Math Exam Notes free essay sample

Check your solution by substituting into both original equations, or into the statements of a word problem -When given a question in words, begin by defining how variables are assigned Investigate Equivalent Linear Relations and Equivalent Linear Systems -Equivalent linear equations: equations that have the same graph -Equivalent linear systems: pairs of linear equations that have the same point of intersection -For any linear equation, an equivalent linear equation can be written by multiplying the equation by any real -Equivalent linear systems have the same solution; the graphs of linear relations in the system have the same point of intersection -Equivalent linear systems can be written by writing equivalent linear equations for either or both of the equations, or by adding or subtracting the original equations The Method of Elimination -Solving a linear system by adding or subtracting to eliminate one of the variables -To solve a linear system by elimination: -Arrange the two eq uations so that like terms are aligned -Choose the variable you wish to eliminate -If necessary. We will write a custom essay sample on Math Exam Notes or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Multiply one or both equations by a value so that they have the same or opposite coefficient in front of the variable you want to eliminate -Add or subtract to eliminate one variable -Solve for the remaining variable -Substitute into one of the original equations to find the value of the other variable Solving Problems Using Linear System -You can solve linear systems using any of the three methods: graphing, substitution, or elimination **Solve problems with Distance, Speed, Time** -Downstream d = (p+c)t -Upstream d = (p-c)t **Solve a mixture problem** -Solution: x + y = amount of mixture -Pure acid: %x + %y = %mixture Unit 2 Midpoint of a Line Segment -Midpoint: a point that divides a line segment into two equal line segments (x1+x2 ? 2 = x) (y1+y2 ? = y) -Median: line segment joining a vertex of a triangle to the midpoint of the opposite side -To find an equation for the median of a triangle, first find the coordinates of the midpoint of the side opposite to the vertex. Use the co ordinates of the midpoint and the vertex to calculate the slope of the median. Then, substitute the slope and the coordinates of either point into y = mx + b to solve for the medians y-intercept -Equidistant: equally distant -Right bisector: the line that passes through the midpoint of a line segment and intersects it at a 90Â ° angle -To find an equation for the right bisector of a line segment, first find the slope and midpoint of the segment. Use the line segment’s slope to calculate the slope of a perpendicular line. Then, substitute this slope and the coordinates of the midpoint into y = mx + b to solve for the right bisector’s y-intercept Length of A Line Segment -You can calculate the length, d, of a line segment using its rise and run: d = v(run)2 + (rise)2 or d = v(x2-x1)2 + (y2-y1)2 Equation for a Circle -An equation for the circle with centre at the origin and radius r is x2 + y2 = r2 -The radius of a circle centered at the origin is r = v x2 + y2 Unit 3 Investigate Properties of Triangles -The medians of a triangle meet at a single pint: centroid -Each median bisects the area of the triangle -The median from the vertex, between the equal sides of an isosceles triangle coincide with the altitude to the vertex and bisects the angle at the vertex Verify Properties of Triangles The centroid of a triangle divides each median into two parts, with one part twice the length of the other -The line segment joining the midpoints of two sides of a triangle is parallel to the third side and is half its length Investigate Properties of Quadrilaterals -The diagonals of a parallelogram bisect each other -Joining the midpoints of adjacent sides of any quadrilateral forms a parallelogram -The line segment joining the midpoints of the non-parallel sides of a trapezoid is parallel to the parallel sides and has a length equal to the mean of the lengths of the parallel sides Properties of Circles -Chord: line segment joining two points on a curve The diameters of a circle intersect at the centre of the circle

Capitalization Rules for Names of Historical Periods and Movements

Capitalization Rules for Names of Historical Periods and Movements Capitalization Rules for Names of Historical Periods and Movements Capitalization Rules for Names of Historical Periods and Movements By Mark Nichol When are designations for historically significant phenomena treated with initial capital letters, and when are the names rendered with lowercase letters? Exceptions, as always, are available to confound us, but the rules are fairly straightforward. Names of political and cultural periods or events are often capitalized in their original connotations, but when such nomenclature is used by extension in a generic sense, the designations are (usually) lowercased. For example, one should write, for example, â€Å"The arts and sciences flourished during the Renaissance,† but â€Å"The downtown district is experiencing a renaissance.† (However, to describe someone as well rounded in skills or talents, write â€Å"He’s a Renaissance man† even when he is not a contemporary of Michelangelo.) The same distinction applies for such terms as â€Å"golden age† (â€Å"The Golden Age was the first of Hesiod’s Ages of Man,† but â€Å"Jazz music has experienced several golden ages†) and â€Å"belle à ©poque† (â€Å"The period of peace and optimism in France in the nearly half century before World War I came to be known retrospectively as the Belle Époque,† but â€Å"They look back on that prosperous period as a belle à ©poque†). Similarly, one would write â€Å"China’s infamous Cultural Revolution was a decade-long time of great turmoil,† but â€Å"American society has undergone a cultural revolution of late,† and while references to the mid-twentieth-century tension between Western nations and the Communist Bloc capitalize â€Å"Cold War,† any such conflict without open hostilities is a cold war. The Enlightenment was a specific cultural movement in Europe and Britain’s American colonies during the 1600s and 1700s, or a similar era in any one of several countries. Generic usage is as follows: â€Å"In the Western world, the concept of enlightenment in a religious context acquired a romantic meaning.† However, in specific usage, enlightenment is capitalized: â€Å"The Russian Enlightenment is a period in the eighteenth century in which the government in Russia began to actively encourage the proliferation of arts and sciences.† Adjectives preceding names of political entities are often erroneously capitalized. No civilization has ever gone by the official name of Ancient Greece or Imperial Rome, for example; the first word in such designations is generally a mere descriptor and is therefore lowercased: â€Å"The course is a general overview of the history of ancient Greece†; â€Å"This essay will discuss the economic structure of imperial Rome.† Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Style category, check our popular posts, or choose a related post below:How to Punctuate References to Dates and TimesFor Sale vs. On SaleCharles's Pen and Jesus' Name

Business organisation and policy cartels and monopolies Essay

Business organisation and policy cartels and monopolies - Essay Example On the other hand, buying cartels aim at purchasing raw materials for its members while the output determining cartels determine the quantity of output for each member unit as the name suggests (Sangla 2009, p.181). Without government intervention, an isolated monopolistic firm would only exist in an ideal world. This is because most monopolistic firms make a lot of profits thus encouraging the formation of rival firms. In the long run, the new firms break the monopoly. Most governments in the 1920s embraced mergers and trade unions in key economical sectors such as chemical and metal industries (McTavish 2005, p.52). However, most of the business organizations preferred cartels to the other forms of trade convergence. After the World War II, the business field developed thorough monopolies and restrictive practices, which had salient effects on business organizations (McTavish 2005, p.52). Currently, it is only America in the whole world, which has not legalized cartel formation. One of the most popular cartels today is the organization of petroleum-exporting countries (OPEC). OPEC was established mainly to control the amount of oil each member produced. Member units that form cartels always enjoy a wide variety of benefits. Each member usually has a guarantee to earn fixed minimum profit which is not the case with other business institutions. In addition, all marketing and other secondary functions of the individual business organizations such as transportation, advertisement and marketing research are normally carried out by the cartels (Sangla 2009, p.181). In addition, the member firms also enjoy price control. Since, in working as a pool, the individual firms acquire monopolistic characteristics, they are in a position to charge the prices of their products at their own will. Conversely, the cartels and monopolistic