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26.04.2014
Identifying corresponding parts in similar figures isn't so bad, but you have to know what you're looking for.

How Do You Write an Equation of a Line in Slope-Intercept Form If You Have One Point and a Parallel Line? Want to find the slope-intercept form of a line when you're given a point on that line and another line parallel to that line?

How Do You Write an Equation of a Line in Slope-Intercept Form If You Have One Point and a Perpendicular Line? Want to find the slope-intercept form of a line when you're given a point on that line and another line perpendicular to that line? The midpoint of a line segment is the point midway between the endpoints of the line segment. When you're looking at a map, you can find the point midway between two locations by calculating the midpoint.

How Do You Write an Equation of a Line in Point-Slope Form If You Have the Slope and One Point? How Do You Write the Equation of a Line in Slope-Intercept Form If You Have the Slope and the Y-Intercept? If you have two points on a number line, the midpoint is the point that is located directly midway between the two points.

When you're learning about linear equations, you're bound to run into the point-slope form of a line. If you need to find the distance between to points on the coordinate, you'll probably use the distance formula to get your answer. The Pythagorean theorem is a very popular theorem that shows a special relationship between the sides of a right triangle.

Simulators are a great way to model an experiment without actually performing the experiment in real life.

Venn Diagrams are really great tools for visualizing sets, especially when it comes to how sets intersect and come together. The idea of proportions is that a ratio can be written in many ways and still be equal to the same value.

The means-extremes property of proportions allows you to cross multiply, taking the product of the means and setting them equal to the product of the extremes. A proportion is just an equation where two ratios are equal, and each piece of the proportion has a special name. Ever had someone come up to you on the street, hand you a shape, and ask you to find the perimeter of that shape?

The standard form equation for a circle can tell you quite a bit about the graph of that circle! Sometimes you have an algebraic expression with variables, and you know the values of those variables exactly, and you just need to plug in those values and get the value of the expression. Understanding the multiplication properties of 0 and -1 are fundamental building blocks in learning all there is to know about the operation of multiplication.

Trying to solve an equation with variables on both sides of the equal sign and grouping symbols? Identity equations are equations that are true no matter what value is plugged in for the variable.

Graphing an absolute value equation can be complicated, unless you know how to dissect the equation to find and use the slope and translations. When you're learning about translating absolute value equations, learning about vertical translations is a MUST! When you're learning about translating absolute value equations, learning about horizontal translations is a MUST!

If something decreases in value at a constant rate, you may have exponential decay on your hands. In 2006, the scientific world celebrated the 120th anniversary of one of this most significant archaeological discovery in the study of the Holy Land - the map of Madaba.

When Christianity was adopted as the religion of the Byzantine Empire, the ecclesiastical division of the government was adapted to suit its administrative division. The Chalcedon Order determined that the archbishops of Caesarea, Beisan (Beit Shean) and Petra would come under the rule of the Patriarch of Jerusalem, while the bishops of Arabia and Phoenicia would remain subject to the Patriarch of Antioch.

Thus the church at Madaba was no longer in the area of Palaestina; neither politically nor ecclesiastically.

In 1880, the Bedouin tribe of Aziziat, Christian by faith, settled in the by now ruined, site of Madaba.

The first scholar who appreciated the scientific and artistic value of the floor was Father Kleopas Koikylides, the librarian for the Greek Orthodox Patriarchate in Jerusalem.

This map is the most significant example of the biblical school of mapmaking to have survived and probably descends from the lost map of Eusebius, the bishop of Caesarea.

The surviving sections depict biblical Palestine from Salem, south of Bet Shea€™ an, to the Nile Delta. The biblical focus of the map is immediately apparent, though the mapmaker carefully locates ancient sites within a contemporary framework of the local Roman roads. Natural features include the Jordan River, the Dead Sea, three portions of the Mediterranean coastline, the Nile Delta, and a number of mountain ranges. Jerusalem is seen as if from the air and is presented in three-dimensional form with a considerable degree of realism. Because the anonymous artist wished to emphasize Jerusalema€™s prominence on the map, it is as if he split the city into two: the Cardo, which is its main street, divides it into two projections, the eastern part leans west while the western part slants downwards. The mosaic is the earliest surviving original map of the Holy Land area and the first to show the Twelve Tribes of Israel. Strangely enough, although Madaba was visited a good deal by pilgrims, no pilgrim reports exist about the mosaic. The procedure involved composing a sketch map, drawing the outlines in wet cement, and then placing lines of black cubes; the interior was filled in next with colored cubes. The map was damaged, probably during the Iconoclastic Controversy in the eighth or ninth century. Damage was repaired by filling in the obliterated spaces with a random assortment of cubes. Jeromea€™s version of Eusebiusa€™ map, known from a 12th century copy, bears some similarities to the Madaba Mosaic, particularly in the rectangular format and treatment of the Nile Delta and Mediterranean Sea. Other researchers were aided by inscriptions found in a nearby cistern, in which there is mention of the Emperor Justinian (A.D. Another researcher, Thompson, draws a parallel between the mosaic floor and another Madaba mosaic in the Church of the Apostles, built in the days of Bishop Sergius in 579. Besides its scientific and historical value for the study of Eretz-Israel in the Byzantine period, the Madaba map is a unique and priceless source of information and documentation of the Land of Israel and of Jerusalem for those interested in places that are sacred to Judaism and to Christianity. In summary the over 150 captions in the Map, most of which have been positively identified, refer to localities of the Near East extending from Tir and Sidon to the north up to and including the Nile Delta to the south, and from the Mediterranean Sea to the Arabian Desert. The map is oriented to the East, as are the cities and buildings therein represented as well as the captions accompanying them. The way the locality is represented gives an indication of its importance: Jerusalem, Neapolis, Ascalon, Gaza and Pelusium are distinguishable from minor cities the like of Kerak, Lod, Iabneel, Ashdod, Eleutheropolis, smaller towns of a certain importance such as Jericho, Bet Zachar, Bersabea down to mere symbols such as a gate with lateral towers or simply a church representing a village or shrine.

