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first feature movie was the Australian movie The Story of the Kelly Gang of 1906. In 1933, In the Wake of the Bounty, directed by Charles Chauvel, had Errol Flynn as the main actor. Flynn went on to a celebrated career in Hollywood. The first Australian Oscar was won by 1942's Kokoda Front Line!, directed by Ken G. Ha... | 200 |
with movies like Picnic at Hanging Rock, Gallipoli (with Mel Gibson), The Man From Snowy River and Crocodile Dundee. Russell Crowe, Cate Blanchett and Heath Ledger became global stars during the 1990s and Australia starring Nicole Kidman and Hugh Jackman made a lot of money in 2008.\n\nAustralia is also a popular desti... | 201 |
destinations in the world.\n\nSport \n\nSport is an important part of Australian culture because the climate is good for outdoor activities. 23.5% Australians over the age of 15 regularly take part in organised sporting activities. In international sports, Australia has very strong teams in cricket, hockey, netball, ru... | 202 |
sports include Australian Rules Football, horse racing, soccer and motor racing. Australia has participated in every summer Olympic Games since 1896, and every Commonwealth Games. Australia has hosted the 1956 and 2000 Summer Olympics, and has ranked in the top five medal-winners since 2000. Australia has also hosted t... | 203 |
Other major international events held regularly in Australia include the Australian Open, one of the four Grand Slam tennis tournaments, annual international cricket matches and the Formula One Australian Grand Prix. Corporate and government sponsorship of many sports and elite athletes is common in Australia. Televise... | 204 |
Games and the grand finals of local and international football competitions.\n\nThe main sporting leagues for males are the Australian Football League, National Rugby League, A-League and NBL.\nFor women, they are ANZ Netball Championships, W-League and WNBL.\n\nFamous Australian sports players include the cricketer Si... | 205 |
60 years ago, Australia had only one big art festival. Now Australia has hundreds of smaller community-based festivals, and national and regional festivals that focus on specific art forms.\n\nWildlife \nAustralia is home to many animals that can be found nowhere else on Earth, which include: the koalas, the kangaroos,... | 206 |
are found only on the continent or on the neighbouring island of New Guinea. Wildfires from global warming in 2020 have decreased their population.\n\nReferences\nNotes\n\nReferences\n\nOther websites \n\n Official website for australia travel Official website for Australia travel.\n Australia travel informations User... | 207 |
"American English or US English is the dialect of the English language spoken in the United States of America. It is different in some ways from other types of English, such as British English. Most types of American English came from local dialects in England.\n\nUse \nMany people today know about American English ev... | 208 |
people hear and read American English through the media, for example movies, television, and the Internet, where the most common form of English is American English.\n\nBecause people all over the world use the English language, it gets many new words. English has been changing in this way for hundreds of years. For e... | 209 |
words to go along with its British English base and many other words from the various Indian languages.\n\nSometimes people learn American English as it is spoken in the US. For example, in telephone call centers in India and other places, people often learn American English to sound more like their customers who call ... | 210 |
are many words that sound the same in both American and British English but have different spellings. British English often keeps more traditional ways of spelling words than American English.\n\nVocabulary \nThere are also some words in American English that are a bit different from British English, e.g.:\n aeroplane ... | 211 |
toilet is called \"bathroom\", \"restroom\" or \"comfort station\"\n lorry is called \"truck\"\n nappies are called \"diapers\"\n petrol is called \"gas\" (or \"gasoline\")\n the boot of a car is called a \"trunk\"\n a dummy is called a \"pacifier\"\n trousers are called \"pants\"\n underground is called \"subway\"\n f... | 212 |
are a type of clothing worn around the lower leg by males to stop socks/sox from sagging, and around the upper leg by women wearing stockings)\n\nRegional accents \nGeneral American English is the kind most spoken in mass media. It more vigorously pronounces the letter \"R\" than some other kinds do. \"R-dropping\" is ... | 213 |
