For the triangle ABC, we are given that A = 48°, B = 62°, and c
= 35.0. Find the length of side b, rounded to the nearest tenth.
Show work.

Answers

Answer 1

The length of side b, rounded to the nearest tenth, is 8.6 by using the cosine law.

The given values are Angle A = 48 degrees, Angle B = 62 degrees, and c = 35.0. We need to find the length of side b. Let us use the cosine law which states that the square of any side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those two sides multiplied by the cosine of the angle between them.

b² = a² + c² − 2ac cos(B)

The value of cos(B) can be found as cos(B) = cos(180 - A - B) = - cos(A + B)cos(48°+ 62°) = cos 110° = - 0.342

b² = a² + c² − 2ac cos(B)

b² = a² + c² − 2ac (- 0.342)

As we are solving for b, we can re-arrange the equation as

b² = c² + a² − 2ac cos(B)

b² = 35² + a² − 2(35)(a)(- 0.342)

b² = 1225 + a² + 23.73a

Now we need to find the value of a.

To do that, we can use the fact that the sum of angles in a triangle is equal to 180 degrees.

A + B + C = 180°

48° + 62° + C = 180°

C = 70°

The value of cos(C) can be found as cos(C) = cos(180 - A - B) = - cos(A + B)cos(48°+ 62°) = cos 70° = 0.342

Now, we can use the cosine law to find the value of a.

a² = b² + c² − 2bc cos(A)

a² = b² + 35² − 2(b)(35)(cos 48°)

a² = b² + 1225 − 53.53b

Now we have two equations for a².

Equate them to solve for b²:

b² = 1225 + a² + 23.73a

and, a² = b² + 1225 − 53.53b

Substituting the second equation into the first:

b² = 1225 + (b² + 1225 − 53.53b) + 23.73b

b² = 2450 − 29.8bb² + 29.8b − 2450 = 0

b² + b − 82.55 ≈ 0

Using the quadratic formula:

$$b = {-1 \pm \sqrt{1 - 4(1)(-82.55)} \over 2(1)}$$

$$b = {-1 \pm \sqrt{1 + 330.2} \over 2}$$

$$b = {-1 \pm \sqrt{331.2} \over 2}$$

As length can not be negative, only the positive value is valid:

b = 8.6 (rounded to the nearest tenth)

Therefore, the length of side b, rounded to the nearest tenth, is 8.6.

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Related Questions

true or false if false correct the statement
1. global warming is caused only by natural factors

Answers

It is false that global warming is caused only by natural factors.

What is global warming?

Global warming refers to the heating of Earth's surface including ocean and atmosphere. It is as a result of human activities.

Cause of global warming are:

Variations in Solar ActivityChanges in the Earth's ReflectivityVolcanic Activity.

Hence, It is false that global warming is caused only by natural factors.

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What type of government has a collective
market?
Constitutional Monarchy
Democracy
Communism

Answers

Answer:

Your hint is "collective." Communism operates on collective goals or results.

What is OSHA in the Philippines?

Answers

In OSHA accordance with the constitutional responsibility to protect the worker's social and economic well-being as well as his physical safety and health,

the Occupational Safety and Health Standards were created in 1978. The 1978 Standards, which were adopted through the tried-and-true democratic process of tripartism, are regarded as a turning point in Philippine labor and social law. The modifications to the OSHA Standards were accepted in August 1989 thanks to cooperation from the Bureau of Working Conditions, the International Labor Organization (ILO) Manila Office, and the tripartite sectors. All institutions covered will now have a stronger tool for creating and maintaining a safe and conducive working environment thanks to the most recent updates to the Standards.

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training power for 2 days before moving on to 2 days of strength training would be an example of what kind of periodization?

Answers

Periodization is a form of training that involves organizing the training program into cycles or periods of time. The two days of power training followed by two days of strength training is an example of block periodization.