Apart from the rivers, the sea and mountains, the mosaicist used other symbols which are easily understood: palm trees that go with the oases in the Jordan Valley, bushes along the river banks, the fording places of the River Jordan with the characteristic pulley-drawn ferries, fish represented in the water and the two ships figured in the Dead Sea.

The representation of Jerusalem reaches the apex of the art of representation in this mosaic. The contents of the captions, especially the direct references to the tribes of Israel, names, quotation of biblical benedictions, clearly indicate that the Map is primarily a document of biblical geography based on the Onomasticon of biblical locations by Eusebius (sixth century). The addition of places mentioned in the New Testament, and the primary importance given to Christian shrines, churches and to the Basilica of the Holy Sepulcher makes of the map a Christian re-reading of the story of salvation in a geographic context. This tutorial shows you how to take a word problem and use indirect measurement to turn it into a proportion. This tutorial shows you how to take two endpoints and figure out the midpoint of the line segment. This tutorial takes you through the process of finding the point midway between two cities. This form is quite useful in creating an equation of a line if you're given the slope and a point on the line. In this tutorial, you'll get introduced to the Pythagorean theorem and see how it's used to solve for a missing length on a right triangle! This tutorial will teach you those names, and this will help you understand cross multiplication when you learn it later! You'll see how to use the scale from a blueprint of a house to help find the actual height of the house.

Well, one of those rules is called the subtraction property of inequality, and it basically says that if you minus a number from one side of an inequality, you have to minus that same number from the other side of the inequality as well.

Well, one of those rules is called the addition property of inequality, and it basically says that if you add a number from one side of an inequality, you have to add that same number from the other side of the inequality as well. In this tutorial, you'll learn what the sine ratio is and how to use it to find angle measurements in a right triangle. Well, if that's what you have to do, then you've come to the right place, because this tutorial will show you exactly how to do it! Just multiply the fraction away by multiplying by the reciprocal and then perform the order of operations in reverse! Watch this tutorial to figure out how remove the grouping symbols and get those variables together to solve the equation. In this tutorial, you'll see how to take a word problem and use it to write and solve an equation with variables on both sides!

This means that no matter what value is plugged in for the variable, you will ALWAYS get a contradiction. Literal equations allow use to represent things like distance, time, interest, and slope as variables in an equation.

Follow along as this tutorial shows you how to identify the necessary parts of the equation and use them to graph the absolute value equation.

Check out this tutorial and see what it takes to translate an absolute value equation vertically.

Check out this tutorial and see what it takes to translate an absolute value equation horizontally. This tutorial shows you how to create a table and identify a pattern from the word problem.

This tutorial takes you through the process of applying product of powers rule to simplify an expression.

In this tutorial, you'll see how to use the quotient of powers rule to simplify an expression. Learn how to split that exponent and put it in the numerator and denominator of your fraction using the power of a quotient rule. Connect to Bluetooth wireless technology-enabled cellular phones to make and receive cellular calls with the ease and comfort of a home phone system. This map, actually a mosaic floor, was revealed when the foundations were being dug for the construction of a Greek Orthodox church in a place that had once been a central town in the biblical kingdom of Moab on the floor of a late sixth century Byzantine church in Madaba, a town about fifteen miles from the Dead Sea which is today in Jordan. Michael Avi-Yonah, who worked on the mosaic together with several other researchers, dated the building of the mosaic floor to the second half of the sixth century (A.D.

614), Madaba was on the eastern border of the province of Palaestina, the smallest of the provinces of the Byzantine Empire.

These were the main districts of the province, which were later divided into sub-districts. Each administrative area was headed by a bishop, who was the head of the churches in his district. It is therefore amazing that the church maintained such a close relationship with Eretz-Israel and Jerusalem. Members of the Greek Orthodox community living in the area had flourished, and while involved in construction work, had discovered the mosaic floor, with its depiction of the Holy Land in the form of a map. The new church was therefore situated partly on the foundations of the ancient church, and later the construction itself actually destroyed parts of it (the part of the floor depicting the area between Hebron and Beersheba, the southern area till the Zered Stream, and more). Koikylides halted the reconstruction, which tragically had damaged the mosaic, and drew scholarly attention to this unique and splendid artifact. The map is oriented with East at the top, and the Mediterranean coastline runs straight from left to right, aligning Alexandria with the Holy Land coast and tracing the Nile east to west.

The regions of five of the Twelve Tribes of Israel are distinguished in the existing sections.

