Solve please:
1/4x + 1/2 - 8 = 3x - 3/4

Answers

Answer 1

Answer:

x=-27/11

Step-by-step explanation:

This answer is x=-27/11


Related Questions

The temperature outside dropped 23 degrees in 6 hours. The final temperature was -6, what was the starting temperature?

Answers

The starting temperature would be 29 degrees.

What are the initial value and final value?

Initial value refers to the starting value or the value of a variable at the beginning of a process or time period. Final value refers to the end value or the value of a variable at the end of a process or time period. In the context of a mathematical function, the initial value would be the value of the function at the beginning of the domain and the final value would be the value of the function at the end of the domain.

If the temperature outside dropped 23 degrees in 6 hours. The final temperature was -6,

The starting temperature would be 29 degrees (-6 + 23).

Hence, the starting temperature would be 29 degrees.

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Ten balls in five lines Puzzle – Solution The puzzle Place 10 balls in 5 rows in such a way that each row contains exactly 4 balls.

Answers

Ten balls in five lines Puzzle – Solution The puzzle Place 10 balls in 5 rows in such a way that each row contains exactly 4 balls below figures are:

A puzzle is a sport, trouble, or toy that examines a person's ingenuity or understanding. In a puzzle, the solver is anticipated to position pieces together (or take them aside) in a logical manner, so that you can arrive at the appropriate or a laugh solution to the puzzle. There are special genres of puzzles, which include crossword puzzles, phrase-search puzzles, variety puzzles, relational puzzles, and good judgment puzzles. the academic take look at puzzles is referred to as enigmatology.

Puzzles are often created to be a form of leisure however they can also get up from critical mathematical or logical problems. In such cases, their solution can be a substantial contribution to mathematical research. Puzzles expand memory competencies, as well as the capability to devise, check ideas and solve troubles. even as completing a puzzle, children want to recollect shapes, colors, positions, and techniques to complete them.

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What is ittttttttttttttt

Answers

The value of (a)  125 / 78125 and  (b)  1296 / 7776.

What is exponential power?

In mathematics, power defines a base number raised to the exponent, where the base number is the factor that is multiplied by itself and the exponent denotes the number of times the same base number is multiplied.

To solve 5³ * 5⁻⁷, we can simplify the exponents first:

5³ = 125

5⁻⁷ = 1 / 5⁷

So, the expression simplifies to:

125 * (1 / 5⁷) = 125 / 78125

To solve 6⁴ * 6⁻⁵, we can simplify the exponents first:

6⁴ = 1296

6⁻⁵ = 1 / 6⁵

So, the expression simplifies to:

1296 * (1 / 6⁵) = 1296 / 7776

Hence, The value of (a)  125 / 78125 and  (b)  1296 / 7776.

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Skarleth is considering whether to apply for a credit card or debit card at her bank. The credit card will charge 3% interest if she does not pay her balance in full each month. If she spends $2,000 this month and doesn’t pay it back, how much will she owe in interest?

Answers

The interest on the spent of $2000 will be $60.

What is the percentage?

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Skarleth is considering whether to apply for a credit card or debit card at her bank. The credit card will charge 3% interest if she does not pay her balance in full each month. If she spends $2,000.

The amount of interest will be calculated as:-

Amount = 2000 x 3%

Amount = ( 2000 x 3 ) / 100

Amount = $60

Therefore, the interest on the spent of $2000 will be $60.

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1\2 y= 1 in standard form

Answers

Answer:

y=2

Step-by-step explanation:

Are these ratios equivalent 40/18 and 27/11

Answers

The ratios 40/18 and 27/11 are not equal because 20/9 and 3/1 are different fractions. They stand for various proportional connections between two quantities, in other words.

Why are there ratios not equivalent?

We need to see if the ratios of 40/18 and 27/11 fall to the same fraction when the numerator and denominator are both divided by their largest common factor (GCF).

Given that the GCF of 40 and 18 is 2, we can obtain 20/9 by reducing both the numerator and denominator of 40/18 by 2. Since the GCF of 27 and 11 is also 11, we obtain 3/1 when we divide the numerator and denominator of 27/11 by 11.

