obtiene aplicando la fórmula D = b2 - 4ac y su signo indica si las soluciones son reales y distintas (positivo), reales e iguales (cero) o complejas (negativo). Se proveen ejemplos del cálculo del discriminante y su interpretación.
This document discusses writing linear equations in slope-intercept form and point-slope form by given information such as the slope, y-intercept, or two points on the line. It provides examples of finding the equation of a line given its slope and y-intercept, two points, or one point and the slope. The key methods covered are using the slope-intercept form y=mx+b and point-slope form y-y1=m(x-x1).
This document discusses different ways to prove that two triangles are congruent, including:
1) Side-Side-Side (SSS), which proves congruence if all three sides of one triangle are congruent to the corresponding sides of the other triangle.
2) Side-Angle-Side (SAS), which proves congruence if two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle.
3) Angle-Side-Angle (ASA), which proves congruence if two angles and the side between them of one triangle are congruent to the corresponding parts of the other triangle.
The document provides an overview of calculus and analytical geometry presented by Group D. It discusses various topics related to integration including the history and development of integration, the definition and purpose of integration, common integration rules and formulas like integration by parts and integration by partial fractions, and real-life applications of integration in fields like engineering, medicine, and physics. Examples are provided to demonstrate how to use integration techniques like integration by parts and integration by partial fractions to evaluate definite integrals.
This document discusses similarity and congruence of plane figures. It defines similar figures as those where corresponding angles are equal and corresponding side ratios are equal. Examples of similar figures include rectangles where the ratio of length to width is equal. The document provides examples of similar and congruent triangles and quadrilaterals. It also lists key terms and learning objectives related to identifying similar and congruent plane figures based on corresponding side lengths and angles.
Ecuaciones de tercer grado por el metodo ruffini0105790638
El documento describe los pasos para resolver una ecuación de segundo grado dividiendo por números divisibles del término independiente. Primero se identifican los coeficientes de la ecuación original. Luego se divide por números divisibles del término independiente para simplificar la ecuación hasta dejarla como una ecuación de primer grado y finalmente de cero orden, obteniendo la solución final.
This document discusses irrational numbers, which are numbers that cannot be expressed as a ratio of two integers, such as the square root of 2. It provides examples of irrational numbers that arise from calculations involving the sides of geometric shapes, such as the square root of 2 being the length of the diagonal of a unit square. The document also covers operations involving irrational numbers, stating that the product and quotient of irrational numbers are irrational numbers.
Pre-5.1 - trigonometry ratios in right triangle and special right triangles.pptMariOsnolaSan
Right triangle trigonometry is based on ratios of the sides of right triangles. The six trigonometric functions - sine, cosine, tangent, cotangent, secant, and cosecant - are defined by ratios of the opposite, adjacent, and hypotenuse sides. To find a missing angle or side, the appropriate trigonometric ratio is selected based on the known sides and then calculated. There are special right triangle theorems for 45-45-90 and 30-60-90 triangles that allow determining side lengths based on one known side length.
The document discusses linear inequalities in two variables and their graphical representations. It introduces the Cartesian coordinate system developed by Rene Descartes and its importance. It explains how to graph linear inequalities by first drawing the line as an equation, then determining whether to shade above or below the line based on whether a test point satisfies the inequality. Students are assigned to bring graphing paper, coloring materials, and a ruler to class on Monday to graph linear inequalities.
The document provides instructions on how to add and subtract monomials. It defines key terms like coefficient, base, exponent, degree of a monomial, degree of a polynomial, and like terms. It explains that to add monomials, you add the coefficients and keep the base, and to subtract monomials you subtract the coefficients and keep the base. Examples are given of simplifying expressions by combining like terms.
1. The document discusses solving equations involving absolute value, including equations with a single absolute value and equations with two absolute values.
2. To solve an equation with a single absolute value, the equation is isolated so it is in the form |ax + b| = c, then the absolute value is separated into two cases: ax + b = c and ax + b = -c. These two equations are then solved.
3. To solve an equation with two absolute values, the equation is also separated into two cases since the values inside the absolute values could be the same or opposite. Each case is then solved.
