Free Essays on Dr. Bloodstein About Stuttering

Computers Since the beginning of human life, we as a people have always strived to obtain machines or tools to make our lives easier. Before the computer was invented in 1822, people were performing boring, repetitive tasks that we now take for granted. The computer, a modern complex machine, now accomplishes things we never thought possible. Computers, in general, have many benefits for they provide entertainment, help modern cities function, above all, make the most aggravating and mundane tasks incredibly simple. One of the least important aspects of computers is that it provides entertainment and yet this is the sole reason why many people buy computers. The gaming and entertainment industry has become extremely large in the world, the products they sell range from shareware games to adult blood and gore. For instance, the 3D-shooter series, Quake, has sold millions of copies and essentially everyone in the world has seen it or played it. The entertainment industry not only provides gaming amusement but it also contributes learning programs, for children and adults, to help individuals excel in a certain trouble areas. Furthermore, computers also are also capable of training military personal in a virtual reality environment. An example of this is the U.S. and Canadian military, they both train soldiers and pilots in the ways of war using high tech computers and virtual reality equipment. To sum up, entertainment on the computer may not be important but is does satisfy million of people wor ldwide. Cities as we know them today would not exist if it were not for the help of the computer. In a modern city hundreds of items are under control by computers and most of them we take for granted. For example, the traffic lights at all intersections are controlled by computers and sometimes even with the support of underground sensors. Without computers the entire electrical grid would fail and all of the world’s neoteric popul... Free Essays on Dr. Bloodstein About Stuttering Free Essays on Dr. Bloodstein About Stuttering Computers Since the beginning of human life, we as a people have always strived to obtain machines or tools to make our lives easier. Before the computer was invented in 1822, people were performing boring, repetitive tasks that we now take for granted. The computer, a modern complex machine, now accomplishes things we never thought possible. Computers, in general, have many benefits for they provide entertainment, help modern cities function, above all, make the most aggravating and mundane tasks incredibly simple. One of the least important aspects of computers is that it provides entertainment and yet this is the sole reason why many people buy computers. The gaming and entertainment industry has become extremely large in the world, the products they sell range from shareware games to adult blood and gore. For instance, the 3D-shooter series, Quake, has sold millions of copies and essentially everyone in the world has seen it or played it. The entertainment industry not only provides gaming amusement but it also contributes learning programs, for children and adults, to help individuals excel in a certain trouble areas. Furthermore, computers also are also capable of training military personal in a virtual reality environment. An example of this is the U.S. and Canadian military, they both train soldiers and pilots in the ways of war using high tech computers and virtual reality equipment. To sum up, entertainment on the computer may not be important but is does satisfy million of people wor ldwide. Cities as we know them today would not exist if it were not for the help of the computer. In a modern city hundreds of items are under control by computers and most of them we take for granted. For example, the traffic lights at all intersections are controlled by computers and sometimes even with the support of underground sensors. Without computers the entire electrical grid would fail and all of the world’s neoteric popul...