This type of periodization allows for a focus on one specific training goal for a period of time and then shifts to a new goal for the next period. This type of periodization is beneficial in that it allows for the athlete to focus on one goal for a period of time, allowing for a more concentrated effort and greater progress towards that goal.

For example, the two days of power training followed by two days of strength training allows the athlete to focus on increasing power for two days and then shift to strength training for two days.

This allows the athlete to make greater gains in power and strength while avoiding overtraining and burnout.

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If the embryo can't live on its own, how can
you prove that it's a separate human life?

Answer with your own opinion

Answers

Answer:

you can't prove it.

Explanation:

because it hasn't happened yet. you need to wait for it to be born.

There is no way to prove it, it is not alive and cannot live on its own yet

Which factor accounts for the language patterns evident in Central Asia? a. Diffusion along historic trade routes
b. Former Russian control of the region
c. Introduction of Internet technologies
d. Adoption of Islam as the official religion

Answers

Option b is the correct choice.

Language trends in Central Asia are a result of the former Russian occupation of the area.

The expansion of Islamic trade directly contributed to the growth of the Islamic faith. Muslims soon expanded throughout West Africa as traders carried their faith there. Islam was expanded via missionaries, trade, pilgrimage, and military conquest.

Culture of West Africa

The westernmost portion of the African continent is West Africa. The region has been inhabited for thousands of years, and its people is ethnically varied yet rather homogeneous in terms of culture. Native communities practise a number of indigenous African religions as well as Islam, Christianity, and other faiths.

As a result of the trade routes' role in the widespread acceptance of Islam throughout the Middle Ages, West African culture was influenced by them.

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When minority youth identify in some ways with their ethnic culture and in other ways with the majority culture, they are developing a(n)

Answers

Ethnic identity involves the identification of the youths who are in the

minority with their ethnic culture and in other ways with the majority culture.

Culture is defined as way of living by a set of people. Culture is very

diverse and unique. Such unique examples include way of dressing, foods

eaten and predominant occupation of the people.

The minority usually have to identify with the majority tribe as a result of

their way of things being commonly and more frequently done.

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Why could it be said that the Progressive Era failed African Americans?

Answers

Explanation:

Although the Progressive Era brought reform to government and business and increased political power for many citizens, its benefits were limited to white Americans; African Americans and other minorities continued to experience discrimination and marginalization during this era.

what are the similarities and differences between the two creation accounts in genesis

Answers

The book of Genesis in the Bible contains two creation accounts, found in Genesis 1:1-2:4a (the "Priestly" account) and Genesis 2:4b-25 (the "Yahwist" account).

While there are similarities between the two accounts, there are also notable differences in terms of their narrative structure and emphasis.

Similarities:

Divine Creation: Both accounts affirm that God is the creator of the heavens, the earth, and all living things. They emphasize God's role as the ultimate creator and the source of all existence.

Order and Purpose: Both accounts convey a sense of order and purpose in the act of creation. They depict a deliberate and systematic process through which God brings forth the various elements of the world.

Human Creation: In both accounts, humans are portrayed as being created by God. They highlight the special status of humanity as being made in the image of God and given a role of stewardship over the earth.

Differences:

Narrative Structure: The two accounts differ in their narrative structure. The first account in Genesis 1 follows a strict six-day creation framework, with God creating different elements of the world on each day and culminating in the creation of humans on the sixth day. The second account in Genesis 2 focuses more on the creation of humans and their immediate surroundings.

Order of Creation: The order of creation varies between the two accounts. In Genesis 1, the creation of light, sky, land, plants, celestial bodies, sea creatures, land animals, and finally humans follows a sequential order. In Genesis 2, the emphasis is primarily on the creation of humans and then the formation of the Garden of Eden, followed by the creation of animals and the naming of those animals by Adam.

Focus and Emphasis: The first account in Genesis 1 emphasizes the grandeur and cosmic scope of God's creation, highlighting the order and hierarchy in the natural world. The second account in Genesis 2 focuses more on the intimate relationship between God, humans, and the natural environment, emphasizing themes of companionship, naming, and the formation of the first human couple.