as in the words \"car\" and \"card\" sounding like \"cah\" and \"cahd\". This occurs in the Boston area.\n\nReferences" | 214 |
"Aquaculture is the farming of fish, shrimp, abalones, algae, and other seafood. Aquaculture supplies fish, such as catfish, salmon, and trout. It was developed a few thousand years ago in China. Aquaculture supplies over 20% of all the seafood harvested. \n\nFish farming has been practiced, in some parts of the wor... | 215 |
China, and the Roman Empire farmed oysters and other seafood. Today, half of the seafood eaten in the U.S. is farmed. To help meet the growing global demand for seafood, aquaculture is growing fast.\n\nThe environmental impact of fish farming varies widely, depending on the species being farmed, the methods used and ... | 216 |
way that has very little impact to the environment. Such operations limit habitat damage, disease, escapes of farmed fish and the use of wild fish as feed.\n\nReferences \n\nAquaculture" | 217 |
"An abbreviation is a shorter way to write a word or phrase. People use abbreviations for words that they write a lot. The English language occasionally uses the apostrophe mark ' to show that a word is written in a shorter way, but some abbreviations do not use this mark. More often, they use periods, especially the o... | 218 |
is, e.g. [exempli gratia] for example, and et al. [et alia] and others.\n\nSome new abbreviations have been created by scientists, by workers in companies and governments, and by people using the Internet.\n\nPeople often think words are abbreviations when in fact they are acronyms.\n\nHere are examples of common acron... | 219 |
computer company IBM comes from the words \"International Business Machines\". The name of the part of the United States government that sends rockets into outer space is NASA, from the words \"National Aeronautics and Space Administration\". When people using the Internet think that something is very funny, they somet... | 220 |
Soon As Possible\".\n\nOther websites \n Acronym Finder - largest acronym site with many ways to search for acronyms and abbreviations in many languages. Over 10-year history.\n All Acronyms - a website with a large number of abbreviations and acronyms\n Acronyms Abbreviations and Slang - over 3 million different acro... | 221 |
"In many mythologies and religions, an angel is a good spirit. The word angel comes from the Greek word angelos which means \"messenger\". Angels appear frequently in the Old Testament, the New Testament, Qur'an and Aqdas.\n\nDifferent references to angels throughout the Bible suggest different kinds and ranks of ange... | 222 |
of such divine messengers, including not only cherubs or cherubim (the Hebrew plural) and seraphim, but also archangels, powers, principalities, dominions and thrones. \n\nThe study of Angels is called Angelology.\n\nIn the Bible \nAngels are powerful, smart spirits that obey God's commands, praise him with singing, an... | 223 |
in a human form. They can deliver messages to people in person or in dreams. Angels that are named in the Bible are Michael (called a \"chief prince\"), Gabriel (known for telling Mary that she would be the mother of Jesus), and Raphael (in the Apocryphal Book of Tobit). The Ethiopian Book of Enoch also lists four Arc... | 224 |
Lucifer is also known as an angel in the Bible.\n\nTypes\nCherubim (plural of cherub) are described as \"winged creatures\" which have four wings Cherubim guard the Eden with a sword of fire. This suggests that the author of Genesis was aware of different types of angels. Genesis 3:24 is found in the Book of Ezekiel. A... | 225 |
28:13-14\n13. Thou hast been in Eden the garden of God; every precious stone was thy covering, the sardius, topaz, and the diamond, the beryl, the onyx, and the jasper, the sapphire, the emerald, and the carbuncle and gold: the workmanship of thy tabrets and of thy pipes was prepared in thee in the day that thou wast c... | 226 |
thou wast upon the holy mountain of God; thou hast walked up and down in the midst of the stones of fire.\n\nIt describes the sound of their wings, \"like the roar of rushing waters.\"\n\nEzekiel 10:5-7 ; Ezekiel 10:8 reveals that they have hands like a man under their wings .\n\nEzekiel 1:7 KJV reveals that they look ... | 227 |
ch 1, and 10 describe the cherubim creatures ascending and descending from the earth with wheels. Ezekiel 1:14-20 ; Ezekiel 10:16\n\nEzekiel 10:9-13 describes what the wheels appeared to look like, and how they moved around, how they moved or flew through the sky quickly but turned not as they went; and how the inside ... | 228 |