How to Write a 10-Page Term Paper

How to Write a 10-Page Term Paper How to Write a 10-Page Term Paper How to Write a 10-Page Term PaperWhen being assigned to write a 10-page term paper, most students give way to despair for the workload they have to accomplish seems to be incredibly extensive. This is true, it is difficult to write a 10-page term paper well, still, it is possible, and in this article we will tell you how to do it. If you are writing, for example, 15 page term paper or long term paper 10 pages, you need to devote enough time to planning your time. Alternatively, you may simply order custom term paper writing service at our site and get at least 250 words a page term paper written from scratch!The first thing you should keep in mind when getting started to write your 10-page term paper is that an elaborative plan of actions will make your writing process much easier. That is why we strongly recommend you start your work with making a schedule. Find out when your deadline is and calculate the number of days at your disposal. Your writing process will include the fol lowing steps:Choosing a topic;Gathering material;Taking notes and organizing ideas;Writing;Editing.Some useful tips on how to write a 10-page term paper also seem to be right in time for you. So, here they are:How to write a 10-page term paper: Researching materialWhen dealing with sources, use reviews. They usually present additional information, references, and leads. This is a good path for you to understand the primary sources better and analyze them deeper in your paper. Still, you should go beyond this, since a paper based only on secondary sources is regarded as weak. How to write a 10-page term paper: Writing techniques and styleUsually, term papers are required to be written in an academic language. So, no colloquial speech words like slang or jargons are accepted. Imagine yourself to be a fully-fledged researcher. How would you present your research in the paper?How to write a 10-page term paper: Making an introductionWe advise you make only some notes on your introduction and come back to it after you finish to write your 10-page term paper. Usually, this part includes the purposes of research, the writers expectations from it, and the research question he/she is going to answer in the paper.How to write a 10-page term paper: Working out the main bodyThis part consists of several smaller ones where you discuss the works by other researchers devoted to your research question. In data presentation part, tell what approaches to the question exist. In analysis, explain what the data presented might mean, how it can be interpreted.How to write a 10-page term paper: Drawing a conclusionIn this part, tell what you have come up to after completing the research. What conclusions have you withdrawn? If you want to write a 10-page term paper or term paper 15 pages successfully and get a high grade, do your best to meet all the requirements your professor set.

banning the game

banning the game Banning the Game?As enjoyable as football can be there are many downsides of this dangerous sport. Every year new students try out for football, but they don't know what they're getting themselves in to. A game in which you clash together to get a ball somewhere seems like a lot to risk your life for. Not joining your football team in high schools will cause fewer injuries. Using your head as a battering ram is not helping the brain of the student. Before thinking about joining your team, know what the effects after starting to play. Stop and think about your life before joining the football team.From a recent study 67 percent of a football team get concussions every season. If a student is trying to play football, there's the probability that he will be part of the 67 percent. When you ram your helmet into another helmet, you're not safe. The helmet does not help the brains of teens and protecting it, it makes your head shake in between the metal that covers your head. According to a recent study, teens that faced two or more concussions, reported mental problems at higher and faster rates. In addition, if teens step away from this sport you will be less likely to forget everything.Traumatic brain injury can hurt destroy your brain. A recent study was made that showed that football can cause traumatic brain injury. TBI usually shows in people that play in sports in which you are more likely to hit your head. Recent football players ended up having this disease and destroying their brain. The result of all the brain hits is amnesia. Amnesia is when an individual loses their memory, and can't remember anything about their life. Teens who start hitting their brains in to...English: Anisocoria (right eye instiled by tropica...

HIV Uses Trojan Horse Method to Infect Cells

