Answer the following about equations and inequalities.
1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
2) How is graphing linear inequalities different? What does it help us understand?
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
4) Name one original real-world application for graphing a SYSTEM of inequalities.
This post is worth 8 points (2 per problem). You will be graded based upon the completeness and thoughtfulness of your answers.
1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
ReplyDeleteIn our opinion, the point of graphing linear equations is to visualize the slope of the line and sometimes clearly see the intersection between lines.
2) How is graphing linear inequalities different? What does it help us understand?
Graphing linear inequalities are different because, for inequalities, you might have a dotted line, and you need shade different coordinates of the graph. In our opinion, the point of graphing linear equations is to visualize the estimated amount of area the solution covers.
You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
Dinosaurs represents disjunctions because, it doesn’t care what it eats, both grass or animals. It is similar to disjunction because, disjunction is expressed by using the word “or”, which means the every possibility. However, we compared cows to conjunctions because, cows mostly only eat grass out of a lot of varieties of food in this world. Conjunction is expressed by using the word “and,” and only represents the intersection.
Name one original real-world application for graphing a SYSTEM of inequalities. You will be graded based upon the completeness and thoughtfulness of your answers.
1.
You are selling orange juice and grape juice for your math market place project.
The orange juice costs $2 and grape juice costs $4. The rule is that you cannot sell over 100 cups of orange juice a day. Also, you need to make at least $1000 to get a good grade. In order for you to get a good grade, how many orange juice and grape juice do you at least have to sell?
2. Fredrick is organizing a party and he is planning to serve at least 120 pounds of meat. The roast beef costs $5 per pound and the chicken cost $2 per pound. Fredrick have a budget of at most $600 for meat of the party. What are the possible amounts of roast beef and chicken?
1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
ReplyDeleteIn our opinion, the point of graphing linear equations are that it shows the visual solution. Since there are a lot of solutions for one linear equation, and it’s impossible to find them all out, by graphing a line, you can find out all possible solutions. This is because every point on the line is a solution for the linear equation. This helps us to understand that there are a lot of possible solutions that satisfy the equation. It is very hard to figure out every single possible solution without graphing.
2) How is graphing linear inequalities different? What does it help us understand?
Graphing linear inequalities are different because they show what pair of ordered pairs “might” work. If you graph a linear equation, every point on the line must work, but the shaded part on a linear inequality show all the possibilities that might satisfy the equation. This helps us understand that there are a lot of possibilities for the inequality because it’s not an equal sign. There can be more than one solution. Without graphing, it is hard to know this because you don’t have an visual aid to show which part is shaded and which part is not.
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
The conductor(conjunction) of the orchestra only cares if the whole orchestra is playing together harmonically. He doesn’t care if each individual can play well. The only thing that matters to him is how the orchestra sounds together. This represents conjunction because conjunctions represent only the intersection, which, in this case, is the orchestra playing together. On the other hand, the drum player(disjunction) does not care as long as he’s playing. He likes both playing with the group or alone. This represents disjunction because the drum player doesn’t care as long as he’s playing. He likes both playing with the band and alone. This is similar to disjunction because disjunction is graphing every possible outcome.
Name one original real-world application for graphing a SYSTEM of inequalities.
You really want to buy a painting to hang in your new house. The cheapest painting costs $200, so you need to earn at least that amount of money. Currently, you can only work at most 20 hours a week. You have two jobs, teaching, and walking the dog. While teaching, you get $15 per hour. While walking the dog, you get $5 per hour. Write and graph a system of inequalities to show all the possible combinations of jobs you can do to make sure you have enough for the painting.
1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
ReplyDeleteIn our personal opinion, the point of graphing linear equation, to make sure we understand the idea of linear equation and to understand the concepts of linear equations visually. Also, it could tell us the solution directly by coloring the graph line and how it got increased or decreased through numbers. It tell us if the slope is negative or positive by where the line passes or designed.
2) How is graphing linear inequalities different? What does it help us understand?
Graphing linear equations and graphing linear inequalities seems like it’s similar but it’s not. Graphing linear equalities are mostly same as graphing linear equations. However, there’s one difference. Depends on its inequalities symbol, the region where we shade are different and also the lines are divided into two which are dotted lines, and solid line. If the inequalities symbol represents greater than or equal to nor less than or equal to, the line will looks like a solid line. The solid line represents that the solution also includes the border line. However, if the inequalities symbol represents greater than or less than, the line will looks like a dotted line. The dotted line symbolizes that the solution excludes the border line. Graphing linear inequalities helps us understand where the solution are located through shaded region or groups not only as a point on the graph line.