of the wheels was the color of \"Amber\" Stone. There are four separate wheels in both accounts, one for each single cherub which is there.\n\nSeraphim (plural of seraph, which means \"burning\")they also are depicted having wings, six of them. They are known for singing and praising God. They can shout so loud, they s... | 229 |
angel. They are considered saints in the Catholic church. However, in the King James Version of the Bible; they are another type of angel. In the Book of Revelation the Angel Michael casts the 'great dragon' Satan out of heaven and down to earth in a great battle between the good and bad angels, just before the Great J... | 230 |
that goes: 'out of his mouth' like a dragon. Isaiah 30:6 also talks of a 'fiery flying serpent'. Compare Revelation 20:2: , where an angel: 'laid hold on the dragon, that old serpent, which is the Devil, and Satan, and bound him a thousand years'.\n\nIn art\nThey are often shown in art as having wings and a halo. The... | 231 |
art always appear as baby faced angels with very small, non-useful wings.\n\nThe cherubim statue or bronze casting of cherubim in the Temple of Solomon depicted them as two four winged creatures whose wings touched at the peak of the ark that they were making.\n\nThe same cherubim creatures were said to be cast in gold... | 232 |
and was attempted by Leonardo da Vinci.\n\nIn literature \nAngels are generally held to be holy and virtuous, hence the term is used loosely to apply to anyone particularly good or kind, or having a good influence. In his novel Far From the Madding Crowd, Thomas Hardy chooses the name of an angel, Gabriel, for his kind... | 233 |
of the name Angelo is ironic, since Angelo is a character who likes to see himself as virtuous, but who is concealing evil aspects of his nature. Fallen angels, who are no longer holy or virtuous, are also known as devils.\n\nHowever, since angels are held to be spirits (that is, non-material beings), medieval theologi... | 234 |
a theory was put forward that angels must make themselves a body out of the nearest thing to the non-physical, i.e. from air. Hence in his famous poem Aire and Angels, the seventeenth century metaphysical poet John Donne uses this idea to write a cynical comment on women, whose love, he says, is like an angel's body of... | 235 |
\nFrom the era of the Romantics onwards, there has developed the widely held belief that everyone has an angel assigned to guard them. This concept is probably based on Jesus' comment in Matthew 18:10 regarding children, though it is not mentioned elsewhere in the Bible.\n\nIn superstitions\nSeeing repetitive numbers a... | 236 |
that angels communicate with humans through repetitive appearances of numbers. Humanity has studied and used numbers since the dawn of time, and no matter what the culture is, there are certain numbers that hold specific value or meaning over other numbers.\n\nReferences\n\nOther websites" | 237 |
"Ad hominem is a Latin word for a type of argument. It is a word often used in rhetoric. Rhetoric is the science of speaking well, and convincing other people of your ideas.\n\nTranslated to English, ad hominem means against the person. In other words, when someone makes an ad hominem, they are attacking the person the... | 238 |
homo, which means human. Hominem is a gender neutral version of the word homo. In ancient Rome it referred to all free men, or in other words, all free human beings.\n\nAd hominem can be a way to use reputation, rumors and hearsay to change the minds of other people listening. When a social network has already excluded... | 239 |
is most of the time considered to be a weak and poor argument. In courts and in diplomacy ad hominems are not appreciated.\n\nAd hominems are not wrong every time. For example, when people think that someone can't be trusted, things that they have said previously can be doubted.\n\nWhat an ad hominem argument looks lik... | 240 |
arguments, to reach a conclusion.\n\nNormal (valid) proof \n All humans are mortal.\n Socrates is human.\n Therefore, Socrates is mortal.\n\nAd hominem example \n Person A thinks abortion should be illegal.\n Person A is uneducated and poor.\n Therefore, abortion should not be illegal.\n\nIn this example it can be seen... | 241 |
prove that abortion should not be illegal.\n\nRelated pages\n Fallacy for a list of other types of (false) rhetorical arguments.\n\nLatin words used in English" | 242 |
"Native Americans (also called Aboriginal Americans, American Indians, Amerindians or indigenous peoples of the Americas) are the people and their descendants, who were in the Americas when Europeans arrived.\n\nSometimes these people are called Indians, but this may be confusing, because it is the same word used for p... | 243 |