HIV Uses Trojan Horse Method to Infect Cells Like all viruses, HIV is not able to reproduce or express its genes without the help of a living cell. First, the virus must be able to successfully infect a cell. To do so, HIV uses a veil of human proteins in a Trojan horse manner to infect immune cells. To go from cell to cell, HIV is packaged in an envelope or capsid made from viral proteins and proteins from human cell membranes. Like the Ebola virus, HIV relies on proteins from human cell membranes to gain entrance into a cell. In fact, Johns Hopkins scientists have identified 25 human proteins that have been incorporated into the HIV-1 virus and aid its ability to infect other body cells. Once inside a cell, HIV uses the cells ribosomes and other components to make viral proteins and to replicate. When new virus particles are formed, they emerge from the infected cell cloaked in a membrane and proteins from the infected cell. This helps the virus particles avoid immune system detection. What Is HIV? HIV is the virus that causes the disease known as acquired immunodeficiency syndrome, or AIDS. HIV destroys cells of the immune system, making an individual infected with the virus less equipped to fight off infection. According to the Centers for Disease Control (CDC), this virus may be transmitted when infected blood, semen, or vaginal secretions come in contact with an uninfected persons broken skin or mucous membranes. There are two types of HIV, HIV-1, and HIV-2. HIV-1 infections have mostly occurred in the United States and Europe, while HIV-2 infections are more prominent in West Africa. How HIV Destroys Immune Cells While HIV may infect different cells throughout the body, it attacks white blood cells called T cell lymphocytes and macrophages in particular. HIV destroys T cells by triggering a signal that results in T cell death. When HIV replicates within a cell, viral genes get inserted into the genes of the host cell. Once HIV integrates its genes into T cell DNA, an enzyme (DNA-PK) uncharacteristically sets off a sequence that leads to the death of the T cell. The virus thereby destroys the cells that play a major role in the bodys defense against infectious agents. Unlike T cell infection, HIV infection of macrophages is less likely to lead to macrophage cell death. As a result, infected macrophages produce HIV particles for a longer period of time. Since macrophages are found in every organ system, they can transport the virus to various sites in the body. HIV-infected macrophages may also destroy T cells by releasing toxins that cause nearby T cells to undergo apoptosis or programmed cell death. Engineering HIV-Resistant Cells Scientists are attempting to develop new methods for fighting HIV and AIDS. Stanford University School of Medicine researchers has genetically engineered T cells to be resistant to HIV infection. They accomplished this by inserting HIV-resistant genes into the T-cell genome. These genes successfully blocked the entry of the virus into the altered T cells. According to researcher Matthew Porteus, We inactivated one of the receptors that HIV uses to gain entry and added new genes to protect against HIV, so we have multiple layers of protection what we call stacking. We can use this strategy to make cells that are resistant to both major types of HIV. If it is shown that this approach to treating HIV infection could be used as a new type of gene therapy, this method could potentially replace current drug therapy treatment. This type of gene therapy would not cure HIV infection  but would provide a source of resistant T cells that could stabilize the immune system and prevent the deve lopment of AIDS. Sources: NIH/National Institute of Allergy and Infectious Diseases. Scientists discover how HIV kills immune cells; Findings have implications for HIV treatment. ScienceDaily. ScienceDaily, 5 June 2013. (www.sciencedaily.com/releases/2013/06/130605144435.htm).Herbein G. and Kumar A. The macrophage: a therapeutic target in HIV-1 infection. Molecular and Cellular Therapies. Published 2 April 2014. (molcelltherapies.com/content/2/1/10).Stanford University Medical Center. Immune cells engineered in lab to resist HIV infection, study shows. ScienceDaily. ScienceDaily, 22 January 2013. (sciencedaily.com/releases/2013/01/130122101903.htm).

History of the Dust Bowl Ecological Disaster

History of the Dust Bowl Ecological Disaster The Dust Bowl was the name given to an area of the Great Plains (southwestern Kansas, Oklahoma panhandle, Texas panhandle, northeastern New Mexico, and southeastern Colorado) that was devastated by nearly a decade of drought and soil erosion during the 1930s. The huge dust storms that ravaged the area destroyed crops and made living there untenable. Millions of people were forced to leave their homes, often searching for work in the West. This ecological disaster, which exacerbated the Great Depression, was only alleviated after the rains returned in 1939 and soil conservation efforts had begun in earnest. It Was Once Fertile Ground The Great Plains was once known for its rich, fertile, prairie soil that had taken thousands of years to build up. Following the Civil War, cattlemen over-grazed the semi-arid Plains, overcrowding it with cattle that fed on the prairie grasses that held the topsoil in place. Cattlemen were soon replaced by wheat farmers, who settled in the Great Plains and over-plowed the land. By World War I, so much wheat grew that farmers plowed mile