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Select the graph of the solution. Click until the correct graph appears.



| x | + 3 > 7

Answers

The inequality can be rewritten into:

x > 4 or x < -4

And the graph can be seen in the image at the end.

How to solve the inequality?

We want to solve the inequality below and then graph it, the inequality is:

|x| + 3 > 7

moving the 3 to the right side we get:

|x| > 7 - 3

|x| > 4

Now we can break the absolute value part into two:

x > 4

x < -4

That is the solution:

x > 4 or x < -4

The graph is the one below.

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help me please!!!!!!!

Answers

Answer: x= 4 and y= 540

You should read the corresponding values inorder to figure out the other value

the answers are 4 and 540.

4 goes in the blank under x and 540 goes in the blank under 360.

hope this helps.

Find the value of x.
Round to the nearest tenth.
X =
[?]°
А.
37
X
B
20
23
Law of Cosines: c² = a² + b² - 2ab cos C

Answers

The value of x is 28.4°. The solution has been obtained using the law of cosines.

What is law of cosines?

The law of cosines, commonly referred to as the cosine rule or the cosine formula, in trigonometry essentially connects the length of the triangle to the cosines of one of its angles.

Law of Cosines: c² = a² + b² - 2ab cos C

We are given a= 37, b=23 and x= 20

Using the law of cosines,

⇒x² = a² + b² - 2ab cos x

⇒20² = 37² + 23² - 2(37)(23) cos x

⇒20² = 37² + 23² - 2(37)(23) cos x

⇒400 = 1369 + 529 - 1702 cos x

⇒400 = 1898 - 1702 cos x

⇒1702 cos x = 1498

⇒cos x = 1498 /1702

⇒cos x = 0.88

⇒x = [tex]cos^{-1} (0.88)[/tex]

x = 28.4°

Hence, the value of x is 28.4°.

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The table shows the length, in inches, of fish in a pond.


11 19 9 15
7 13 15 28


Determine if the data contains any outliers. If so, list the outliers.
There is an outlier at 28.
There is an outlier at 7.
There are outliers at 7 and 28.
There are no outliers.

Answers

Answer:

Step-by-step explanation:

THE OUTLINER IS 28!

What is the best method for solving a quadratic formula?

Answers

The best method for solving a quadratic equation depends on the specific equation and the context in which it is being used. However, the quadratic formula is a universally applicable method and it is one of the most widely used methods for solving quadratic equations.

The quadratic formula is a method for solving a quadratic equation, which is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants.

The quadratic formula is:

x = (-b ± √(b^2 - 4ac))/(2a)

It allows to find the solutions or roots, x, of a quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are constants.

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Find the Domain:
And Range:

Answers

Domain: Real numbers.

Range: Set of output value.

What is the Range and domain of the function?

The domain of the function is the set of all input values, or the set of x-values, for which the function is defined.

The range of the function is the set of all possible output values, or the set of y-values, that the function can produce.

The domain of the function is all real numbers since there are no restrictions on the input x.

The range of the function is the set of output values, which in this case is {5}.

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Do these measurements produce a triangle? Yes or no AND WHY!
a.3 in, 5 in, 7 in
b. 5 cm, 7 cm, 13 cm
c. 14.23 ft, 18.23 ft, 36.23 ft

Answers

The measurements in (a) 3 inch, 5 inch, 7 inch  produce a triangle. Other two measurements do not produce a triangle.

What is triangle and what their properties are?

A triangle is a three-sided polygon that consists of three edges and three vertices.

The properties of the triangle are:

The sum of all the angles of a triangle (of all types) is equal to 180°.The sum of the length of the two sides of a triangle is greater than the length of the third side.

Using second properties we find that which of the following measures produce a triangle.

In a) 3 inch, 5 inch, 7 inch, the sum of the length of two smallest sides are

3 + 5 = 8 inch, which is greatest from the third side.

So this measures produce a triangle because the sum of the length of the two sides of a triangle is greater than the length of the third side.