Americas. He was in the Caribbean but thought he was in the East Indies, so he called the people Indians.\n\nThere are many different tribes of Native American people, with many different languages. Some tribes were hunter-gatherers who moved from place to place. Others lived in one place and built cities and kingdoms.... | 244 |
that came with the Europeans but were new to the Native Americans. There were battles with the Europeans. Many native people were hurt, killed, or forced to leave their homes by settlers who took their lands.\n\nToday, there are more than three million Native Americans in Canada and the U.S. combined. About 51 million ... | 245 |
and have their own cultural practices, while others have adopted some parts of Western culture. Many Native Americans face problems with discrimination and racism.\n\nOrigins \nThe ancestors of Native Americans came to the Americas from Asia. Some of them may have come to America 15,000 years ago when Alaska was connec... | 246 |
Siberia when there was an ice bridge across the Bering Strait. The cold but mainly grassy plain which connected Siberia with Canada is called Beringia. It is reckoned that a few thousand people arrived in Beringia from eastern Siberia during the Last Glacial Maximum before moving into the Americas sometime after 16,5... | 247 |
blocking the way southward melted, but before the bridge was covered by the sea about 11,000 years BP.\n\nBefore European colonization, Beringia was inhabited by the Yupik peoples on both sides of the straits. This culture remains in the region today, with others. In 2012, the governments of Russia and the United State... | 248 |
Among other things this agreement would establish close ties between the Bering Land Bridge National Preserve and the Cape Krusenstern National Monument in the United States and Beringia National Park in Russia.\n\nNative Americans are divided into many small nations, called First Nations in Canada and tribes elsewhere... | 249 |
be grouped together depending on region. For example, the tribes living in Mesoamerica have similar cultures.\n\nFood \nNative Americans ate many different things depending on where they lived.\n\nNative Americans from Mesoamerica introduced vanilla, avocados, and chocolate to the world.\n\nReligion \nBefore Europeans ... | 250 |
had their own different beliefs.\n\nToday, many Native Americans practice Christianity, a religion that was brought to the Americas by Europeans. Meanwhile, others still practice their own religions.\n\nLanguages \nNative Americans today speak over a thousand different languages. Some of these languages had writing sys... | 251 |
are speaking European languages and not teaching Native American languages to their kids.\n\nMusic \nNative Americans make musical instruments using the things around them.\n\nArt \nNative Americans make a lot of different art.\n\nToday\n\nNorth America\n\nUnited States\nAccording to the 2010 United States census, 0.9%... | 252 |
are both Native American and something else. They are not evenly spread out through the United States. About a third of the people in Alaska are Native Alaskan and about a sixth of the people in Oklahoma are Native American.\n\nIn the United States, most Native Americans live in cities. About 28% of Native Americans... | 253 |
of violence against Native Americans persists today in higher rates of violence against Native American people than white people.\n\nMexico\nMost Mexicans are of Native American ancestry.\n\nCanada\nCanada has a higher Native American population than the United States.\n\nCentral America\n\nGuatemala \nAbout 40% of the... | 254 |
descendants of the Maya.\n\nMany Native Americans in Guatemala are poor. Many of them have left the country to find better jobs elsewhere.\n\nSouth America\n\nBolivia \nThe majority of Bolivians belong to indigenous groups.\n\nPeru \nPeru has a large indigenous population, around 80% of Peru's population identify as in... | 255 |
Native Americans started to protest the unfair treatment they experienced from the societies they lived in.\n\nSome Native Americans have become famous in politics. For example, an Aymara man named Evo Morales was elected as president of Bolivia in 2005. He was the first indigenous presidential candidate in Bolivia and... | 256 |
"Apple is the edible fruit of a number of trees, known for this juicy, green or red fruits. The tree (Malus spp.) is grown worldwide. Its fruit is low-cost and popular, and is harvested all over the world. \n\nApplewood is a type of wood that comes from this tree.\n\nThe apple tree comes from southern Kazakhstan, Kyrgy... | 257 |