Overall, while there are common themes and elements in the two creation accounts, they present different perspectives and emphasize distinct aspects of the creation narrative. These differences have led scholars to interpret them as complementary accounts, offering different theological insights rather than contradictory information.

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Ocean and Associates, CPAs, audited the financial statements of Drain Corporation. As a result of Ocean's negligence in conducting the audit, a material misstatement in the financial statements went undetected. Ocean was unaware of this fact. The financial statements and Ocean's unqualified opinion were included in a registration statement and prospectus for an initial public offering of stock by Drain. Sharp purchased shares in the offering. Sharp received a copy of the prospectus prior to the purchase but did not read it. The shares declined in value as a result of the misstatements in Drain's financial statements becoming known. Under which of the following acts is Sharp most likely to prevail in a lawsuit against Ocean?
1. The Securities Exchange Act of 1934, the Securities Act of 1933, and the Sarbanes-Oxley Act of 2002 provide equal likelihoods of prevailing.
2. The Securities Exchange Act of 1934.
3. The Securities Act of 1933.
4. The Sarbanes-Oxley Act of 2002.

Answers

Thanks for the points

The Qur'an is believed to be the word of God, transmitted through the Prophet

answer both maybe please

The Qur'an is believed to be the word of God, transmitted through the Prophetanswer both maybe please

Answers

Answer:

Question 4: Mohammed

Question 5: Sunni

Explanation:

Islam is a religion founded by prophet Mohammed in 622, when he moved from Mecca to Mohammed. His word became the basis of the new religion, based on the teaching that there is only one God. Qur'an is the holy book of Muslims.

After Mohammed died, his successors divided into a couple of sects. Most of the Muslims today. Sunnis are representing most of the Muslims today, around 90 percent.


how
to improve the recognition of the lst year of life?

Answers

To improve the recognition of the first year of life, here are a few ways that can be implemented:

1. Interact with infants: Adults can interact with infants by talking, singing, or cooing to them. They can also look directly into the infant's eyes and smile. This is how infants can develop social and communication skills.

2. Playtime: Parents or caregivers can provide toys that are age-appropriate, which will enhance the infant's cognitive development. They can also encourage the infant to grasp or touch objects, which can develop the infant's fine motor skills.

3. Reading: Reading books to infants can help in their language development, which will improve their recognition skills.

4. Encourage tummy time: Tummy time helps in strengthening the baby's head, neck, and shoulders. Infants can also improve their vision, as they will see the world from a different perspective.

5. Responding to their cues: When the infants cry, adults should attend to their needs promptly, which can help build trust between the infant and the caregiver.

6. Engage in face-to-face communication: Infants love to look at faces, and this can be a way to enhance their recognition skills. When adults engage in face-to-face communication, they can observe the infant's reactions to the conversation, which can help in understanding their moods and emotions. In conclusion, adults can improve the recognition of the first year of life by interacting with infants, engaging in playtime, reading, encouraging tummy time, responding to their cues, and engaging in face-to-face communication.

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The _____ is an agreement that dramatically lowered trade barriers worldwide and created the new world trade organization (wto).

Answers

The General Agreement on Tariffs and Trade (GATT) is an agreement that dramatically lowered trade barriers worldwide and created the new world trade organization (WTO).

What is WTO agreement?

WTO agreements encompass all three types of property: products, services, and intellectual property. They set forth the guiding principles of the liberalization as well as its permitted exceptions. They include commitments made by each country to create and uphold open services markets as well as reduce customs tariffs and other trade barriers.

The General Agreement on Tariffs and Trade (GATT) was established to facilitate global trade. The World Trade Organization (WTO) extended the General Agreement on Tariffs and Trade (GATT) in 1995 after absorbing it.

The sole international organization in charge of enforcing rules governing international trade is the World Trade Organization (WTO). Its major objective is to ensure that trade proceeds as smoothly, reliably, and freely as possible.