In b) 5cm, 7cm, 13 cm, the sum of the length of two smallest sides are

5 + 7 = 12 cm, which is smallest from the third side

So this measures does not produce a triangle because the sum of the length of the two sides of a triangle is smaller than the length of the third side.

In c) 14.23ft, 18.23ft, 36.23ft, the sum of the length of two smallest sides are

14.23 + 18.23 = 32.46ft, which is smallest from the third side.

So this measures does not produce a triangle because the sum of the length of the two sides of a triangle is smaller than the length of the third side.

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The graph shows a scuba divers ascent over time. Use the graph to find the slope of the line. Complete the description of what the slope means in context.

Answers

The slope of the line is 0.05. This indicates that the diver ascends at a rate of 0.05 m/s.

What is slope?

The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.

Given that, the graph shows a scuba diver ascent over time.

We see that,

He goes up 2 meters in every 40 seconds,

then, in 20 seconds, he will go 1 meter up

so,

1/20 = 0.05

Hence, the slope of the line is 0.05. This indicates that the diver ascends at a rate of 0.05 m/s.

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Elementary and Middle School Mathematics: Teaching Developmentally.

Answers

"Elementary and Middle School Mathematics: Teaching Developmentally" is a widely used textbook for teaching math at elementary and middle school levels.

What is developmentally ?

In education, the term "developmentally" refers to the idea that students should be taught in a way that is appropriate for their developmental level. Developmental teaching is a student-centered approach that takes into account the students’ abilities, interests, and needs as they learn.

Elementary and Middle School Mathematics: Teaching Developmentally is a textbook that provides an overview of the principles and practices of teaching mathematics in the elementary and middle school levels. It is designed to help teachers understand the mathematical concepts and skills that students need to learn at each grade level, as well as the best ways to teach those concepts and skills. The book covers a wide range of topics, including number sense and operations, algebra, geometry, measurement, and data analysis. It also provides strategies for differentiating instruction, using technology, and assessing student learning. The book is written by John A. Van de Walle and Karen S. Karp, and it is widely used as a textbook for teacher education programs and professional development workshops.

"Elementary and Middle School Mathematics: Teaching Developmentally" is a widely used textbook for teaching math at elementary and middle school levels.

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Determine the sample of the following situation :Mr.Blue wants to randomly select 10 athletes on the track team to lead stations for the day. Need answer quick please help

Answers

The sample when Mr.Blue wants to randomly select 10 athletes on the track team to lead stations for the day is 20 athletes.

What is a sample?

Sampling is the process of choosing a portion of a statistical population to estimate characteristics of the entire population in statistics, quality control, and survey methodology. Samples that are representative of the population under study are sought after by statisticians.

A representative subset of a population is chosen, processed, and analyzed using the statistical analysis technique known as data sampling. It is also used to spot trends and extrapolate patterns in a population as a whole. The sample here are the 10 athletes picked.

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ignore my dirty computer

help please :))

Answers

Answer:

The sentence "Eight more than the quotient of a number and 4 equals 5" can be translated into the following equation:

(b / 4) + 8 = 5

Where b is the unknown number, and 4 is the divisor.

Answer:

b = - 12

Step-by-step explanation:

let the number be b

the quotient ( division ) of b and 4 is [tex]\frac{b}{4}[/tex] , then

[tex]\frac{b}{4}[/tex] + 8 = 5 ← equation

to solve for b

subtract 8 from both sides

[tex]\frac{b}{4}[/tex] = - 3 ( multiply both sides by 4 to clear the fraction )

b = - 12 ← value of b

Anyone know the answer ?x

Answers

The probability that a student, chosen at random, does not study Chemistry is 0.49.

What is Probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

From the Venn diagram -

The number of students that study biology and physics = 2

The number of students that study biology and chemistry = 6

The number of students that study chemistry and physics = 4

The number of students that study only physics = 5

The number of students that study only biology = 7

The number of students that study only chemistry = 8

The number of students that study all the subjects = 3

The number of students that study none = 6

So, the total number of students a = 2 + 6 + 4 + 5 + 7 + 8 + 3 + 6 = 41

The number of students that study chemistry = 8 + 6 + 3 + 4 = 21

The number of students that do not study chemistry b = 41 - 21 = 20 students

The probability chosen at random that child does not study chemistry =  b/a -

= 20/41

= 0.49

Therefore, the probability value is 0.49.

