What theme (lesson about life) does Beowulf's defeating evil, in the form of Grendel and Grendel's mother, yet losing his own life, suggest about the struggle between good and evil?

To answer the question, I will start with a discussion of Beowulf’s death. During his battle with the dragon, the creature deals him a deadly blow when its tusks enter their poison into Beowulf's bloodstream; however, this is not an instantaneous death. Beowulf's final action is to split the dragon in two with his dagger. While Beowulf does die from his wound, he also still defeats the dragon.
This shows that good always triumphs over evil, but certain sacrifices have to be made.
The way this relates to the elements of this Old English epic are its inclusion of an epic hero. The epic hero is a man of noble character and extreme courage, like the idea of a perfect person. The epic hero is willing to do whatever it takes to defeat the evils that threaten his people, to whom he is undoubtedly loyal. All that Beowulf accomplishes is in service of others: each monster he defeats was hurting people. To stop the evil from continuing to ravage the land, Beowulf willingly sacrifices his life. Therefore, his death is not proof that evil wins, but rather further evidence that good will go to great lengths in vanquishing evil.

Can someone please help me with the role of Holden's family? With quotes and page numbers or chapters please.

Holden Caulfield's conflict with life stems from many different areas, including his family. Most importantly, Holden's brother Allie, who passed away before the novel begins, leads Holden to experience a tremendous amount of grief and depression. Holden says of Allie,

it wasn’t just that he was the most intelligent member in the family. He was also the nicest . . . God, he was a nice kid (38).

Holden has an inability to fully let go of his grief and mourning for Allie. Young children frequently remind him of Allie, and Holden feels the need to protect them due to his inability to save Allie from leukemia. Part of Holden's contempt for adults stems from his inability to let go of childhood.
Phoebe, Holden's sister, also serves an important role, particularly at the end of the novel. Just like with Allie, Holden holds Phoebe dear to his heart. He feels the need to protect her from the cruel and perverse world of adulthood. After visiting her before planning to leave the city, he is convinced by her innocence and beauty to stay. Holden and Phoebe spend the day together, and when he takes her to the zoo, she happily rides the carousel in the rain. Watching his sister's innocent joy, Holden feels happy for the first time in the novel:

I felt so damn happy all of a sudden, the way old Phoebe kept going around and around. I was damn near bawling (213).

Holden's parents are the anxious type, the kind that would have "two hemorrhages a piece" if Holden were to tell anything personal about them. They are a driving force in the novel, and he is partially convinced not to return home after leaving school by the thought of encountering his hysterical mother. The novel reads:

I didn't want to go home or anything till they got it and thoroughly digested it and all. I didn't want to be around when they first got it. My mother gets very hysterical (51).

Holden's mother and father are still scarred by Allie's death, perhaps even more than he is, and as a consequence, they aren't able to be proper parents to Holden or Phoebe. Holden's relationship with them becomes strained; he is afraid to break their hearts with more bad news, but he is distant from them and unable to properly communicate his issues.

Is a turtle a reptile?

Turtles are reptiles.
Turtles (including tortoises and terrapins) belong to the order Testudines, which is a part of the class Reptilia. 
The characteristics that turtles share with all other reptiles include:
Scales. Reptiles do not have feathers, fur, or slime, which respectively characterize birds, mammals, and amphibians.
Large-yolked eggs. Unlike amphibian eggs, reptile eggs retain water and do not need to be submerged. Reptile eggs are typically leathery, unlike bird eggshells, which are typically made of brittle mineral. Also, a few reptiles are viviparous, meaning they bear live young—however, they do so by retaining their eggs inside their bodies, rather than the more complex means by which mammals incubate fetuses.
Ectothermia, or cold-bloodedness. Reptiles cannot regulate their own body temperature and rely on the external environment to keep themselves able to move and the chemicals in their cells able to react. Turtles may bask in the sun to warm themselves, and they may hibernate during colder months when activity is impossible.