Here is the system of inequalities for the cross-country team problem:
Let x = number of water bottles sold to students
Let y = number of water bottles sold to others
x + y ≤ 100 (they have 100 bottles total)
3x + 5y ≥ 400 (they need at least $400)
Graph the regions defined by these inequalities and the overlapping region is the solution.
2. فيما سبق: درست التمثيل البياني للمعادل ت
الخطية.
وال:ن:
أتعرف عدد حلول نظام مكون من معادلتين
خطيتين.
أحل نظاما مكونا من معادلتين خطيتين بيانيا.
.ً
.ً
.ً
3. المفردا ت
نظام من معادلتين
النظام المتسق
النظام المستقل
النظام غير المستقل
النظام غير المتسق
4. لماذا؟
بلغت تكاليف إعداد مادة أشرطة علمية
0051 ريال، وكان تسجيل الشريط الواحد
يكلف 4 ريال ت ويباع بـ 01 ريال ت،
ويرغب مدير النتاج في معرفة عدد
الشرطة التي عليه بيعها حتى يحقق ربحا.
.ً
5. لماذا؟
إن التمثيل البياني لنظام المعادل ت يساعد
على معرفة الوضع الذي يحقق ربحا، ويمكن
.ً
التعبير عن تكاليف النتاج الكلية بالمعادلة
ص = 4س + 0051؛ حيث ص تمثل تكلفة
النتاج، س عدد الشرطة المنتجة.
6. لماذا؟
يمكن تمثيل القيمة الكلية للمبيعا ت بالمعادلة
ص = 01س، حيث تمثل ص القيمة الكلية
للمبيعا ت، س عدد عدد الشرطة المبيعة.
7. لماذا؟
يمكننا تمثيل هاتين المعادلتين بيانيا من معرفة
اّ
متى يبدأ تحقيق الربح. وذلك بتحديد النقطة
التي يتقاطع فيها المستقيمان، وهو ما يحدث
عند بيع 052 شريطا؛ أي أن تحقيق الربح يبدأ
.ً ْ
عند بيع أكثر من 052 شريطا.
.ً
8. لماذا؟
عدد الحلول الممكنة: تشكل المعادلتان
لّ
ص = 4س + 0051، ص = 01س
نظاما من معادلتين، ويسمى الزوج المرتب
سُ
.ً
الذي يمثل حال لكال من المعادلتين حال للنظام.
.ً
.ً
9. لماذا؟
إذا كان للنظام حل واحد على اللقل يسمى
نظاما متسقا، وتتقاطع تمثيالته البيانية في نقطة
.ً
.ً
واحدة، أو تشكل مستقيما واحدا.
.ً
.ً
لّ
10. لماذا؟
إذا كان للنظام حل واحد فقط، يسمى نظاما مستقال،
.ً
.ً
وإذا كان له عدد ل نهائي من الحلول يسمى
نظاما غير مستقل؛ وهذا يعني وجود عدد غير
.ً
محدد من الحلول تحقق كلتا المعادلتين.
11. لماذا؟
إذا لم يكن للنظام أي حل، يسمى نظاما غير متسق،
.ً
وتشكل تمثيالته البيانية مستقيما ت متوازية.
13. إرشادا ت للدراسة
عدد الحلول
عندما تكتب كل من المعادلتين على الصيغة
سُ
ص = م س + ب، فإن لقيم م، ب تحدد عدد الحلول.
المقارنة بين قيم م، ب
قيمتا م مختلفتا:ن
قيمتا م متساويتا:ن، وقيمتا ب
مختلفتا:ن
قيمتا م متساويتا:ن، وقيمتا ب
متساويتا:ن
عدد الحلول
1
ل يوجد
ل نهائي
14. عدد الحلول
مثال1
استعمل التمثيل البياني المجاور لتحدد إذا كان النظام التي
متسقا أم غير متسق، ومستقال أم غير م
.ً
.ً
أ( ص = -2س + 3
ص=س-5
15. أ( ص = -2س + 3
ص=س-5
بما أن المستقيمين اللذين يمثالن
المعادلتين يتقاطعان في نقطة واحدة،
فهناك حل واحد للنظام،
ويكون النظام متسقا ومستقال.