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PLEASE HELP WILL GIVE BRAINLIST

The Chess Club president brought donuts to the club meeting each week. As the club grew, more donuts were needed so that each member could have a donut. The table below shows the ratios of boxed donuts to the cost.


Donuts 2 4 B 8
Cost A 31.60 39.50 C


Determine which table has the correct values for A, B, and C.

A Donuts 2 4 5 8
Cost 15.80 31.60 39.50 63.20

B Donuts 2 4 6 8
Cost 7.90 31.60 39.50 63.20

C Donuts 2 4 7 8
Cost 7.09 31.60 39.50 56.72

D Donuts 2 4 6 8
Cost 15.80 31.60 39.50 56.72

Answers

The table which has the correct values for A, B, and C is;

A. Donuts    2        4          5           8

   Cost      15.80  31.60   39.50   63.20

What is a proportional relationship?

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

k is the constant of proportionality.y and x represent the variables in a proportional relationship.

Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 31.60/4

Constant of proportionality, k = 7.9

When the value x = 2, the value of A can be calculated as follows;

y = kx

A = 7.9 × 2

A = 15.80

When the value y = 39.50, the value of B can be calculated as follows;

x = k/y

B = 39.50/7.9

B = 5.

When the value x = 8, the value of C can be calculated as follows;

y = kx

C = 7.9 × 8

C = 63.20.

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What is the value of x?

Answers

Answer: number c I think

Step-by-step explanation:

A study was done to investigate the relationship between a new anti-inflammatory medicine and weight gain. The correlating linear
model is shown below, where x represents the number of days on the medicine, and y represents the weight gain, in pounds.
Interpret the slope.
y = 0.71

Answers

For the linear function y = 0.7x, option A: An additional day on the medicine is associated with 0.7 pounds of weight gain is the correct answer.

What is a linear function?

A linear function is a function that, when plotted, creates a straight line. Typically, it is a polynomial function with a maximum degree of 1 or 0. Nevertheless, calculus and linear algebra are also used to represent linear functions.

The given linear function is y = 0.7x.

Where x represents the number of days on the medicine.

y represents the weight gain, in pounds.

The slope intercept form is y = mx + b, where m is slope.

So, the slope of y = 0.7x is m = 0.7.

If x = 2 , then y will be -

y = 0.7(2)

y = 1.4

If x = 3 , then y will be -

y = 0.7(3)

y = 2.1

Therefore, it can be seen that when the number of days on the medicine is increased the weight gain also increases with 0.7 pounds.

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PLS DO NUMBER 5 WILL MARK BRAINLIEST AND ADD 100 MORE POINTS HURRY PLEASE! THANK YOU

Answers

Answer: The 2nd table (blue)

Step-by-step explanation:

Find the missing side, round to the nearest tenth.

Answers

Answer:

x=40 HZ

..............

What is the intermediate step in the form (x+a)2=b as a result of completing the square for the following equation?

Answers

The completing square form of the equation is  [tex](x+1)^2=-25[/tex].

What is completing square method?

By altering the equation's form so that the left side is a perfect square trinomial, a quadratic equation can be solved using the "Completing the Square" approach. One approach to locating the roots of the given quadratic equation is to complete the square method.

Here the equation [tex]x^2+2x=-26[/tex]

To completing the square of the equation add 1 on both sides then,

=> [tex]x^2+2x+1=-26+1[/tex]

=> [tex]x^2+2.x.1+1^2=-25[/tex]

=> [tex](x+1)^2=-25[/tex]

Hence the completing square of the equation is  [tex](x+1)^2=-25[/tex].

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Which of the following best described the line that is passing through the ordered pairs given below? Select all that apply

(-4, 6) & (-4, 1)

Answers

The slope of the line is undefined.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (-4, 6) and (-4, 1)

Now,

Since, The equation of line passes through the points (-4, 6) and (-4, 1)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (1 - 6) / (-4 - (-3))

m = - 5 / 0

m = ∞

Thus, The slope of the line is undefined.