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alexandra is told that research supports the value of cosmetic surgery for boosting self-esteem. belinda is told that the esteem-enhancing value of cosmetic surgery has been refuted by research. both women consider the research findings to be common sense. this best illustrates the power ofillusory correlation.the double-blind procedure.the placebo effect.hindsight bias.

Answers

Aexandra is instructed that research helps the cost of beauty surgical procedure for enhancing shallowness. belinda is advised that the esteem-improving cost of cosmetic surgical treatment has been refuted by means of research.

Studies is "innovative and systematic art work undertaken to growth the stock of know-how". It includes the impartial collection, employer and analysis of statistics to boom information of a topic or trouble.

Research is a process of systematic inquiry that includes collection of statistics; documentation of crucial data; and evaluation and interpretation of that information/records, in accordance with suitable methodologies set with the aid of unique expert fields and educational disciplines.

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A student decided to find the density of her house key to try and identify the type
of metal from which it is made. She found the volume of the key to be 5 mL and the
mass to be 39.5 g.
Using the chart above, from which type of metal is the key made?
HELPPPPP PLZZZZZ

A student decided to find the density of her house key to try and identify the typeof metal from which

Answers

Steel is the correct answer

Many people in north america believe that sports are.

Answers

Answer:

A Tradition

Explanation:

I'm not sure what you looking for chef

Answer:

what are you try to say? sir

believing that depression involves internal belief systems characterizes a. cognitive theories. b. biological theories. c. psychoanalytic theories. d. biosocial theories.

Answers

Cognitive theories (a) of depression focus on how individuals' thoughts, beliefs, and interpretations of events contribute to the development and maintenance of depressive symptoms.

These theories propose that negative and distorted thinking patterns play a significant role in the onset and persistence of depression. According to cognitive theories, individuals with depression tend to have negative self-perceptions, engage in self-blaming, have pessimistic views of the world, and interpret events in a negative light. They may also have cognitive biases, such as selective attention to negative information and overgeneralization of negative experiences.

By targeting these maladaptive thought patterns and helping individuals develop more realistic and positive thinking patterns, cognitive therapies aim to alleviate depressive symptoms. Cognitive-behavioral therapy (CBT) is a commonly used approach that incorporates cognitive restructuring techniques to challenge and modify negative thoughts and beliefs.

Overall, cognitive theories emphasize the role of internal belief systems and cognitive processes in the experience of depression.

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james is conducting interviews with students who have dropped out of school. he asks each student the same set of questions in an effort to determine what factors are important in terms of why students drop out. james is doing a(n)

Answers

In an effort to ascertain what elements are crucial in determining why students drop out, James poses an identical set of questions to every student. James is conducting a structured interviews.

In order to gather information on a topic, a structured interview focuses on asking questions in a predetermined sequence. They frequently have a quantitative bent. Structured interviews are best used when you already have a firm understanding of your subject.

There are numerous ways to conduct structured interviews. For instance, you may conduct them over the phone, in person, and online utilizing software like social medio or a video phone. In structured interviews, open-ended or closed-ended questions may be asked.

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what impact do you think gpa and extracurriculars might have on the college options available to you and how much you will have to pay?

Answers

GPAs and extracurriculars can have a significant impact on the college options available to a student, as well as the amount they may have to pay for their education.

Having a high GPA and a strong record of extracurricular activities can improve a student's chances of getting into more competitive and selective colleges, which may offer better financial aid packages, scholarships, or grants. This can significantly reduce the amount a student will have to pay for their education, making higher education more accessible.

On the other hand, a lower GPA or lack of extracurricular activities may limit a student's college options, as they may not be accepted into more competitive colleges, and may not be offered as much financial aid. This can increase the amount a student will have to pay for their education, making it more difficult for them to afford higher education.

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What role did Sybil Ludington play in the American Revolution?

Answers

Answer:

was a heroine of the American Revolutionary War. On April 26, 1777, at age 16, she made an all-night horseback ride to alert militia forces in the towns of Putnam County, New York, and Danbury, Connecticut, of the approach of British forces.