ReplyDelete3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
When the sentence in c is formed by joining the sentences in a and b by the words and, this is called a conjunction. In other words, conjunction is “and”. In the other case, this is when two separate inequalities are joined by the word or. Basically, disjunction is “or”.Since my student is having a difficult time understanding conjunction and disjunction. Before we move on to graphing disjunction and conjunction, I will teach unique way of remembering each term. First of all, Conjunction starts with letter “C”. Don’t just think “C” as an alphabet or letter. Think this as a shape. “C” has a two point on the right side and it connects with curvy lines. However, it only connects the two points and there is an extra space left over.
Like what I’ve told you before, think also Disjunction as shape “D”. It’s closed shape. Therefore, there’s more two points that meet together. The points inside the D and the points on the D border are all possibilities. Therefore, think this as “OR”. Now, you’ll be able to know what disjunction and conjunction is. Then, it’s time for us to figure out how to graph conjunction and disjunction. In order to solve a conjunction of two open sentences in a given variable such as x nor other alphabets, you find the values of the variable for which both sentences are true. This is just like a solving an equation. However, you have to be careful because when you divide or multiply negative integers, the sign has to be flipped. In the other side, in order to solve a disjunction of two open sentences, you fin the values of the variable for which at least one of the sentence is true. Also the graph includes two graphs. Lastly, you have to leave the point where you mark on the graph line empty, when the solution is greater than or less than. However, when the solution is greater than or equal to or less than or equal to, you have to fill the point.
4) Name one original real-world application for graphing a SYSTEM of inequalities.
Christina’s mom ordered Christina to buy pineapples and strawberries. Christina has $100. Pineapple costs $10 each and strawberry costs $15 each. Christina’s mom wants Christina to use at least $85. Then, how many strawberries and pineapple can Christina buy? This could be an example of real-world application. If we write this word-problem in equation, it is When we let x equals number of pineapple and let y equals number of strawberries.
10x + 15y ≥ 85 and 10x+15y≤100
Your explanation of conjunctions and disjunctions was very confusing.
DeleteLISA & SARAH (8A):
ReplyDelete1.) In our opinion, the point of graphing linear equations is to get a clearer understanding in the amount of increase or decrease in something over a certain amount of time. The steeper the line is, the more increase or decrease there is, and it helps people, such as people working in companies to organize and find out their increase or decrease in profits and etc. , helping them to decide what they could do better.
2.) Graphing linear inequalities are different by shading in the inequalities to show a certain set of data. It helps us to understand the answers through a number set (as a group), not just a specific point. When we graph linear inequalities, there are many points that can be solutions, while linear equations have only a certain number of points.
3.) "D" isjunctions can be when someone is playing a video game named "D" evil's Run, they don't care what they play, either with a friend, or without a friend to play against. "C" onjunctions is when you play a team games, as a "C" ouple like basketball or soccer, since you can't play alone, and have to have someone to play with.
4.) Lisa and Sarah are preparing for their friend's wedding. They have to serve 50 servings of coffee and wine (since it's their precious friend's wedding!), with only $150 for their budget. Coffee is $0.50 per cup, and wine is $2 per glass, to make it. We can use graphing inequalities to find out how many coffee and wine they can serve.
The last example would work if you had to serve AT LEAST 50 servings of coffee and wine. Then it would be an example of a system of inequalities. You currently have one inequality and one equation (x + y =50).
Delete1) In our opinion the point of graphing linear equations is to recognize which area contains all the solutions for the linear equations. It helps us to understand the increase and decrease.
ReplyDelete2) Graphing linear inequality different from graphing linear equation because graphing linear inequality is looking for the difference and which is bigger or smaller. You also need to shade the side of the lines in the graph. It help us understand if the unknown number is bigger or smaller than the other number.
3) Conjunctions are cats and disjunction are dogs. Cats are calm so they only fight when did meet another cat (intersect). Dogs are very energetic so they always fight and bark whatever it is. So doesn’t matter if the dogs meet or not they will always fight and bark. The word cat have the letter “a” in it so you use “and”. The word dog have the letter “o” it it so you use “or”.
4) At a pet store, there are always at least 10 cats. The pet store decided to bring at most 7 more dogs than cats. Solve and graph. By graphing we could know how many cats and dogs does the pet store have.
-Jun and Heesun 8A-
Your explanation in #2 if confusing.
Delete1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
ReplyDeleteIn my opinion, the point of graphing the linear equation is because we will get to learn how to properly graph the slope and the y-intercepts. After we learn how to graph the equations we will then know how to apply them to our real world. For example, you become a business man and have to make a report on how many items you sold. You will need to use your knowledge of linear equations, graphing the slope, and graphing y-intercepts to graph the Revenue price in a break-even graph. The linear equations help us understand how the output value changes over input values.