The twin mountains of Gerizein and Gegal are shown twice in different locations in deference to both Jewish and Samaritan traditions. It occupies the center and is shown in intricate detail, nearly ten times larger than other parts of the map. Despite the schematic interpretation, the stereotypical design of the buildings and the selectivity in choosing them, it gives a tangible depiction of Jerusalem in the sixth century, with its walls, towers and gates, its streets and main buildings. The buildings in the western part of the city are displayed from their western side except for the Church of the Holy Sepulcher and a few other important buildings whose faA§ades point eastward. The largest is the one erroneously called The Tower of David and which probably should be called The Tower of Phasael, built by King Herod. It was innovative at the time in being orientated to the east and the artist tried to unite both the floor plan and view in the same way that such drawings are made today.

This might be explained by the fact that the Persians attacked Palestine in 614 AD and left behind only the burning ruins of the holy places.

Usually a patron or the ruler of the land lent his name to such an important work but the section where this name was generally placed is severely damaged. In the mountainous areas, the hills were drawn first, then captions, and finally the symbols for villages and churches.

The Iconoclasts, followers of the Byzantine emperors, believed that it was idolatrous to portray living figures in churches. Unfortunately, the map suffered again while the church was being rebuilt in the 19th century, and these portions have been replaced by brown and tan cement. Both show a huge inlet, called on Jeromea€™s map the Egyptian Sea, between Palestine and the Nile Delta (also visible on medieval maps like the Matthew Paris map of Palestine and the Hereford world map of about 1275, Book IIB, #225 and #226).

Madaba was on a Roman road that linked Damascus, Philadelphia (Amman), and Petra with Aela (Eilat) on the Gulf of Aqaba and that brought incense and spice caravans from the East to the Roman Empire. It illustrates the scholarly work of Eusebius and the technical capabilities of provincial mapmakers and mosaicists. Apart from this the physical characteristics of Palestine are so realistically rendered as to make them easily identifiable.

In a certain way the City is the ideal center of the whole composition even if it is not physically situated in the center of the map. As to the rest of the contents it owes its sources to an antique journey diary, updated to cater for the needs of the sixth century Christian pilgrims who visited the Holy Land, with the Bible at hand. The Map therefore covers the territory of the 12 biblical tribes and the surrounding regions, defined, as it were in the boundaries of Canaan promised to Abraham. The Holy City of Jerusalem is represented at the center of the redeemed ecumene, and the building which is given the greatest importance is the Constantine complex built upon Calvary and Jesusa€™ Sepulcher.

Then see how to use the mean extremes property of proportions to cross multiply and solve for the answer. In this tutorial, you'll see how to find the slope using the slope of the perpendicular line. Follow along as this tutorial shows you how to take a linear equation from standard form and convert it into slope-intercept form and point-slope form. Follow along as this tutorial shows you how to take a linear equation from point-slope form and convert it into standard form and slope-intercept form.

Follow along with this tutorial as you see how use the information given to write the equation of a vertical line.

Follow along with this tutorial as you see how use the information given to write the equation of a horizontal line. Plug those values correctly into the point-slope form of a line and you'll have your answer! If you have two linear equations that have the same slope but different y-intercepts, then those lines are parallel to one another!

The midpoint of a line segment is the point located midway between the endpoints of the line segment. The endpoints of a line segment are just the 'points' located at the 'ends' of the line segment! Check out this tutorial and see how to use this really helpful theorem to find that missing side measurement!

In this tutorial, you'll be introduced to the names for the different parts of a right triangle.

Ingredients sometimes need to be mixed using ratios such as the ratio of water to cement mix when making cement.

Learn about identity equations in this tutorial, and then create your own identity equation. Then you can see how to create an exponential function from the data and solve the function to get your answer! Mobile Notifications let you know when your Android mobile phone receives a text, e-mail or social media update.

All the bishops were subject to the rule of the Archbishop of Caesarea who sat at the administrative and ecclesiastic center of Palaestina and was head of all the churches in the area.

This relationship is clearly expressed in the mosaic floor which apparently decorated a church or magnificent public edifice, and which avoided the use of religious symbols or portraits of political and ecclesiastic rulers of the period. Notice of the discovery was conveyed to the Greek Orthodox Patriarch of Jerusalem, Nicodemos (1883-1890), but he did not recognize its importance. According to witnesses who saw the floor before the builders got to work, the mosaic had been almost complete at that time. A study of the source material and three fragments elsewhere in the floor indicates that originally the map measured nearly seven by twenty-two meters, plus a wide margin, and depicted the area from Byblus and Damascus in the north to Alexandria and the Red Sea in the south. There are numerous sites associated with the Old Testament, such as the Oaks of Mamre, Jacoba€™s Well, the Desert of Zin that figured in the Exodus, and the location of the brazen serpent, which saved the Israelites. Specific Roman references include several mileposts outside of Jerusalem and the Hot Springs of Callerhoe, where Herod, the Roman King of Palestine, took a rest cure.

Virtually all the buildings in the city, such as the Church of the Holy Sepulcher, may be identified. This is the most ancient pictorial representation of Jerusalem ever found and it is a primary source for studying the plan of the city.