Explanation:

hope this helps:)

Answer:

Sybil Ludington was an American Revolutionary War Woman who became famous for her horseback ride through upstate New York to warn militia that British troops were raiding and burning Danbury, Connecticut.

Explanation:

Please mark brainliest ._.

To what does the term "going public" refer? a. action taken by a president to communicate directly with the people in order to influence public opinion and put pressure on Congress b. a public statement written by the president and attached to a particular bill to outline the president's interpretation of the legislation c. a public statement issued by the president declaring that if Congress passes a particular bill that the president dislikes, it will ultimately be vetoed d. an agreement between the United States and one or more foreign countries that is not a formal treaty, so it does not need Senate approval

Answers

Answer:

The term "going public" refers to:

a. action taken by a president to communicate directly with the people in order to influence public opinion and put pressure on Congress.

Explanation:

When a president goes public, that means he addresses the people directly in order to "sell" his programs. That is, instead of presenting his policy agendas to the Congress, the president presents it to the people first. By doing so, the president is able to get the people on his side, which pressures the Congress. However, such a tactic offers risk. If a president fails after "going public", he may appear ineffective.

Which of these is true of the relationship between the Indians and the
Jamestown settlers?
O A. The settlers outnumbered the Indians; yet the Indians were not
afraid of them.
O B. The Indians did not like the settlers but wanted to convert to their
religion.
C. The settlers looked down on the Indians, yet they were dependent
on the Indians for survival.
D. The Indians were afraid of the settlers because the settlers
considered them uncivilized.

Which of these is true of the relationship between the Indians and theJamestown settlers?O A. The settlers

Answers

C the settlers looked down on the Indians yet they were dependent on the Indians for survival

When should you use in-text citations within your paper? This is
APA Format
Group of answer choices
At the end of each sentence.
At the end of each paragraph if you are citing one source.
At the begin

Answers

In APA format, in-text citations should be used within your paper to attribute credit to the original source of information. The correct placement of in-text citations depends on the specific circumstances and the type of citation needed.

In-text citations in APA format are typically used to indicate the source of information when you directly quote, paraphrase, or summarize someone else's work. The general rule is to include an in-text citation immediately after the borrowed information. This means that in-text citations should be used at the end of each sentence or phrase where you have used information from a source. However, if you are citing the same source multiple times within a paragraph, you can place the in-text citation at the end of the paragraph. The goal is to ensure that readers can easily identify and locate the original source of the information you have referenced in your paper.

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Jessica spilt milk on herself at the lunch table. For the rest of the school day, she walks around, mortified that everyone is staring at the stain on her shirt. What does this experience illustrate? O Metacognition
O The personal fable O The invincibility fallacy
O The imaginary audience

Answers

The correct option is D, The experience described in the scenario illustrates the concept of the imaginary audience.

An audience refers to a group of individuals who are recipients of a message, performance, or presentation. They are the intended receivers of information, entertainment, or persuasion in various forms of communication, such as speeches, films, concerts, advertisements, or written content. The audience is crucial in determining the effectiveness and impact of the communication process.

Audiences can be diverse in terms of their demographics, interests, knowledge, and attitudes. They may consist of individuals with different backgrounds, ages, genders, cultural beliefs, and socioeconomic statuses. Understanding the audience is essential for communicators as it helps them tailor their message to suit the specific needs and preferences of the intended recipients.

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Which of the following is NOT a key component of emotional intelligence? a. accurately perceiving others' emotions b. understanding one's own emotions c. using emotions to make decisions d. preventing emotional feelings

Answers

The option that is NOT a key component of emotional intelligence is d. preventing emotional feelings.

Emotional intelligence comprises accurately perceiving others' emotions (a), understanding one's own emotions (b), and using emotions to make decisions (c). It is about recognizing, understanding, and managing emotions, both in oneself and in others, rather than suppressing or preventing them.