.ً
.ً
16. عدد الحلول
مثال1
استعمل التمثيل البياني المجاور لتحدد إذا كان النظام اليتي
متسقا أم غير متسق، ومستقال أم غير م
أ ً
أ ً
ب( ص = -2س - 5
ص = -2س + 3
17. ب( ص = -2س - 5
ص = -2س + 3
بما أن المستقيمين اللذين يمثالن
المعادلتين متوازيان فال يوجد حل
للنظام، ويكون النظام غير متسق.
19. الحــــــــل
بما أن المستقيمين اللذين يمثلن المعادلتين متقاطعان في نقطة
واحدة فهناك حل واحد للنظام ويكون النظام متسق ومستقل
اذن للنظام حل وحيد ) 0 ، 3 (
21. الحـــــــــــــــل
بما أن المستقيمين اللذين يمثلن المعادلتين متقاطعان في
نقطة واحدة فهناك حل واحد للنظام ويكون النظام متسق ومستقل
اذن للنظام حل وحيد ) 0 ، ــ 5 (
22. الحل بالتمثيل البياني: من الطرائق المستعملة
في حل نظام من المعادل ت يتمثيلها بيانيا في
أ ً
المستوى البياني نفسه، وإيجاد النقطة التي
يتقاطع عندها المستقيمان والتي يتمثل حل
النظام.
24. الحل بالتمثيل البياني
مثال2
مثل كل نظام مما يأيتي بيانيا، وأوجد عدد
أ ً
لّ
حلوله، وإذا كان واحدا فاكتبه:
أ ً
أ( ص = -3س + 01
ص=س–2
25. أ( ص = -3س + 01
ص=س–2
يظهر من التمثيل البياني أن
المستقيمين يتقاطعان في النقطة
)3، 1(، ويمكن التحقق من ذلك
بالتعويض عن س بـ 3، وعن ص بـ 1
ِ
34. مثل كل نظام مما يأتي بيانيا، وأوجد عدد حلوله،
،ً
لّ
وإذا كان واحدا فاكتبه:
،ً
يمكننا استعمال أنظمة المعادل ت
لحل مسائل متنوعة من واقع
الحياة تتضمن متغيرين أو أكثر.
36. كتابة نظام من معادلتين وحله
من واقع الحياة
مثال 3
تمور: يزداد إنتاج مزرعتي نخيل من التمور بانتظام تقريبا عبر عدد
،ً
ُ
من السنين. استعمل المعلوما ت الواردة في الجدول أدناه للتنبؤ بالسنة
التي يصبح فيها إنتاج المزرعتين متساويا على اعتبار أن معدل الزيادة
،ً
يبقى ثابتا خلل السنوا ت القادمة في كلتا المزرعتين.
،ً
المزرعة
اللولى
الثاتنية
كمية التنتاج عام
9241هـ )بالطن(
903
814
معدل الزيادة السنوية
)بالطن(
8
3
41. تحقق
استعمل التعويض للتحقق من صحة الجابة.
إذن، سيكون إنتاج الم
زرعتين
،ً
متساويا بعد 22 سنة
من
ْ
9241هـ؛ أي في عام
1541هـ،
إذا بقي معدل الزياد
،ً
ة ثابتا في كلتا
المزرعتين.
42. تحقق من فهمك
3( ساعا ت: يرغب كل من محمود ورائد في شراء ساعة
يدوية، فإذا كان مع محمود 41 ريال، ويوفر 01 ريال ت في
،ً
السبوع، ومع رائد 62 ريال ويوفر 7 ريال ت في السبوع،
،ً
فبعد كم أسبوعا يصبح معهما المبلغ نفسه؟
،ً
45. تأكد
استعمل التمثيل البياني المجاور لتحدد إذا
،ً
كان كل من أنظمة المعادل ت التية متسقا
ٌّ
أم غير متسق، ومستقل أم غير مستقل:
،ً
1( ص = -3س + 1
ص = 3س + 1
46. بما أن المستقيم متقاطعين في النقطة
)0 ،1( إذا النظام متسق ومستقل
47. تأكد
استعمل التمثيل البياني المجاور لتحدد إذا
ً
كان كل من أنظمة المعادل ت التية متسقا
ٌّ
أم غير متسق، ومستقال أم غير مستقل:
ً
3( ص = س - 3
ص=س+3