of years in Asia and Europe. They were brought to North America by European settlers. Apples have religious and mythological significance in many cultures.\n\nApples are generally propagated by grafting, although wild apples grow readily from seed. Apple trees are large if grown from seed, but small if grafted onto roo... | 258 |
characteristics. Different cultivars are bred for various tastes and uses: cooking, eating raw and cider production are the most common uses. \n\nTrees and fruit are attacked by fungi, bacteria and pests. In 2010, the fruit's genome was sequenced as part of research on disease control and selective breeding in apple pr... | 259 |
of the total.\n\nBotanical information \nThe apple has a small, leaf-shedding tree that grows up to tall. The apple tree has a broad crown with thick twigs.\nThe leaves are alternately arranged simple ovals. They are 5 to 12 centimetres long and 3\u20136 centimetres (1.2\u20132.4 in) wide. It has a sharp top with a so... | 260 |
The flowers are white. They also have a slightly pink color. They are five petaled, and 2.5 to 3.5 centimetres (0.98 to 1.4 in) in diameter. The fruit matures in autumn. It is usually 5 to 9 centimetres (2.0 to 3.5 in) in diameter. There are five carpels arranged in a star in the middle of the fruit. Every carpel has o... | 261 |
They grow wild in the mountains of Central Asia in the north of Kazakhstan, Kyrgyzstan, Tajikistan, and Xinjiang, China, and possibly also Malus sylvestris. Unlike domesticated apples, their leaves become red in autumn. They are being used recently to develop Malus domestica to grow in colder climates.\n\nHistory\n\nTh... | 262 |
over thousands of years. It is said that Alexander the Great discovered dwarf apples in Asia Minor in 300 BC. Asia and Europe have used winter apples as an important food for thousands of years. From when Europeans arrived, Argentina and the United States have used apples as food as well. Apples were brought to North A... | 263 |
be near Boston in 1625. In the 1900s, costly fruit industries, where the apple was a very important species, began developing.\n\nIn culture\n\nPaganism \n\nIn Norse mythology, the goddess I\u00f0unn gives apples to the gods in Prose Edda (written in the 13th century by Snorri Sturluson) that makes them young forever. ... | 264 |
in Germanic paganism. It was from there, she claims, that Norse paganism developed. She points out that buckets of apples were discovered in the place of burial for the Oseberg ship in Norway. She also remarks that fruit and nuts (I\u00f0unn having been described as changing into a nut in Sk\u00e1ldskaparm\u00e1l) have... | 265 |
been discovered somewhere else on the continent of Europe. She suggests that this may have had a symbolic meaning. Nuts are still a symbol of fertility in Southwest England.\n\nCooking \nSometimes apples are eaten after they are cooked. Often apples are eaten uncooked. Apples can also be made into drinks. Apple juice a... | 266 |
from sour to sweet. Apples used for cooking are sour, and need to be cooked with sugar, while other apples are sweet, and do not need cooking. There are some seeds at the core, that can be removed with a tool that removes the core, or by carefully using a knife.\n\nThe scientific name of the apple tree genus in the Lat... | 267 |
apples are good to eat raw (not cooked), and are also used in many kinds of baked foods, such as apple pie. Apples are cooked until they are soft to make apple sauce.\n\nApples are also made into the drinks apple juice and cider. Usually, cider contains a little alcohol, about as much as beer. The regions of Brittany i... | 268 |
one wants to grow a certain type of apple it is not possible to do this by planting a seed from the wanted type. The seed will have DNA from the apple that the seeds came from, but it will also have DNA from the apple flower that pollinated the seeds, which may well be a different type. This means that the tree which ... | 269 |
a small twig, or 'scion', is cut from the tree that grows the type of apple desired, and then added on to a specially grown stump called a rootstock. The tree that grows will only create apples of the type needed.\n\nThere are more than 7,500 known cultivars (varieties) of apples. Different cultivars are available for ... | 270 |
is at the National Fruit Collection in England. Most of these cultivars are grown for eating fresh (dessert apples). However, some are grown simply for cooking or making cider. Cider apples are usually too tart to eat immediately. However, they give cider a rich flavor that dessert apples cannot.\n\nMost popular apple ... | 271 |