The Church of the Theodokos was consecrated on November 23, 542, and the Wall built by Eudocia to enclose Mt. Believers assumed this to signify that Jerusalem was situated at the center of the world and many manuscripts and early maps really did portray the city in this manner. As mentioned above, the most important section is the plan of Jerusalem, which is depicted oval-shaped, a novel interpretation as it had always previously been shown circular.

According to one of the mosaics inscriptions, construction was sponsored entirely by the inhabitants of Madaba. In the plains the order was reversed, and the placement of symbols preceded the inscriptions.

They effaced scenes of a lion chasing a gazelle in the wilderness of Moab, and sailors rowing two boats on the Dead Sea. Otherwise, the Madaba Mosaic has been preserved as it was constructed over fourteen hundred years ago.

The Madaba Mosaic, however, probably reflects the lost map of Eusebius more accurately than Jeromea€™s does. All the cities on the mosaic lie along major routes; lesser towns near roads are depicted to the exclusion of larger but more remote places. This epigraphic evidence has been discounted by other researchers because of the lack of any connection between the cistern and the church; despite their proximity, the cistern is outside the wall of Jerusalem and the church is within its walls. Both of these mosaics resemble the floor of Hirams grave near the city of Tyre, dating from 573. Upon the central axis, formed by the flow of the Jordan River and the Dead Sea, there extend the trans-jordanian plateau with its deep valleys (wadi) to the east, and to the west the mountains of Samaria and Judea distinctly separated by the Mediterranean coastal plain. Notwithstanding the unavoidable approximations, due to the limited space available, it is obvious that the disposition of the localities followed the road network prevailing at the time in the region. The birda€™s eye view of the city is shown with its walls, gates, streets and major buildings that are partly identifiable even today. This can be clearly seen from the preponderance of churches and shrines over other public buildings.

In this tutorial, you'll see how to use two points on the line to find the change in 'y' and the change in 'x'. Watch this tutorial and see what needs to be done to write an equation in slope-intercept form!

In this tutorial, you'll see how to find the slope of your line and use that slope, along with the given point, to write an equation for the line in slope-intercept form. Then, use this slope and the given point to write an equation for the line in slope-intercept form. Watch this tutorial and see what needs to be done to write an equation in point-slope form! Slope is the rise over the run, the change in 'y' over the change in 'x', or the gradient of a line. Then, plot those ordered pair on a coordinate plane and connect the points to make your graph!

In any event, it is certain that the map was made during the Byzantine period and it is one of the most beautiful geographical testimonies extant to the biblical Land of Israel, from Babylon to Egypt and from the Arabian dessert to the Mediterranean Sea.

This hierarchy lasted until the days of Juvenal, who was bishop of Jerusalem in the first half of the fifth century. His successor, the Patriarch Gerasimos, (1890-1897) realized the significance of the discovery and determined to erect a church at the site. Individual gates are designated as well as a column thought to be the point of reference for Roman surveyors and road builders. The walls of the city are pierced by six gates, the number of gates in the wall until the New Gate was opened in the Christian Quarter in the 1890a€™s. The city is also shown narrowing from west to east but this may have been because the background mountains restricted the artist. The project required at least three mosaicists as well as a specialist in biblical topography. In addition to the close textual relationship, the mosaic is divided by the territories of the Twelve Tribes of Israel, a distinguishing feature of Eusebiusa€™ map. From the artistic point of view, the Map must be viewed in the context of a return to the classical style prevailing in the Justinian epoch (half way through the sixth century), of which the mosaics of Madaba and its surrounding region have given us many a dated witness. If you get a false statement, then you can be sure that your triangle is not a right triangle. You get the same answer no matter which method you use, so be sure to add this method to your arsenal!

Juvenal contended for, and won, the title of Patriarch of Antioch in the decisive meeting at Chalcedon (A.D. The floor is made up of North African mosaics, which closely resemble other mosaics found in another ruined church in the old town of Madaba. The artist chose from a wide selection of cubes: eight different colors were used, as well as ten additional shades of red and blue.

Finally, a column is shown in Jerusalem that was the point of reference for local surveyors, and two mileposts are identified just outside the city. In the Jordan Plain there are palm trees, and adjacent to each item are written explanations. Check out this tutorial and learn how use the Pythagorean theorem to see if a triangle is a right triangle!

It features Virtual Multi-Line Operation which allows you to pair up to two cellular lines and one landline with your cordless system.

The artist lavished on this work the resources of an unusually varied palette: four shades of red, five to six of green-blue, dark brown, violet, black, white, yellow and grey.

Madaba and Caesarea, where Euscbius had been bishop over a century earlier, were both under the jurisdiction of the Patriarchate of Jerusalem.

The map measured 190 square meters and the number of mosaic cubes used in a square decimeter numbered up to 150 in the most elaborate parts.

More importantly, most of the inscriptions and place names are identical with the unique surviving Greek manuscript of Eusebiusa€™ text. Next to the names of some of the cities, are the names of important events that occurred later in the area. It is believed that the total number of cubes approached over two million for the whole floor.

An accomplished mosaic artist can lay up to 150-200 cubes per hour, so the Madaba map mosaic demanded approximately 1,000 working days of twelve hours each day. Taking into consideration that the preparation of the cubes also took time, one can get an idea of the immense amount of work involved.

It is reasonable to assume that the creator was of Eastern origin, familiar with the language and the layout of the land. He may have been a monk and the map may have been intended to offer devout pilgrims a view of the city of Jerusalem as witness of a great past.