2) How is graphing linear inequalities different? What does it help us understand?
In linear equations, we only graph the equations that include slope and the y-intercept. However in linear inequalities we will have to not just only graph the equations that include slope and the y-intercept but we also have to determine its solution by shading. We also have different ways of graphing the inequalities. Greater than or equal to and less than or equal to will have continuous line. But just greater than or less than will have dotted lines. The linear inequalities help us understand to determine the solution sets of particular inequality. There will be fixed amount of solutions in a particular inequality.
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
First of, conjunctions refer as “and” graph. “And” graphs are when it’s solutions are in between the two integers. Next, disjunction refer as discontinuous graph or “or” graph. “Or” graphs are when the inequality equation could have two solutions. Either it’s x is less than or equal to some integer, or x is greater than or equal to some integer. There also could be x is less than some integer. Or greater than some integer.
One unique original way of remembering what each term means and how to graph it for “and” graph (conjunction) is that Islam are allowed to have many wives. However the husband need to be kind and be able to take care of all the wives. So we could refer the two integers in a inequality as the two wives. While x will be the husband. X (the husband) will need to be faithful for both integers (both wives). So when we graph this inequality, you will have to shade the regions in between the two integers (the two wives).
One unique original way of remembering what each term means for “or” graph (disjunction) is that in Islam male adults are allowed to have many wives. However the husband need to be kind and be able to take care of all the wives. But, there are sometimes some Islam husbands who always change their way of treating their wives (which is against their religion!). These bad husbands will be nice to his second wife, while be mean to his first wife and next day. Then, he suddenly changes his mind and be nice to his first wife only, while he is really mean to his second wife. This husband could be nice and kind or be cruel and mean to the first wife. In the other hand this husband could be nice and kind or be cruel and mean to the second wife. This will be a great example of a disjunction graph!
4) Name one original real-world application for graphing a SYSTEM of inequalities.
ReplyDeleteYou are trying to bring your friends in a baseball game and also a basketball game. You only have $200.00 that you can spend. The baseball ticket cost you $40.00 per game and the basketball ticket cost $30.00 per game. During the games, as a snack you and your friends would like to spend some money on hot dogs and hamburgers. Hot dogs cost $2.00 and hamburgers cost $5.00. Every time you go to the baseball game you always buy a hotdog since you love it! Every time you go to the basketball game, you always buy a hamburger because you also love it! We cannot spend no more than $100.00 on the snacks. So what is the maximum number tickets you can buy for each game while the maximum number of hot dogs and hamburgers could be purchased?
baseball ticket = $40.00
basketball ticket = $30.00
40x + 30y ⩽ 200
2x + 5y ⩽ 100
Answer the following about equations and inequalities.
ReplyDelete1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
The point of graphing linear equations is to see which ordered pairs can make the equations true. So, graphing the linear equations shows us their solutions. It helps us to understand that there are certain points on a coordinate plane that can make the linear equation true, which are the linear equation’s solutions.
2) How is graphing linear inequalities different? What does it help us understand?
In linear inequalities, you shade the side of the coordinate plane that makes the inequality true. The shaded portion indicates the solutions of the linear inequalities. Also, the lines can be dotted or solid depending on the inequality symbol. Graphing linear inequalities helps us to understand that there are solutions to the inequalities that aren’t necessarily on the line. Therefore, linear inequalities have MANY more solutions than linear equations.
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
When 2 or more sentences are joined by the word “and”, it’s a conjunction of sentences. Also, when 2 or more inequalities are joined by the word “and”, it’s a conjunction of inequalities. It’s easy to remember when you think of conjunctions this way. When graphing, the two inequalities are graphed on a number line and their intersection is shaded.
When 2 or more sentences are joined by the word “or”, it’s a disjunction of sentences. When 2 or more inequalities are joined by the word “or”, it’s a disjunction of inequalities. The word “or” makes it easy to remember how disjunctions of sentences and disjunctions of inequalities are essentially the same things. When graphing, the two inequalities of the disjunction are graphed on a number line and all possible solutions are shaded, regardless of whether they intersect or not.
4) Name one original real-world application for graphing a SYSTEM of inequalities.
Mr. Jobe is buying mechanical pencils and pens for his math class. Mechanical pencils cost $1.00, and pens cost $1.50. Mr. Jobe needs to buy at least 30 writing utensils, and he can spend no more than $20. Write a system of linear inequalities, graph them, and name one combination of pens and pencils that Mr. Jobe can buy for his class.
Not a very unique, effective way of remembering disjunctions/conjunctions.
DeleteAnswer the following about equations and inequalities.
