Question

5.4.4 practice: modeling: two variable system of inequalities

Answer 1

Explanation:

1 Group A was known to be outstanding students. They received incredible grades, never experienced trouble with any teacher, and everyone likes them. Group B are known as the bad students in the school. They could care less about their grades, make rude remarks to fellow students, and have a problem with authority. The one thing both groups have in common is their trust and respect in the people that are in the groups. One school day it had been announced that someone broke into Mr. Vanta's computer, copied answers from a school test, and passed the answers along to other students. A student from Group A accused Group B of stealing the answers because they are never up to any good. The other students in the group agreed. Group B was infuriated and stood up for themselves. Both groups argued about it untilan authoritative figure stopped them. After that day, the two groups despised each other. One day, Group B was so angry that they confronted Group A outside of school. Their talking narrowed down and fighting eventually occurred. Now, a week later, the people who stole the answers were found and punished. Group A was wrong about group B. They were the actual ones at fault. They believed that if they'd blame Group B, people would believe them due to the group always getting caught up in trouble. Well, the truth was uncovered.

2 In-group bias: The tendency to favor and feel positively toward one's own social group. Out-group homogeneity: The tendency to think that members of the out-group are all the same while failing to see them as individuals. Out-group derogation: The tendency to put down other groups and treat them unfairly. In-group bias- Some cellmates were not including each other in their cooperation with the opposite group(the guards)Out-group homogeneity - Prison caused people to become disorganized internally. Out-group derogation example - The guards treated the cellmates terribly even though it was only an experiment.

3 Out-group homogeneity: The tendency to think that members of the out-group are all the same while failing to see them as individuals. For starters, I would have to find out if race is an actual factor or if it is a random subject that both groups are fighting just because their peers are. If it is a factor, then I'd address the issue. I'd have to keep in thought that my race could possibly influence each group's decision. After that, I'd find out where the problem started, when it began, and how exactly it developed over time. The farther back it goes, the more I'd have to beat down the differences between both groups. I'd ask them, "Did it have to do with anything personal," and "Was anyone else involved?" Also, "What was the base of this argument?

Answer 2

Explanation:

To solve a two-variable system of inequalities, we need to graph the solution set. The solution set is the overlapping region between the two inequalities.

Let's take an example of a two-variable system of inequalities:

3x + 2y ≤ 12

x - y > 1

To graph this system of inequalities, we will first graph each inequality separately.

For the first inequality, we will start by finding its intercepts:

When x = 0, 2y = 12, so y = 6.

When y = 0, 3x = 12, so x = 4.

Plotting these intercepts and drawing a line through them gives us the boundary line for the first inequality:

3x + 2y = 12

Next, we will shade one side of the line to indicate which half-plane satisfies the inequality. To determine which side to shade, we can choose a test point that is not on the line. The origin (0,0) is a convenient test point. Substituting (0,0) into the inequality gives us:

3(0) + 2(0) ≤ 12

0 ≤ 12

Since this is true, we shade the side of the line that contains the origin:

[insert image of shaded half-plane]

Now let's graph the second inequality:

For this inequality, we will again start by finding its intercepts:

When x = 0, -y > 1, so y < -1.

When y = 0, x > 1.

Plotting these intercepts and drawing a line through them gives us the boundary line for the second inequality:

x - y = 1

Note that this line is dashed because it is not part of the solution set (the inequality is strict).

Next, we will shade one side of the line to indicate which half-plane satisfies the inequality. To determine which side to shade, we can again choose a test point that is not on the line. The origin (0,0) is a convenient test point. Substituting (0,0) into the inequality gives us:

0 - 0 > 1

This is false, so we shade the other side of the line:

[insert image of shaded half-plane]

The solution set for the system of inequalities is the overlapping region between the two shaded half-planes:

[insert image of overlapping region]

So the solution set is 3x + 2y ≤ 12 and x - y > 1 .

In summary, to solve a two-variable system of inequalities, we need to graph each inequality separately and shade one side of each boundary line to indicate which half-plane satisfies the inequality. The solution set is the overlapping region between the shaded half-planes.