How Do You Write an Equation of a Line in Slope-Intercept Form If You Have One Point and a Parallel Line? Want to find the slope-intercept form of a line when you're given a point on that line and another line parallel to that line?

How Do You Write an Equation of a Line in Slope-Intercept Form If You Have One Point and a Perpendicular Line? Want to find the slope-intercept form of a line when you're given a point on that line and another line perpendicular to that line? The midpoint of a line segment is the point midway between the endpoints of the line segment. When you're looking at a map, you can find the point midway between two locations by calculating the midpoint.

How Do You Write an Equation of a Line in Point-Slope Form If You Have the Slope and One Point? How Do You Write the Equation of a Line in Slope-Intercept Form If You Have the Slope and the Y-Intercept? If you have two points on a number line, the midpoint is the point that is located directly midway between the two points.

When you're learning about linear equations, you're bound to run into the point-slope form of a line. If you need to find the distance between to points on the coordinate, you'll probably use the distance formula to get your answer. The Pythagorean theorem is a very popular theorem that shows a special relationship between the sides of a right triangle.

Simulators are a great way to model an experiment without actually performing the experiment in real life.

Venn Diagrams are really great tools for visualizing sets, especially when it comes to how sets intersect and come together. The idea of proportions is that a ratio can be written in many ways and still be equal to the same value.

The means-extremes property of proportions allows you to cross multiply, taking the product of the means and setting them equal to the product of the extremes. A proportion is just an equation where two ratios are equal, and each piece of the proportion has a special name. Ever had someone come up to you on the street, hand you a shape, and ask you to find the perimeter of that shape?

The standard form equation for a circle can tell you quite a bit about the graph of that circle! Sometimes you have an algebraic expression with variables, and you know the values of those variables exactly, and you just need to plug in those values and get the value of the expression. Understanding the multiplication properties of 0 and -1 are fundamental building blocks in learning all there is to know about the operation of multiplication.

Trying to solve an equation with variables on both sides of the equal sign and grouping symbols? Identity equations are equations that are true no matter what value is plugged in for the variable.

Graphing an absolute value equation can be complicated, unless you know how to dissect the equation to find and use the slope and translations. When you're learning about translating absolute value equations, learning about vertical translations is a MUST! When you're learning about translating absolute value equations, learning about horizontal translations is a MUST!

If something decreases in value at a constant rate, you may have exponential decay on your hands. In 2006, the scientific world celebrated the 120th anniversary of one of this most significant archaeological discovery in the study of the Holy Land - the map of Madaba.

When Christianity was adopted as the religion of the Byzantine Empire, the ecclesiastical division of the government was adapted to suit its administrative division. The Chalcedon Order determined that the archbishops of Caesarea, Beisan (Beit Shean) and Petra would come under the rule of the Patriarch of Jerusalem, while the bishops of Arabia and Phoenicia would remain subject to the Patriarch of Antioch.

Thus the church at Madaba was no longer in the area of Palaestina; neither politically nor ecclesiastically.

In 1880, the Bedouin tribe of Aziziat, Christian by faith, settled in the by now ruined, site of Madaba.

The first scholar who appreciated the scientific and artistic value of the floor was Father Kleopas Koikylides, the librarian for the Greek Orthodox Patriarchate in Jerusalem.

This map is the most significant example of the biblical school of mapmaking to have survived and probably descends from the lost map of Eusebius, the bishop of Caesarea.

The surviving sections depict biblical Palestine from Salem, south of Bet Shea€™ an, to the Nile Delta. The biblical focus of the map is immediately apparent, though the mapmaker carefully locates ancient sites within a contemporary framework of the local Roman roads. Natural features include the Jordan River, the Dead Sea, three portions of the Mediterranean coastline, the Nile Delta, and a number of mountain ranges. Jerusalem is seen as if from the air and is presented in three-dimensional form with a considerable degree of realism. Because the anonymous artist wished to emphasize Jerusalema€™s prominence on the map, it is as if he split the city into two: the Cardo, which is its main street, divides it into two projections, the eastern part leans west while the western part slants downwards. The mosaic is the earliest surviving original map of the Holy Land area and the first to show the Twelve Tribes of Israel. Strangely enough, although Madaba was visited a good deal by pilgrims, no pilgrim reports exist about the mosaic. The procedure involved composing a sketch map, drawing the outlines in wet cement, and then placing lines of black cubes; the interior was filled in next with colored cubes. The map was damaged, probably during the Iconoclastic Controversy in the eighth or ninth century. Damage was repaired by filling in the obliterated spaces with a random assortment of cubes. Jeromea€™s version of Eusebiusa€™ map, known from a 12th century copy, bears some similarities to the Madaba Mosaic, particularly in the rectangular format and treatment of the Nile Delta and Mediterranean Sea. Other researchers were aided by inscriptions found in a nearby cistern, in which there is mention of the Emperor Justinian (A.D. Another researcher, Thompson, draws a parallel between the mosaic floor and another Madaba mosaic in the Church of the Apostles, built in the days of Bishop Sergius in 579. Besides its scientific and historical value for the study of Eretz-Israel in the Byzantine period, the Madaba map is a unique and priceless source of information and documentation of the Land of Israel and of Jerusalem for those interested in places that are sacred to Judaism and to Christianity. In summary the over 150 captions in the Map, most of which have been positively identified, refer to localities of the Near East extending from Tir and Sidon to the north up to and including the Nile Delta to the south, and from the Mediterranean Sea to the Arabian Desert. The map is oriented to the East, as are the cities and buildings therein represented as well as the captions accompanying them. The way the locality is represented gives an indication of its importance: Jerusalem, Neapolis, Ascalon, Gaza and Pelusium are distinguishable from minor cities the like of Kerak, Lod, Iabneel, Ashdod, Eleutheropolis, smaller towns of a certain importance such as Jericho, Bet Zachar, Bersabea down to mere symbols such as a gate with lateral towers or simply a church representing a village or shrine.