apple shape, and popular flavor are also needed. Modern apples are usually sweeter than older cultivars. This is because popular tastes in apples have become different. Most North Americans and Europeans enjoy sweet apples. Extremely sweet apples with hardly any acid taste are popular in Asia and India.\n\nIn the Unite... | 272 |
The most common apple type grown in England is the 'Bramley seedling', which is a popular cooking apple.\n\nApple orchards are not as common as they were in the early 1900s, when apples were rarely brought in from other countries. Organizations such as Common Ground teach people about the importance of rare and local v... | 273 |
of the United States and Canada. In many areas where apple growing is important, people have huge celebrations:\n\n Annapolis Valley Apple Blossom Festival - held five days every spring (May-June) in Nova Scotia\n Shenandoah Apple Blossom Festival - held six days every spring in Winchester, Virginia.\n Washington State... | 274 |
of apples \n\nThere are many different varieties of apples, including:\n\n Aport\n Cox's Orange Pippin\n Fuji (apple)\n Gala\n Golden Delicious (sometimes called a Green Delicious Apple)\n Granny Smith\n Jonathan\n Jonagold\n McIntosh\n Pink Lady\n Red Delicious\n Winesap\n\nFamily \nApples are in the group Maloideae. ... | 275 |
reading \n Potter D. et al 2007. Phylogeny and classification of Rosaceae. Plant Systematics and Evolution. 266 (1\u20132): 5\u201343.\n\nOther websites \n\n \n \n \n\nBasic English 850 words\n \nRosaceae" | 276 |
"An Abrahamic Religion is a religion whose followers believe in the prophet Abraham. They believe Abraham and his sons/grandsons hold an important role in human spiritual development. The best known Abrahamic religions are Judaism, Christianity and Islam. Smaller religious traditions sometimes included as Abrahamic rel... | 277 |
(a religion that holds many Abrahamic beliefs) is not called Abrahamic because its followers think Abraham was a false prophet\n\nTrue Abrahamic religions are monotheistic (the belief that there is only one God). They also all believe that people should pray to God and worship God often. Among monotheistic religions, t... | 278 |
"Algebra (from Arabic: \u0627\u0644\u062c\u0628\u0631\u200e, transliterated \"al-jabr\", meaning \"reunion of broken parts\") is a part of mathematics. It uses variables to represent a value that is not yet known. When an equals sign (=) is used, this is called an equation. A very simple equation using a variable is: .... | 279 |
for .\n\nBesides equations, there are inequalities (less than and greater than). A special type of equation is called the function. This is often used in making graphs because it always turns one input into one output.\n\nAlgebra can be used to solve real problems because the rules of algebra work in real life and numb... | 280 |
programming are areas that use algebra all the time. It is also useful to know in surveying, construction and business, especially accounting.\n\nPeople who do algebra use the rules of numbers and mathematical operations used on numbers. The simplest are adding, subtracting, multiplying, and dividing. More advanced ope... | 281 |
used to solve equations and inequalities. Two examples are linear equations (the equation of a straight line, or ) and quadratic equations, which has variables that are squared (multiplied by itself, for example: , , or ).\n\nHistory \nEarly forms of algebra were developed by the Babylonians and the Greek geometers su... | 282 |
Al-Jabr (\"casting\") and comes from a mathematics book Al-Maqala fi Hisab-al Jabr wa-al-Muqabilah, (\"Essay on the Computation of Casting and Equation\") written in the 9th century by a Persian mathematician, Muhammad ibn M\u016bs\u0101 al-Khw\u0101rizm\u012b, who was a Muslim born in Khwarizm in Uzbekistan. He flouri... | 283 |
was brought into Europe and translated into Latin in the 12th century. The book was then given the name 'Algebra'. (The ending of the mathematician's name, al-Khwarizmi, was changed into a word easier to say in Latin, and became the English word algorithm).\n\nExamples\n\nHere is a simple example of an algebra problem:... | 284 |
the same number of candies. How many candies will each have?\n\nThese are the steps you can use to solve the problem:\n\n To have the same number of candies, Ann has to give some to Sue. Let represent the number of candies Ann gives to Sue. \n Sue's candies, plus , must be the same as Ann's candies minus . This is wr... | 285 |