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Andrew bought a fish bowl that holds 1/3 gallons of water. Andrew used a

small container to fill the fish bowl. If it took 5 smaller containers to fill the

fish bowl, how many gallons of water fills one small container?


Answers

One small container fills 1/15 gallons of water. Therefore, if the fish bowl can hold 1/3 gallons of water, then one small container can hold 1/15 gallons of water.

1/3 gallons of water in the fish bowl divided by 5 smaller containers = 1/15 gallons of water in one small container.

Andrew purchased a fish bowl that has the capacity to hold 1/3 gallons of water. To fill the fish bowl with water, he used smaller containers. It took him 5 of these smaller containers to fill the fish bowl. This means that each small container filled 1/15 gallons of water. Therefore, if the fish bowl can hold 1/3 gallons of water, then one small container can hold 1/15 gallons of water.

One small container fills 1/15 gallons of water.

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which two rational numbers does the square root of 14 lies between?

Answers

The value of √14 lies between 3.70 and 3.75.

What is Radical?

The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.

Given:

We have to √14.

So, the value of √14 ≈ 3.74

Now, we can solve for all the answer .

A) 19/6 = 3.1666...

22/7 = 3.1428...

So, It cannot be the answer.

B) Doesn't need to be solved.

3.17

3.71

So, It cannot be the answer.

C)√4 = 2

√9 = 3

So, It cannot be the answer.

D) Doesn't need to be solved.

3.70

3.75

So, It can be the answer.

Hence, √14 lies between 3.70 and 3.75

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two out of three vehicles in a parking lot are SUV's . There are 18 SUV's in the parking lot . How many vehicles are in the parking lot?

Answers

Answer:

27 vehicles

Step-by-step explanation:

2/3 vehicles = 18

1/3 vehicles = 18 ÷ 2 = 9

3/3 vehicles = 9 x 3 = 27

The temperature changes from 45.2 degrees at 8:00 pm to 32.7 degrees at 1:00 am.
What rational number represents the average change in temperature per hour?

Answers

There is the average decrease in temperature which is -2.5 degrees per hour.

Explain the term average rate of change?The average rate where the one quantity changes in relation to another's change is referred to as the average rate of fluctuation function. A method that determines the amount of variation in one item divided mostly by corresponding amount of variation in another is known as just an average rate of change function.

For the given data:

Temperature at 8:00 pm : 45.2 degrees Temperature at 1:00 am : 32.7 degrees

So,

Difference in temperature =  32.7 - 45.2

                                            =  -12.5

Total time from 8:00 pm to 1:00 am = 5 hours.

             

Then,

Average change in temperature per hour = -12.5 / 5 = -2.5 degrees.

Thus, there is the average decrease in temperature which is -2.5 degrees per hour.

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conjecture for the relationship between the volume of a sphere with a radius that equals to y and the volume of a sphere with a radius equal to 2y

Answers

The relationship between the volume of a sphere with a radius that equals to y and the volume of a sphere with a radius equal to 2y is V₂ = 8V₁.

What is volume?

The volume of a thing is the area that it takes up in three dimensions. Simply said, a thing occupies space.

The volume of the sphere,

= 4/3πr³, with the radius r.

So, if the radius of the sphere is y.

Then the volume of the sphere,

V₁ = 4/3πy³.

So, if the radius of the sphere is 2y.

Then the volume of the sphere with the radius 2y,

V₂ = 4/3π(2y)³.

= 8(4/3)π(y)³.

= 8 x the volume of the sphere with the radius y.

= 8V₁

Therefore, the relationship is V₂ = 8V₁.