after mile of soil, taking the unusually wet weather and bumper crops for granted. In the 1920s, thousands of additional farmers migrated to the area, plowing even more areas of grassland. Faster and more powerful gasoline tractors easily removed the remaining native Prairie grasses. But little rain fell in 1930, thus ending the unusually wet period. The Drought Begins An eight-year drought started in 1931 with hotter than usual temperatures. Winter’s prevailing winds took their toll on the cleared terrain, unprotected by indigenous grasses that once grew there. By 1932, the wind picked up and the sky went black in the middle of the day when a 200-mile-wide dirt cloud ascended from the ground. Known as a black blizzard, the topsoil tumbled over everything in its path as it blew away. Fourteen of these black blizzards blew in 1932. There were 38 in 1933. In 1934, 110 black blizzards blew. Some of these black blizzards unleashed large amounts of static electricity, enough to knock someone to the ground or short out an engine. Without green grasses to eat, cattle starved or were sold. People wore gauze masks and put wet sheets over their windows, but buckets of dust still managed to get inside their homes. Short on oxygen, people could barely breathe. Outside, the dust piled up like snow, burying cars and homes. The area, which had once been so fertile, was now referred to as the â€Å"Dust Bowl,† a term coined by reporter Robert Geiger in 1935. The dust storms grew bigger, sending swirling, powdery dust farther and farther, affecting more and more states. The Great Plains were becoming a desert as over 100 million acres of deeply plowed farmland lost all or most of its topsoil. Plagues and Illnesses The Dust Bowl intensified the wrath of the Great Depression. In 1935, President Franklin D. Roosevelt offered help by creating the Drought Relief Service, which offered relief checks, the buying of livestock, and food handouts; however, that didn’t help the land. Plagues of starving rabbits and jumping locusts came out of the hills. Mysterious illnesses began to surface. Suffocation occurred if one was caught outside during a dust storm – storms that could materialize out of nowhere. People became delirious from spitting up dirt and phlegm, a condition which became known as dust pneumonia or the brown plague. People sometimes died from their exposure to dust storms, especially children and the elderly. Migration With no rain for four years, Dust Bowlers by the thousands picked up and headed west in search of farm work in California. Tired and hopeless, a mass exodus of people left the Great Plains. Those with tenacity stayed behind in hopes that the next year is better. They didn’t want to join the homeless who had to live in floorless camps with no plumbing in San Joaquin Valley, California, desperately trying to seek enough migrant farm work to feed their families. But many of them were forced to leave when their homes and farms were foreclosed. Not only did farmers migrate but also businessmen, teachers, and medical professionals left when their towns dried up. It is estimated that by 1940, 2.5 million people had moved out of the Dust Bowl states. Hugh Bennett Has an Idea In March 1935, Hugh Hammond Bennett, now known as the father of soil conversation, had an idea and took his case to lawmakers on Capitol Hill. A soil scientist, Bennett had studied soils and erosion from Maine to California, in Alaska, and Central America for the Bureau of Soils. As a child, Bennett had watched his father use soil terracing in North Carolina for farming, saying that it helped the soil from blowing away. Bennett also had witnessed areas of land located side by side, where one patch had been abused and become unusable, while the other remained fertile from nature’s forests. In May 1934, Bennett attended a Congressional hearing regarding the problem of the Dust Bowl. While trying to relay his conservation ideas to the semi-interested Congressmen, one of the legendary dust storms made it all the way to Washington D.C. The dark gloom covered the sun and the legislators finally breathed what the Great Plains farmers had tasted. No longer in doubt, the 74th Congress passed the Soil Conservation Act, signed by President Roosevelt on April 27, 1935. Soil Conservation Efforts Begin Methods were developed and the remaining Great Plains farmers were paid a dollar an acre to try the new methods. Needing the money, they tried. The project called for the phenomenal planting of two hundred million wind-breaking trees across the Great Plains, stretching from Canada to northern Texas, to protect the land from erosion. Native red cedar and green ash trees were planted along fencerows separating properties. The extensive re-plowing of the land into furrows, planting trees in shelterbelts, and crop rotation resulted in a 65 percent reduction in the amount of soil blowing away by 1938. However, the drought continued. It Finally Rained Again In 1939, the rain finally came again. With the rain and the new development of irrigation built to resist drought, the land once again grew golden with the production of wheat.