There is no one best leadership style. Leadership theory helps us understand the different types of leaders and define their characteristics from diverse perspectives. Identify a well-known leader and briefly describe the characteristics that best differentiate him/her from others. Apply Fiedler’s Contingency Theory, Path-Goal Theory, Normative Decision Theory and Visionary Leadership to this leader’s style. Determine which theory best describes the leader you identified.

Angela Merkel has been in the news more and more lately, and it's not hard to see why. In 2015, she won TIME Magazine's person of the year award. As the Chancellor of Germany at age 59, she may be one of the most influential and successful world leaders today. Not only is she young, she has been, for all practical purposes, the leader of the European Union for about 9 years now. Her major accomplishments have been managing Europe's debt crisis, keeping the European Union intact, and managing to set Greece on the path to recovery from the brink of collapse.
Merkel is certainly one of the most powerful and influential female leaders in the world today, and this is due in part to her ability to negotiate under extreme pressure, her willingness to stand alone as a minority voice, her ability to "lead from behind," her unflinching dedication to her own values, and attention to hard data. All of this, coupled with her steadfast determination and calm demeanor have helped make her a respectable, moral voice for a group of nations desperately in need of someone to take a stand for them.
These leadership qualities are unique in that most politicians have built a career studying politics and leadership, and many are great at rallying people because they have a flair for the dramatic. Yet Merkel sets herself apart by refusing to play that political game, and instead remains focused on her values, which are based on hard evidence and proven effectiveness, and keeps a few manageable end goals in mind, which will serve to deliver what the people want to them and show that she is true to her word. In fact, she never studied politics at all, instead pursuing a career as a politician after studying chemistry.
According to Fiedler's Contingency Theory, which asserts that effective leadership depends on the unique situation and includes many factors, like the nature of the task, the leader's personality, and the makeup of the group being led. Make no mistake, Europe was desperate and in dire need of someone to take the wheel, and they wanted nothing short of a complete overhaul of the current solutions in place. Nothing was working, and they were eager for a change. Doing away with their current means of achieving a solution seemed the only way to manage the debt crisis that was threatening to tear them apart.
Angela Merkel was a shining beacon of hope that provided the perfect answer to their needs: she didn't have as much charisma as the other politicians, but she paid attention to data, offered a hard-working persona and an analytical mind, and delivered on her word. Not only was she the perfect candidate to solve a problem such as this one, she had the intelligence and determination to do it successfully, and that is what made her success as a leader so definite. Chemists by nature are very task-oriented people and Merkel is no exception.
In Path-Goal Leadership, a leader must consider employee characteristics and task and environment characteristics, select the best leadership style, and focus on a clear path with defined goals. In Merkel's case, she had goals defined almost immediately, as well as a clear path set out in order to achieve those goals. People trust her because she does not just spew the same lofty rhetoric involving "freedom" and "values" as other world leaders tend to do. First, she is pragmatic in both her goals and her vision for achieving them; she knows what the numbers are and she knows that Germany cannot continue to be so generous when it comes to spending. She also knows that she does not want to see her beloved country go through the same system collapse that it saw during the 20th century. The environment of Germany and the EU as a whole is one that is still recovering, and thus must be considered as such, in order to be able to ensure future prosperity. Because of this, a leader must be both competitive and practical, forging alliances and strengthening bonds where necessary instead of relying on national pride and emotional decision-making to get ahead.
Normative Decision Theory decides the best decision to make, assuming there is an ideal decision-maker who is both rational and able to compute with accuracy. The practical application of this would be "decision analysis," otherwise identified as how people should make decisions, given a set of values. It is an approach aimed at finding better ways to make decisions, such as different methodologies and software. This sort of lens works almost perfectly when studying Merkel's behavior as a leader because she is so analytical and rational that other leaders find it hard to compete with her data-driven arguments. Not only that, but her values seem to line up perfectly with her proposed solutions and the values that her people hold dear. As a leader, she makes a habit of shying away from choosing to do anything which is reminiscent of failed past endeavors and using hard data to fuel her arguments, which is certainly the most rational approach to problem-solving and planning.
As a general rule, visionary leaders are quite uncommon, but their characteristics include imagination, persistence, and unwavering conviction. Visionary leaders tend to possess an extraordinary amount of openness to new ways of doing things and to new information. Angela Merkel certainly possesses all of these qualities, and more. As Chancellor of Germany, she has continually sought new alliances, new ways of doing things which would bring Germany into the 21st century and level the playing field with other nations. While Merkel seeks knowledge, and listens to her contemporaries and predecessors, she by no means bows to their way of doing things. By ignoring these norms already in place, she is able to transcend the mistakes of the past and see clearly into the future. To do this requires imagination and vision and she has plenty of those as well.
To choose one leadership style for Merkel is difficult, but if one considers her history as a politician, it seems that Path-Goal Leadership is the clear choice. For example, Merkel has always remained very centrist in terms of German politics and her position on the polls. She was open-minded when it came to sacrificing conservative values to rule in favor of the German popular vote when it came to switching to renewable energies after Fukushima. Yet she is currently governing against the majority of Germans when it comes to the issue of the refugee crisis. Overall, Germans find that she is steadfast in her own values, yet reliable when it comes to serious issues, and that is the reason that she has remained at around 50% support in the polls. She has done controversial things, yes, such as meeting with the prime minister and president in Turkey just before the elections, but she has always had clear goals for her country in mind, and goals that are mainly shared by other Germans. Experts have defined her leadership style as "principled pragmatism" and I tend to agree with that assessment.
https://fortune.com/2014/03/20/worlds-50-greatest-leaders/