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Tamika invested $470 in an account paying an interest rate of 8 1/4% compounded continuously. After 14 years, how much more money would Natalie have in her account than Tamika, to the nearest dollar? What was the purpose of selling bonds by the US government? What are the 5 armed services? what was the message of thomas paines pamphlet the crisis? in 1870, georgia was readmitted into the union after the stateWhat was the last state to be readmitted to the Union and what year? Into the Wild *Enrichment* OUTSIDE articleDeath of an Innocent : How Christopher McCandless Lost His Way in the WildLearning Focus: I can independently read and comprehend grade-level texts [CCSS.ELA.11-12.RI.10]Directions: The article you are about to read is what inspired Jon Krakauer to write the novel, Into the Wild. This article, when published, developed and inspired more mail and response than any other article had in the magazines history. Krakauer felt such a connection to Chris that he traced his journey for a year, turning it into a national bestseller that has inspired audiences since its publication in 1996. As you read the article, complete the chart below, using evidence to support your claims. Question/ CommentaryYour Answer1. James Gallien is not the first person to meet Alex (aka Chris) on his journey, but he is the man that brings him to the final destination of his journey where Chriss body is later found. He noticed that Chris did not fit the typical look of a hitchhiker, and seemed to have an educated air about him. What worries Gallien about Chris? Why does he try to dissuade him from beginning his journey?2. On p. 2, Krakauer provides some insight into Chriss character and personality. What type of young man was Chris? What inspired him to begin his journey? What were his goals?3. On p. 3, Krakauer provides insight into the day that Chris was found in the bus. In paragraph 19, Westerberg states that he believed that Chris did too much thinking. Why do you think that Westerberg sees this as a bad thing? What does he truly mean by this statement?4. On p.4, Krakauer provides us with clues about Chriss character. What do these clues tell us about Chris? What is your opinion of him, & what did he believe was important in life?TIP: Leo Tolstoy is a Russian author who wrote the novels Anna Karenina & War and Peace. He was a moral thinker, social reformer, and a believer of a literal interpretation of social values.5. On p. 5-6, Krakauer discusses the final postcard that Chris sent Westerberg. Do you believe, as some people did, that Chris really entered the wild with the intention of dying? Why/ why not? Also, what was the relationship between Chris and Westerberg?6. On p. 5-6 Krakauer makes a personal connection to Chris. Explain it. What does he mean when he states Thats a very different thing from wanting to die? (paragraph 39) TIP: Hubris is the Greek word for excessive pride. This is often found as one of the qualities of a tragic hero according to the Greek philosopher Aristotle. 7. On p. 7, we are given more information about Chris as a teenager, and how his cross-country teammates respected him. What did his workout Road Warriors foreshadow about his future life and travels?8. On p. 8, Krakauer discusses how Chris changed in college. What do you think drove Chris to become an introvert? What aspects of college life changed Chris, and how did this impact him in his future choices?TIP: Introvert: a person characterized by concern primarily with his own thoughts and feelings9. On p. 10, Krakauer compares Chris to monks. What similarities does he believe Chris shared with them? What does this illustrate about Krakauers opinion of Chris as an individual?10. On p. 11, Krakauer describes Chriss first days after arriving in Alaska. Briefly describe his first weeks in seclusion there, and the obstacles he faced.TIP: Extremist: a person who goes to extremes, especially in political matters.Aesthetic Voyager: concerned with the study of the mind and emotions in relation to the sense of beauty.11. On p. 12, Krakauer delves into the final moments of Chriss journey. Do you think that Chris was truly ready to go home? What do you think he meant by the entry Family happiness?12. Toward the bottom of p. 12, Krakauer explains Chriss decisions and the notion of him being extremely obsessed with the idea of being self-reliant. Do you think that Chris took this idea to the extreme? Why or why not?13. On p. 13-14, Krakauer explains Chriss final days, and his succumbing to starvation. Look again at the verses of the poem that Chris tore out of his book. Why do you believe he focused on these specific lines? What do they mean? how do the four main oop principles (inheritance, encapsulation, abstraction, and polymorphism) work together to make a well-designed application? how do they allow a programmer to create more reusable and maintainable code? What was the term for the forced removal and relocation of Japanese Americans living on the West Coast during World War II internment detention concentration custody? In which quadrant does the midpoint of the line segment joining the points 1 2 and 3 for lice? in teaching a patient with sle about the disorder, the nurse knows that the pathophysiology of sle includes the production of a variety of autoantibodies directed against components of the cell nucleus??