Systems of Equations in SAT Math Algebra Prep and Practice

Systems of Equations in SAT Math Algebra Prep and Practice SAT / ACT Prep Online Guides and Tips Sure, you’ve done your paces on single variable equations and now they’re no problem, but what do you do when presented with multiple equations and multiple variables at once? These are what we call â€Å"systems of equations† and, luckily for us, they are extremely predictable types of problems with multiple methods for solving them. Depending on how you like to work best, you can basically choose your own adventure when it comes to system of equation problems. But before you choose the method that suits you (or the individual problem) best, let’s look at all the various options you have available as well as the types of questions you’ll see come test day. These questions will always show up once or twice on any given test, so it's best to understand all the strategies you have at your disposal. This will be your complete guide to systems of equations questions- what they are, the many different ways for solving them, and how you’ll see them on the SAT. What Are Systems of Equations? Systems of equations are a set of two (or more) equations which have two (or more) variables. The equations rely on each other and can be solved only with the information that each provides. The majority of the time on the SAT, you will see a system of equations that involves two equations and two variables, but it is certainly not unheard of that you will see three equations and/or a three variables, in any number of combinations. Systems of equations can also be solved in a multitude of ways. As always with the SAT, how you chose to solve your problems mostly depends on how you like to work best as well as the time you have available to dedicate to the problem. The three methods to solve a system of equations problem are: #1: Graphing#2: Substitution#3: Subtraction Let us look at each method and see them in action by using the same system of equations as an example. For the sake of our example, let us say that our given system of equations is: $$2y + 3x = 38$$ $$y - 2x = 12$$ Solving Method 1: Graphing There will only ever beonesolution for the system of equations, and that one solution will be the intersection of the two lines.In order to graph our equations, we must first put each equation into slope-intercept form. If you are familiar with lines and slopes, you know that slope intercept-form looks like: $y = mx + b$ So let us put our two equations into slope-intercept form. $2y + 3x = 38$ $2y = -3x + 38$ $y = {-3/2}x + 19$ And $y - 2x = 12$ $y = 2x + 12$ Now let us graph each equation in order to find their point of intersection. Once we graphed our equation, we can see that the intersection is at (2, 16). So our final results are: $x = 2$ and $y = 16$ Solving Method 2: Substitution In order to solve our system of equations through substitution, we must isolate one variable in one of the equations and then use that found variable for the second equation in order to solve for the remaining variable. For example, we have two equations, $2y + 3x = 38$ $y - 2x = 12$ So let us select just one of the equations and then isolate one of the variables. In this case, let us chose the second equation and isolate our $y$ value. $y - 2x = 12$ $y = 2x + 12$ Next, we must plug that found variable into the second equation. (In this case, because we used the second equation to isolate our $y$, we need to plug in that $y$ value into the first equation.) $2y + 3x = 38$ $2(2x + 12) + 3x = 38$ $4x + 24 + 3x = 38$ $24 + 7x = 38$ $7x = 14$ $x = 2$ And finally, you can find the numerical value for your first variable ($y$) by plugging in the numerical value for your second variable ($x$) into either equation. $2y + 3x = 38$ $2y + 3(2) = 38$ $2y + 6 = 38$ $2y = 32$ $y = 16$ Or $y - 2x = 12$ $y - 2(2) = 12$ $y - 4 = 12$ $y = 16$ Either way, you have found the value of both your $x$ and $y$. Again, $x = 2$ and $y = 16$ Solving Method 3: Subtraction As the last method for solving systems of equations, you can subtract one of the variables completely in order to find the value of the second variable. We do this by subtracting one of the entire equations from the other, complete, equation. Do take note that you can only do this if the variables in question (the one you wish to eliminate) are exactly the same. If they are NOT the same, then we must first multiply the entire equation by the necessary amount in order to make them the same. In the case of our two equations, none of our variables are equal. $2y + 3x = 38$ $y - 2x = 12$ In this case, let us decide to subtract our $y$ values and cancel them out. This means that we must first make them equal by multiplying our second equation by 2, so that both $y$ values match. $2y + 3x = 38$ $y - 2x = 12$ Becomes: $2y + 3x = 38$ (This first equation remains unchanged) And $2(y - 2x = 12)$ = $2y - 4x = 24$ (The entire equation is multiplied by 2) And now we can cancel out our $y$ values by subtracting the entire second equation from the first. $2y + 3x = 38$ - $2y - 4x = 24$ $3x - -4x = 14$ $7x = 14$ $x = 2$ Now that we have isolated our $x$ value, we can plug it into either of our two equations to find our $y$ value. $2y + 3x = 38$ $2y + 3(2) = 38$ $2y + 6 = 38$ $2y = 32$ $y = 16$ Or $y - 2x = 12$ $y - 2(2) = 12$ $y - 4 = 12$ $y = 16$ Our final results are, once again, $x = 2$ and $y = 16$. Though there are many ways to solve your problems, don't let this knowledge overwhelm you; with practice, you'll find the best solving method for you. No matter which method we use to solve our problems, a system of equations will either have one solution- meaning that each variable will have a numerical value attached- no solution, or infinite solutions. In order for a system of equations to have infinite solutions, each system is actually identical. This means that they are the same line. In order for a system of equations to have no solution, the $x$ values will be equal when the $y$ values are set to 1 (which means that both variables- $x$ and $y$- will be equal). The reason this is true is that it will result in two parallel lines, as the lines will have the same slope. The system has no solution because the two lines will never meet and therefore have no point of intersection. For instance, Because our system will have no solution when both our $y$ values and our $x$ values are equal, this means that there will be no solution where we have eliminated both our variables by canceling them out. In this case, the most expedient solution to this problem will be subtraction. Why? We can see this because the two $x$ values ($2x$ and $4x$) are multiples of one another, so we can easily multiply one equation in order to equal them out. $2x - 5y = 8$ $4x + ky = 17$ Now, let us multiply the top equation in order to equal out our $x$ values. So the system pair, $2(2x - 5y = 8)$ $4x + ky = 17$ Becomes, $4x - 10y = 16)$ - $4x + ky = 17$ $-10y - ky = -1$ In order to have NO solution, our two $y$ values must balance out to zero. So let us set our two $y$ values equal to one another: $-10y - ky = 0$ $-ky = 10y$ $k = -10$ Our $k$ valuemust be -10 in order for our system of equations to have no solution. Our final answer is A, -10. [Note: don’t fall for the bait answer of +10! You are still subtracting your system of equations, so keep close track of your negatives.] Also, if it is frustrating or confusing to you to try to decide which of the three solving methods â€Å"best† fits the particular problem, don’t worry about it! You will almost always be able to solve your systems of equations problems no matter which method you choose. For instance, you could have also chosen to graph this question. If you had done so, you would first have to put each equation into slope-intercept form: $2x - 5y = 8$ $4x + ky = 17$ $2x - 5y = 8$ $-5y = -2x + 8$ $y = 2/5(x) + 8$ And $4x + ky = 17$ $ky = -4x + 17$ $y = {-4/k}(x) + 17$ Now, we know a system of equations will have no solution only when each variable balances out to zero, so let us equate our two $x$ variables in order to solve for $k$. $2/5(x) = {-4/k}(x)$ $2/5 = {-4}/k$ ${2k}/5 = -4$ $2k = -20$ $k = -10$ Again, our $k$ value is -10. Our final answer is A, -10. As you can see, there is never any â€Å"best† method to solve a system of equations question, only the solving method that appeals to you the most. All roads lead to Rome, so don't stress yourself by trying to find the "right" solving method for your systems problems. Typical Systems of Equations Questions Most systems of equations questions on the SAT will let you know that it IS a systems of equations by explicitly using the words â€Å"systems of equations† in the question itself. (We will walk through how to solve this question later in the guide) Other problems will simply present you with multiple equations with variables in common and ask you to find the value of a one of the variables, or even a combination of the variables (such as the value of $x + y$ or $x - y$). (We will walk through how to solve this question later in the guide) And finally, the last type of systems of equation question will ask you to find the numerical value of a variable in which there is NO solution, as with the example from earlier. Want to learn more about the SAT but tired of reading blog articles? Then you'll love our free, SAT prep livestreams. Designed and led by PrepScholar SAT experts, these live video events are a great resource for students and parents looking to learn more about the SAT and SAT prep. Click on the button below to register for one of our livestreams today! Strategies for Solving Systems of Equations Questions All systems of equations questions can be solved through the same methods that we outlined above, but there are additional