https://www.economist.com/special-report/2013/06/13/the-merkel-plan

Othello is both a stranger and a hero, but which of the two words best defines him?

Othello is a notably heroic character, making his manipulated downfall all the more tragic. Although his nobility and honor are some of his primary characteristics, Othello is also a black man in a white man's world, and so, because of the prejudice of many of the the white characters in the play (most notably Iago), it would be more accurate to call Othello a "stranger."
Black individuals were often viewed as strange, rare, and/ or primitive in Shakespeare's time. Othello presents us with a robust contrast to this stereotype, defying prejudice with his nobility and honor. In many ways, Iago's scheme can be seen as a reaction to Othello's defiance of racist stereotypes. Indeed, though he's angry about being passed over for a promotion, Iago is also a white man trying to force a black man to fulfill a stereotyped caricature by provoking his jealousy and anger. In other words, Iago alienates Othello with his deception, forcing the honorable soldier to become a stranger to his community. As such, though Othello is a hero, Iago forces him to become a stranger and stay a stranger by using deception to alienate him from the white community. 

Glencoe Algebra 2, Chapter 2, 2.6, Section 2.6, Problem 8

f(x) = |x-4| , the the domain and range is given as follows
(i)Domain definition:
The domain of a function is the set of the input or argument values for which the function is real and defined.
In this function, The function has no undefined points, so the domain is
-oo (ii)Range definition
It is the set of values of the dependent variable for which a function is defined.
For this function the interval has a minimum point at x = 4 with value f(x) = 0
so the range of |x-4| is f(x) >= 0
It can also be observed from the graph below:

In The Strange Case of Dr. Jekyll and Mr. Hyde, what did Mr. Hyde do after he was transformed?

The broadest and most comprehensive answer is, whatever he wanted.
A slightly more specific answer is, Mr. Hyde did whatever Dr. Jekyll wanted to do but didn't do, because he was concerned about his reputation and social standing.
To get more specific, and get down to details, Mr. Hyde did a number of things readers are explicitly told about.
Mr. Enfield tells the reader the first of these shocking things in the first chapter: when walking late at night, Hyde trampled a little girl to the ground. He stomped on her so hard people could hear her bones shatter.
Another specific and shocking action Hyde took was to beat Sir Danvers Carew to death. He was talking to this respected older gentleman on the street, and then he suddenly beat him to death with Jekyll's cane. (This is described in the chapter titled "The Carew Murder Case.")
Besides doing these things, Hyde did them in public, with witnesses. That's the opposite of Jekyll, who tried to hide his sins and vices.
Those are the main specific actions. Jekyll also tells of Hyde's actions in general in the final chapter. Hyde lusted to cause pain. He feels younger and more sensual. He's rude, and so on.