Apart from the rivers, the sea and mountains, the mosaicist used other symbols which are easily understood: palm trees that go with the oases in the Jordan Valley, bushes along the river banks, the fording places of the River Jordan with the characteristic pulley-drawn ferries, fish represented in the water and the two ships figured in the Dead Sea.

The representation of Jerusalem reaches the apex of the art of representation in this mosaic. The contents of the captions, especially the direct references to the tribes of Israel, names, quotation of biblical benedictions, clearly indicate that the Map is primarily a document of biblical geography based on the Onomasticon of biblical locations by Eusebius (sixth century). The addition of places mentioned in the New Testament, and the primary importance given to Christian shrines, churches and to the Basilica of the Holy Sepulcher makes of the map a Christian re-reading of the story of salvation in a geographic context. This tutorial shows you how to take a word problem and use indirect measurement to turn it into a proportion. This tutorial shows you how to take two endpoints and figure out the midpoint of the line segment. This tutorial takes you through the process of finding the point midway between two cities. This form is quite useful in creating an equation of a line if you're given the slope and a point on the line. In this tutorial, you'll get introduced to the Pythagorean theorem and see how it's used to solve for a missing length on a right triangle! This tutorial will teach you those names, and this will help you understand cross multiplication when you learn it later! You'll see how to use the scale from a blueprint of a house to help find the actual height of the house.

Well, one of those rules is called the subtraction property of inequality, and it basically says that if you minus a number from one side of an inequality, you have to minus that same number from the other side of the inequality as well.

Well, one of those rules is called the addition property of inequality, and it basically says that if you add a number from one side of an inequality, you have to add that same number from the other side of the inequality as well. In this tutorial, you'll learn what the sine ratio is and how to use it to find angle measurements in a right triangle. Well, if that's what you have to do, then you've come to the right place, because this tutorial will show you exactly how to do it! Just multiply the fraction away by multiplying by the reciprocal and then perform the order of operations in reverse! Watch this tutorial to figure out how remove the grouping symbols and get those variables together to solve the equation. In this tutorial, you'll see how to take a word problem and use it to write and solve an equation with variables on both sides!

This means that no matter what value is plugged in for the variable, you will ALWAYS get a contradiction. Literal equations allow use to represent things like distance, time, interest, and slope as variables in an equation.

Follow along as this tutorial shows you how to identify the necessary parts of the equation and use them to graph the absolute value equation.

Check out this tutorial and see what it takes to translate an absolute value equation vertically.

Check out this tutorial and see what it takes to translate an absolute value equation horizontally. This tutorial shows you how to create a table and identify a pattern from the word problem.

This tutorial takes you through the process of applying product of powers rule to simplify an expression.

In this tutorial, you'll see how to use the quotient of powers rule to simplify an expression. Learn how to split that exponent and put it in the numerator and denominator of your fraction using the power of a quotient rule. Connect to Bluetooth wireless technology-enabled cellular phones to make and receive cellular calls with the ease and comfort of a home phone system. This map, actually a mosaic floor, was revealed when the foundations were being dug for the construction of a Greek Orthodox church in a place that had once been a central town in the biblical kingdom of Moab on the floor of a late sixth century Byzantine church in Madaba, a town about fifteen miles from the Dead Sea which is today in Jordan. Michael Avi-Yonah, who worked on the mosaic together with several other researchers, dated the building of the mosaic floor to the second half of the sixth century (A.D.

614), Madaba was on the eastern border of the province of Palaestina, the smallest of the provinces of the Byzantine Empire.

These were the main districts of the province, which were later divided into sub-districts. Each administrative area was headed by a bishop, who was the head of the churches in his district. It is therefore amazing that the church maintained such a close relationship with Eretz-Israel and Jerusalem. Members of the Greek Orthodox community living in the area had flourished, and while involved in construction work, had discovered the mosaic floor, with its depiction of the Holy Land in the form of a map. The new church was therefore situated partly on the foundations of the ancient church, and later the construction itself actually destroyed parts of it (the part of the floor depicting the area between Hebron and Beersheba, the southern area till the Zered Stream, and more). Koikylides halted the reconstruction, which tragically had damaged the mosaic, and drew scholarly attention to this unique and splendid artifact. The map is oriented with East at the top, and the Mediterranean coastline runs straight from left to right, aligning Alexandria with the Holy Land coast and tracing the Nile east to west.

The regions of five of the Twelve Tribes of Israel are distinguished in the existing sections.