strategies you can use to solve your questions most accurately and expediently. #1: To begin, find the variable that is already the most isolated The ultimate goal is the find the value of all the variables, but we can only do this by finding one variable to start with. The easiest way to solve for this one variable isolate (or eliminate) the variable that has the fewest coefficients or is seemingly the most isolated. For instance, $5x - 3y = -13$ $2x + y = 19$ If we are using substitution, it is easiest for us to first isolate the $y$ value in our second equation. It is already the most isolated variable, as it does not have any coefficients, and so we will not have to deal with fractions once we replace its value in the first equation. If, on the other hand, we were using subtraction, it is still best to target and eliminate our $y$ values. Why? Because we have $3y$ and $y$, which means that we only have to multiply the second equation by 3 in order to match up our $y$ values. If we were to target and eliminate our $x$ values, we would have to multiply both equations- the first by 2 and the second by 5- in order to make our $x$ values match. Though you can always find your solutions no matter which variables you choose to isolate or eliminate, it's always nice to save yourself the time, energy, and hassle (not to mention avoid possible mistakes) by going for the easy pickings first. #2: Practice all three solving methods to see which one is most comfortable to you The best way to decide which system of equation solving method suits you the best is by practicing on multiple problems (though it will help your flexibility if you can become comfortable using all the solving methods available, even if one or two suit you better than the other(s)). When you test yourself on systems questions, try to solve each one using more than one method in order to see which one is most comfortable for you personally. #3: Use subtraction for questions that require finding more than just one variable Most â€Å"multiple variable solve† systems of equations questions will ask you to find $x + y$ or $x - y$, which will almost always be most easily found via the subtraction method. It is also most useful to use the method of subtraction when we have three or more variables, especially when it is a combination of multiple variables AND three or more variables. We will see this kind of problem in action in the next section. Ready to tackle your systems problems and put your strategies to the test? Test Your Knowledge Now let us test your system of equation knowledge on real SAT math questions. 1. 2. 3. Answers: 300, E, 12 Answer Explanations: 1. As we outlined in our strategy section, it is almost always easiest to find the value of multiple variables by using the method of subtraction (though, again, it is not the only way). We are restricted somewhat, though, as we have three variables and only two equations. Why is this important? Well, we can find the individual values for each variable if we have the same number of equations as we have variables, but in this case we do not. This means we need to use a solution that will give us $x + y$, since we cannot find the value of $x$ or $y$ alone. So let us use subtraction. To do this, we must subtract like variables and, luckily for us, both equations have a single $x + y$ value. This means we can isolate our variable $z$. $x + y + 3z = 600$ $x + y + z = 400$ So let us subtract them. $x + y + 3z = 600$ - $x + y + z = 400$ - $2z = 200$ $z = 100$ Now that we have the value of $z$, we can replace it in either of the equations in order to find the value of $x + y$. Because it is always easiest to use the most isolated variable (less math involved for us!), let us our second equation to plug in our $z$ value into. $x + y + z = 400$ $x + y + 100 = 400$ $x + y = 300$ Our final answer for the value of $x + y$ is 300. Do note, however, that if you would much prefer to use substitution, you can definitely do so. Because we are trying to find $x + y$, let us isolate it as our wanted variable in one of our equations. $x + y + 3z = 600$ $x + y + z = 400$ Let us use our first equation. $x + y + 3z = 600$ $x + y = 600 - 3z$ And now we can substitute our $x + y$ value into our second equation. $x + y + z = 400$ $(600 - 3z) + z = 400$ $600 - 2z = 400$ $-2z = -200$ $z = 100$ Now that we have found our value for $z$, we can plug it into either equation to find the numerical value for our $x + y$. Let us use the second equation to do so. Why the second? Because each value is already the most isolated and so will be easiest to work with, but each question will work either way. $x + y + z = 400$ $x + y + 100 = 400$ $x + y = 300$ Again, our final answer is $x + y = 300$ As you can see, any method will suit you- it just depends on how you like to work. 2. Again, though not the only way to solve our problem, it is easiest to use subtraction