Developing emotional intelligence enhances self-awareness, empathy, communication, and decision-making, all of which contribute to better interpersonal relationships and overall well-being. Preventing emotional feelings would hinder this growth and prevent individuals from harnessing the power of emotions in a constructive manner.

Therefore, the correct answer is d. preventing emotional feelings.

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The idea of popular sovereignty, the idea that political authority belongs to the people, was a big part of this new constitution. So much so that the preamble to the constitution included?.

Answers

In American history, popular sovereignty, sometimes known as squatter sovereignty, was a divisive political theory that held that the citizens of federal territories should decide whether or not their territory would become slave or free states.

What is popular sovereignty?

In American history, popular sovereignty, sometimes known as squatter sovereignty, was a divisive political theory that held that the citizens of federal territories should decide whether or not their territory would become slave or free states. The idea of popular sovereignty holds that a state's authority and its government are established and upheld with the consent of its citizens, who are the source of all political power. Being a principle, popular sovereignty does not require any specific political implementation.

The phrase "popular sovereignty" was first used by Michigander Lewis Cass, a Democratic candidate for president in the 1848 election. Many southern congressmen began to challenge Congress' authority to decide the legal status of slavery in any area during the heated Wilmot Proviso debate.

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1) How does Canada’s justice system and the youth criminal justice act attempt to treat young offenders fairly and equality?

2) What role do Canada’s citizens and organizations play in the fairness and equality of Canada’s justice system for youth?

Answers

CANADA'S JUSTICE SYSTEM

1. The Canadian justice system and the Youth Criminal Justice Act (YCJA) aim to treat young offenders fairly and equally by recognizing that young people are still developing and are therefore less culpable for their actions than adults. The YCJA sets out specific procedures and principles that must be followed when dealing with young offenders, and it emphasizes the importance of rehabilitating and reintegrating young people into society.

Under the YCJA, young offenders have the right to be treated fairly and with dignity, and to have their privacy protected. They are also entitled to legal representation, and the YCJA requires that they be given an opportunity to participate in the decision-making process that affects their lives.

In addition, the YCJA emphasizes the importance of addressing the underlying causes of young people's offending behavior, such as poverty, social isolation, or mental health issues. This can help to ensure that young offenders are not unfairly punished for circumstances that are beyond their control.

2. Canadian citizens and organizations play a crucial role in ensuring the fairness and equality of Canada's justice system for youth. By participating in the criminal justice process, either as jurors, witnesses, or victims, they can help to ensure that the system is accountable and transparent.

Citizens and organizations can also advocate for changes to the justice system that would better serve the needs of young offenders, such as providing more resources for rehabilitation or addressing systemic issues that contribute to youth offending.

Citizens and organizations can play a role in educating young people about the justice system and their rights within it, which can help to promote a greater understanding and respect for the law among young people.

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What was the second major point of the treaty.
please help me :D

Answers

Germany has to pay $31.4 billion in reparations

what is high comedy?group of answer choicescartoons of political figures.physical comedy such as slapstickedy of character.a caricature.

Answers

The cartoons of political figures can be termed as High Comedy.

A kind of humor known as "high comedy" places an emphasis on wordplay, wit, and social standing. It typically places a focus on intellectual perspectives. High comedy frequently uses juxtaposition and contrast to make jokes

In his Essay on Comedy from 1877, George Meredith introduced the concept of High Comedy.

High comedy sometimes employs satire, which means that it may make light of current social and political situations and offer cutting criticism in an effort to challenge or question them.

High comedy also places a strong focus on human frailties. High comedies, on the other hand, don't engage the audience's emotions.

Therefore a style of comedy known as high comedy or pure comedy is one that features brilliant language, satire, stinging humor, wordplay, or life critique.

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Explain how discrimination would change the lives of people of color moving forward

Answers

Answer:

Discrimination is the unfair or prejudicial treatment of people and groups based on characteristics such as race, gender, age or sexual orientation.

Explanation:

I hope the short answer helps you

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