The twin mountains of Gerizein and Gegal are shown twice in different locations in deference to both Jewish and Samaritan traditions. It occupies the center and is shown in intricate detail, nearly ten times larger than other parts of the map. Despite the schematic interpretation, the stereotypical design of the buildings and the selectivity in choosing them, it gives a tangible depiction of Jerusalem in the sixth century, with its walls, towers and gates, its streets and main buildings. The buildings in the western part of the city are displayed from their western side except for the Church of the Holy Sepulcher and a few other important buildings whose faA§ades point eastward. The largest is the one erroneously called The Tower of David and which probably should be called The Tower of Phasael, built by King Herod. It was innovative at the time in being orientated to the east and the artist tried to unite both the floor plan and view in the same way that such drawings are made today.

This might be explained by the fact that the Persians attacked Palestine in 614 AD and left behind only the burning ruins of the holy places.

Usually a patron or the ruler of the land lent his name to such an important work but the section where this name was generally placed is severely damaged. In the mountainous areas, the hills were drawn first, then captions, and finally the symbols for villages and churches.

The Iconoclasts, followers of the Byzantine emperors, believed that it was idolatrous to portray living figures in churches. Unfortunately, the map suffered again while the church was being rebuilt in the 19th century, and these portions have been replaced by brown and tan cement. Both show a huge inlet, called on Jeromea€™s map the Egyptian Sea, between Palestine and the Nile Delta (also visible on medieval maps like the Matthew Paris map of Palestine and the Hereford world map of about 1275, Book IIB, #225 and #226).

Madaba was on a Roman road that linked Damascus, Philadelphia (Amman), and Petra with Aela (Eilat) on the Gulf of Aqaba and that brought incense and spice caravans from the East to the Roman Empire. It illustrates the scholarly work of Eusebius and the technical capabilities of provincial mapmakers and mosaicists. Apart from this the physical characteristics of Palestine are so realistically rendered as to make them easily identifiable.

In a certain way the City is the ideal center of the whole composition even if it is not physically situated in the center of the map. As to the rest of the contents it owes its sources to an antique journey diary, updated to cater for the needs of the sixth century Christian pilgrims who visited the Holy Land, with the Bible at hand. The Map therefore covers the territory of the 12 biblical tribes and the surrounding regions, defined, as it were in the boundaries of Canaan promised to Abraham. The Holy City of Jerusalem is represented at the center of the redeemed ecumene, and the building which is given the greatest importance is the Constantine complex built upon Calvary and Jesusa€™ Sepulcher.

Then see how to use the mean extremes property of proportions to cross multiply and solve for the answer. In this tutorial, you'll see how to find the slope using the slope of the perpendicular line. Follow along as this tutorial shows you how to take a linear equation from standard form and convert it into slope-intercept form and point-slope form. Follow along as this tutorial shows you how to take a linear equation from point-slope form and convert it into standard form and slope-intercept form.

Follow along with this tutorial as you see how use the information given to write the equation of a vertical line.

Follow along with this tutorial as you see how use the information given to write the equation of a horizontal line. Plug those values correctly into the point-slope form of a line and you'll have your answer! If you have two linear equations that have the same slope but different y-intercepts, then those lines are parallel to one another!

The midpoint of a line segment is the point located midway between the endpoints of the line segment. The endpoints of a line segment are just the 'points' located at the 'ends' of the line segment! Check out this tutorial and see how to use this really helpful theorem to find that missing side measurement!

In this tutorial, you'll be introduced to the names for the different parts of a right triangle.

Ingredients sometimes need to be mixed using ratios such as the ratio of water to cement mix when making cement.

Learn about identity equations in this tutorial, and then create your own identity equation. Then you can see how to create an exponential function from the data and solve the function to get your answer! Mobile Notifications let you know when your Android mobile phone receives a text, e-mail or social media update.

All the bishops were subject to the rule of the Archbishop of Caesarea who sat at the administrative and ecclesiastic center of Palaestina and was head of all the churches in the area.

This relationship is clearly expressed in the mosaic floor which apparently decorated a church or magnificent public edifice, and which avoided the use of religious symbols or portraits of political and ecclesiastic rulers of the period. Notice of the discovery was conveyed to the Greek Orthodox Patriarch of Jerusalem, Nicodemos (1883-1890), but he did not recognize its importance. According to witnesses who saw the floor before the builders got to work, the mosaic had been almost complete at that time. A study of the source material and three fragments elsewhere in the floor indicates that originally the map measured nearly seven by twenty-two meters, plus a wide margin, and depicted the area from Byblus and Damascus in the north to Alexandria and the Red Sea in the south. There are numerous sites associated with the Old Testament, such as the Oaks of Mamre, Jacoba€™s Well, the Desert of Zin that figured in the Exodus, and the location of the brazen serpent, which saved the Israelites. Specific Roman references include several mileposts outside of Jerusalem and the Hot Springs of Callerhoe, where Herod, the Roman King of Palestine, took a rest cure.

Virtually all the buildings in the city, such as the Church of the Holy Sepulcher, may be identified. This is the most ancient pictorial representation of Jerusalem ever found and it is a primary source for studying the plan of the city.

The Church of the Theodokos was consecrated on November 23, 542, and the Wall built by Eudocia to enclose Mt. Believers assumed this to signify that Jerusalem was situated at the center of the world and many manuscripts and early maps really did portray the city in this manner. As mentioned above, the most important section is the plan of Jerusalem, which is depicted oval-shaped, a novel interpretation as it had always previously been shown circular.