when we have three or more variables in our equations or we are trying to find a combination of variables (in this case, the value of $y + z$). In this case, we have both, so let us use subtraction. $3x + 2y + 2z = 19$ $3x + y + z = 14$ Our $x$ values are identical, so let us simply subtract the second equation from the first. $3x + 2y + 2z = 19$ - $3x + y + z = 14$ - $y + z = 5$ Our final answer is E, $y + z = 5$ 3. In this case, let us use the method of substitution in order to isolate one of our values and plug it into one of the other equations in our system. The equations we are given are: $x = 3v$ $v = 4t$ $x = pt$ $v$ is already isolated, so let us plug it back into our first equation. $v = 4t$ $x = 3v$ $x = 3(4t)$ $x = 12t$ Now, we are also told that $x = pt$, so we can equate the two expressions. $x = 12t$ $x = pt$ $12t = pt$ Because 12 and $p$ both act as coefficients (numbers before a variable) for $t$, we can see that they are equal. This means that $p = 12$ Our final answer is 12. You did it! Balloons and confetti for you! The Take-Aways As you can see, systems of equations are some of the most versatile problems when it comes to methods for solving them (though the problems themselves are not terribly varied). Though you can solve many problems on the SAT in a variety of ways, most are not quite so flexible, so take heart that you have many choices for how to proceed for your systems of equations questions. Once you practice and familiarize yourself with these types of questions, you’ll find the best method for you- your strengths, and your timing- for taking the test. And pretty soon, you’ll be able to knock out systems of equations questions in multiple ways, blindfolded, and with hands behind your back (though why you would want to is, frankly, anyone’s guess). What’s Next? Systems were a snap, you say? You're ready for math problems, you say? Well lucky you! We have more math guides than you can shake a stick at, all of which cover crucial aspects of the SAT math section. Lines and angles, polygons, integers, ratios...any topic you need to brush up on is at your fingertips, so make the best of your study time and energy and target any of your known problem areas before test day. Want to know the most valuable strategies for SAT math problems? Check out our guides on plugging in answers and plugging in numbers to help finesse the vast majority of your SAT math questions. Looking to get a perfect score? Look no further than our guide to getting a perfect 800 on the SAT math section, written by a perfect-scorer. Want to improve your SAT score by 160 points? Check out our best-in-class online SAT prep program. We guarantee your money back if you don't improve your SAT score by 160 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math strategy guide, you'll love our program.Along with more detailed lessons, you'll get thousands ofpractice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial:

Corporate Social Responsibility and Profit Essay

Corporate Social Responsibility and Profit - Essay Example This paper illustrates that followers of CSR on the other hand state that being socially responsible is more important because of the social contract, as well as the argument that CSR can actually increase profit. Others in favor of CSR say that it is already an obligation, and the issue is simply one of finding ways in which companies can act in ways that are socially responsible. Even companies who agree that CSR is important often have problems putting CSR principles into practice. The main critics of CSR claim that standards of living have greatly improved over the past 100 years and that this improvement is a result of â€Å"the success of free enterprise†. Critics of CSR attack those in favor of it by saying that profit is a needed and helpful advantage of business because it is this very profit which allows businesses to put funds into helping society. The reduction of profits gained by companies caused by CSR can actually have bad effects on society because lesser prof its mean less ability to help society. If companies spend more time paying for functions that make them socially responsible, they will not be able to focus on the profit which is important for shareholders. Without shareholders, the company does not exist, and so it cannot help society by giving it funds. Many people in favor of CSR say that many business ethics of big corporations are unethical, but critics reply by saying that it is unethical for managers to think of anything else than maximizing shareholder profits. Also, making companies responsible for many different aspects of society risks managers and directors being distracted. Critics also say that there is a big difference between taking account of society’s interests and being accountable for society’s interests; only the former element should be imposed on managers and businesses.