ReplyDelete1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
When i graph linear equations, it is easier for me to visualize and identify how many solutions there are. For example, if lines intersect at one point, I would only have one solution, if lines the lines are parallel, I would have no solution, and if the lines overlap, i have infinite numbers of solutions.
2) How is graphing linear inequalities different? What does it help us understand?
Linear inequalities are different from the linear equations because it replaces equal signs to inequality signs. When you graph linear inequalities, your solutions include the points on the line, or the points not on the line, which defines which inequality signs you’d have. Also, solutions are within the range of linear inequalities. So, linear equations only have solutions on the line but linear inequalities have solutions above, below, on, and not on the lines depending on the inequality signs.
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
Conjunction means "and" and disjunction means "or". “Con” means "with other" and “dis” means "one or the other." when you graph inequalities, conjunction have solutions between two points so they need to have common solutions but for disjunction, solutions are not overlap and it goes to opposite directions. So a fun way to remember is by using the words “caterpillar” for an example of a conjunction, and “dragon” for an example of a disjunction. Caterpillars like to eat plants, so when you place it on top of a leaf, it would start to chew off the leaf, so the caterpillar will get closer and closer to the branches (on the tree). However, dragons don’t like plants. Instead, they like spewing fire, and when they do, the fire recedes away as the dragon continues to spew fire. These two words are a comparison of conjunctions and disjunctions, explaining that conjunctions intersect, meeting one another (the caterpillar and the branch of tree), and disjunctions are far away from each other/opposite (the fire fading away from the dragons mouth).
4) Name one original real-world application for graphing a SYSTEM of inequalities.
You want go on a trip to America and buy a lot of gifts. However, you had $100 but you’ve already spent $45, and still wants to buy candies which costs $3.50 How many candies can you buy?
Great example for conjunctions/disjunctions, but the last example is not a system of inequalities (two inequalities with two variables).
DeleteIn your opinion, what is the point of graphing linear equations? What does it help us understand?
ReplyDeleteI believe that the point of graphing linear equations are to easily understand the interaction between all of the variables that must be compared. It gives us a visual instead of just numbers.
2) How is graphing linear inequalities different? What does it help us understand?
When graphing linear inequalities, you can have a dotted or solid lines depending on the inequality sign and you have to shade the graph. Also, inequalities have more answers than usual equations.Inequalities We believe that graphing inequalities help us estimate the possible solutions for the variable.
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
Conjunctions are two people that like to share. They have common interests and so they act together. They are just like one. Remembering the first three letters, conjunctions “connect”. Disjunctions, on the other hand, are two selfish people. They often do not agree, which cause them to separate in different ways. Even if they do agree occasionally, they do not completely share; instead, they include some of their ways. Again, using the first three letters, disjunctions “disconnect”
4) Name one original real-world application for graphing a SYSTEM of inequalities.
One real world example for graphing a system of inequalities would be business. For example a farmer would have to use system of linear equations. He would have to use them to see how much money he can use on his crops depending on the money he has and the land he owns.
If a farmer is growing different types of crops, and it costs him different amount of money for each types of crops, he would have to use system of inequalities to see the maximum and minimum amount of money he can use on each crops or how much money he can use on each crop.
Answer the following about equations and inequalities.
ReplyDelete1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
In my opinion the reason why we graph linear equation is that by graphing we cans easily visually see where the solutions are and identify patterns of solutions easily, not just in numbers, visually. Also by visually seeing, it gives us clearer understanding of increase or decrease on answers.
2) How is graphing linear inequalities different? What does it help us understand?
Graphing linear equations are different from graphing inequalities in various ways. First of all there are no equal sign. Also, depending on each inequality where to shade and wether to draw a dotted or straight line changes. Also, even though in linear equations, the only solutions are points on the line, in inequalities, you can visually see the range of answers through the shading.
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
Conjunction means where there is an intersect in inequality graph. And Disjunctions mean one or another. So, I used "cranberries" for conjunction and "drug" for disjunction. Cranberries has to taste good and fresh, (intersection, both) because if they are not tasting good or fresh, nobody is going to buy it. However, drugs can cure your diseases or can provide you with substances that you lack of. So, while graphing conjunction, (something and something) think of cranberries which has to be both tasty and fresh, shade where two inequalities intersect. But for Disjunctions, something or something, drugs just has to cure a disease or help your body gain substances, so you shade both of them, or both inequality.
4) Name one original real-world application for graphing a SYSTEM of inequalities.
Your mom gives you $30 for your allowance this month. As soon as you got the money, you deposited $10 on bank account. With you left over money you have to buy at least 20 bags of chips for you party. You have two favorite chips, one costs $1.00 and other one costs $2.00. Draw a chart showing all the combinations for both chips.