According to one of the mosaics inscriptions, construction was sponsored entirely by the inhabitants of Madaba. In the plains the order was reversed, and the placement of symbols preceded the inscriptions.

They effaced scenes of a lion chasing a gazelle in the wilderness of Moab, and sailors rowing two boats on the Dead Sea. Otherwise, the Madaba Mosaic has been preserved as it was constructed over fourteen hundred years ago.

The Madaba Mosaic, however, probably reflects the lost map of Eusebius more accurately than Jeromea€™s does. All the cities on the mosaic lie along major routes; lesser towns near roads are depicted to the exclusion of larger but more remote places. This epigraphic evidence has been discounted by other researchers because of the lack of any connection between the cistern and the church; despite their proximity, the cistern is outside the wall of Jerusalem and the church is within its walls. Both of these mosaics resemble the floor of Hirams grave near the city of Tyre, dating from 573. Upon the central axis, formed by the flow of the Jordan River and the Dead Sea, there extend the trans-jordanian plateau with its deep valleys (wadi) to the east, and to the west the mountains of Samaria and Judea distinctly separated by the Mediterranean coastal plain. Notwithstanding the unavoidable approximations, due to the limited space available, it is obvious that the disposition of the localities followed the road network prevailing at the time in the region. The birda€™s eye view of the city is shown with its walls, gates, streets and major buildings that are partly identifiable even today. This can be clearly seen from the preponderance of churches and shrines over other public buildings.

In this tutorial, you'll see how to use two points on the line to find the change in 'y' and the change in 'x'. Watch this tutorial and see what needs to be done to write an equation in slope-intercept form!

In this tutorial, you'll see how to find the slope of your line and use that slope, along with the given point, to write an equation for the line in slope-intercept form. Then, use this slope and the given point to write an equation for the line in slope-intercept form. Watch this tutorial and see what needs to be done to write an equation in point-slope form! Slope is the rise over the run, the change in 'y' over the change in 'x', or the gradient of a line. Then, plot those ordered pair on a coordinate plane and connect the points to make your graph!

In any event, it is certain that the map was made during the Byzantine period and it is one of the most beautiful geographical testimonies extant to the biblical Land of Israel, from Babylon to Egypt and from the Arabian dessert to the Mediterranean Sea.

This hierarchy lasted until the days of Juvenal, who was bishop of Jerusalem in the first half of the fifth century. His successor, the Patriarch Gerasimos, (1890-1897) realized the significance of the discovery and determined to erect a church at the site. Individual gates are designated as well as a column thought to be the point of reference for Roman surveyors and road builders. The walls of the city are pierced by six gates, the number of gates in the wall until the New Gate was opened in the Christian Quarter in the 1890a€™s. The city is also shown narrowing from west to east but this may have been because the background mountains restricted the artist. The project required at least three mosaicists as well as a specialist in biblical topography. In addition to the close textual relationship, the mosaic is divided by the territories of the Twelve Tribes of Israel, a distinguishing feature of Eusebiusa€™ map. From the artistic point of view, the Map must be viewed in the context of a return to the classical style prevailing in the Justinian epoch (half way through the sixth century), of which the mosaics of Madaba and its surrounding region have given us many a dated witness. If you get a false statement, then you can be sure that your triangle is not a right triangle. You get the same answer no matter which method you use, so be sure to add this method to your arsenal!

Juvenal contended for, and won, the title of Patriarch of Antioch in the decisive meeting at Chalcedon (A.D. The floor is made up of North African mosaics, which closely resemble other mosaics found in another ruined church in the old town of Madaba. The artist chose from a wide selection of cubes: eight different colors were used, as well as ten additional shades of red and blue.

Finally, a column is shown in Jerusalem that was the point of reference for local surveyors, and two mileposts are identified just outside the city. In the Jordan Plain there are palm trees, and adjacent to each item are written explanations. Check out this tutorial and learn how use the Pythagorean theorem to see if a triangle is a right triangle!

It features Virtual Multi-Line Operation which allows you to pair up to two cellular lines and one landline with your cordless system.

The artist lavished on this work the resources of an unusually varied palette: four shades of red, five to six of green-blue, dark brown, violet, black, white, yellow and grey.

Madaba and Caesarea, where Euscbius had been bishop over a century earlier, were both under the jurisdiction of the Patriarchate of Jerusalem.

The map measured 190 square meters and the number of mosaic cubes used in a square decimeter numbered up to 150 in the most elaborate parts.

More importantly, most of the inscriptions and place names are identical with the unique surviving Greek manuscript of Eusebiusa€™ text. Next to the names of some of the cities, are the names of important events that occurred later in the area. It is believed that the total number of cubes approached over two million for the whole floor.

An accomplished mosaic artist can lay up to 150-200 cubes per hour, so the Madaba map mosaic demanded approximately 1,000 working days of twelve hours each day. Taking into consideration that the preparation of the cubes also took time, one can get an idea of the immense amount of work involved.

It is reasonable to assume that the creator was of Eastern origin, familiar with the language and the layout of the land. He may have been a monk and the map may have been intended to offer devout pilgrims a view of the city of Jerusalem as witness of a great past.

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