side of the equal sign must happen on the other side too, for the equation to still be true. So in this case when 12 was subtracted from both sides, there was a middle step of . After a person is comfortable with this, the middle step is not written down.)\n Add to both sides of the equation. This gives: \n Divide bot... | 286 |
Sue 6 candies, they will have the same number of candies.\n To check this, put 6 back into the original equation wherever was: \n This gives , which is true. They each now have 18 candies.\n\nWith practice, algebra can be used when faced with a problem that is too hard to solve any other way. Problems such as building... | 287 |
algebra \nAs in most parts of mathematics, adding to (or plus ) is written as ;\n\nsubtracting from (or minus ) is written as ;\n\nand dividing by (or over ) is written as or .\n\nIn algebra, multiplying by (or times ) can be written in 3 different ways: , or just . All of these notations mean the same t... | 288 |
too much like the letter , which is often used as a variable.\n\nWhen we multiply a number and a variable in algebra, we can simply write the number in front of the letter: . When the number is 1, then it is not written because 1 times any number is that number () and so it is not needed. And when it is 0, we can compl... | 289 |
have to use the letters or in algebra. Variables are just symbols that mean some unknown number or value, so you can use any letter for a variable (except (Euler's number) and (Imaginary unit), because these are mathematical constants). and are the most common, though.\n\nFunctions and Graphs \n\nAn important par... | 290 |
to solve. A function is like a machine you can put a number (or numbers) into and get a certain number (or numbers) out. When using functions, graphs can be powerful tools in helping us to study the solutions to equations. \n\nA graph is a picture that shows all the values of the variables that make the equation or ine... | 291 |
is often a line, and if the line does not bend or go straight up-and-down it can be described by the basic formula . The variable is the y-intercept of the graph (where the line crosses the vertical axis) and is the slope or steepness of the line. This formula applies to the coordinates of a graph, where each point o... | 292 |
can be more than one variable ( and in this case). To find points on the line, one variable is changed. The variable that is changed is called the \"independent\" variable. Then the math is done to make a number. The number that is made is called the \"dependent\" variable. Most of the time the independent variable is... | 293 |
on a graph, using an axis (going left and right) and a axis (going up and down). It can also be written in function form: . So in this example, we could put in 5 for and get . Put in 2 for would get . And 0 for would get . So there would be a line going through the points (5,16), (2,7), and (0,1) as seen in the gr... | 294 |
other power, it will be curved. If it uses an inequality ( or ), then usually part of the graph is shaded, either above or below the line.\n\nRules \nIn algebra, there are a few rules that can be used for further understanding of equations. These are called the rules of algebra. While these rules may seem senseless or ... | 295 |
of mathematics. Therefore, it will be useful to know how these axiomatic rules are declared, before taking them for granted. Before going on to the rules, reflect on two definitions that will be given.\n Opposite: the opposite of is .\n Reciprocal: the reciprocal of is .\n\nCommutative property of addition \n'Commuta... | 296 |
words, the order of the terms in an equation does not matter. When two terms (addends) are being added, the 'commutative property of addition' is applicable. In algebraic terms, this gives .\n\nNote that this does not apply for subtraction (i.e. except if ).\n\nCommutative property of multiplication \nWhen two terms (... | 297 |
In algebraic terms, this gives .\n\nNote that this does not apply for division (i.e. , when and , except if ).\n\nAssociative property of addition \n'Associative' refers to the grouping of numbers. The associative property of addition implies that, when adding three or more terms, it doesn't matter how these terms are... | 298 |
distributive property).\n\nAssociative property of multiplication \nThe associative property of multiplication implies that, when multiplying three or more terms, it doesn't matter how these terms are grouped. Algebraically, this gives . Note that this does not hold for division, e.g. .\n\nDistributive property \nThe d... | 299 |
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