Which function has a horizontal asymptote at y = 3?

Which Function Has A Horizontal Asymptote At Y = 3?

Answers

Answer 1

Answer: A) [tex]f(x)=\frac{6x^2-x+4}{2x^2-1}[/tex]

Step-by-step explanation:

Line [tex]y=L[/tex] is a horizontal asymptote of the function [tex]y=f(x)[/tex], if either [tex]\lim_{x \to \infty} f(x)=L[/tex] or [tex]\lim_{x \to \infty} f(x)=L[/tex], and [tex]L[/tex] is finite.

calculate the limits:

[tex]\lim_{x \to \infty} (\frac{6x^2-x+4}{2x^2-1})=3[/tex]

[tex]\lim_{x \to -\infty} (\frac{6x^2-x+4}{2x^2-1})=3[/tex]

Thus, the horizontal asymptote is [tex]y=3[/tex]


Related Questions


top question only fast pls

Answers

The volume of the triangular prism is V = 18ft³

What is the volume of the prism?

The volume of the prism is equal to the area of the triangular face, times the length of the prism, which is 9ft.

Remember that the area of a triangle of base B and height H is:

A = B*H/2

Here we can see that the base is 2ft and the height is 2ft, then the area of the triangular face is:

A = 2ft*2ft/2 = 2ft²

And thus, the volume of the prism is:

V = 2ft²*9ft

V = 18ft³

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which point lies in the solution set?

A. (4, –0.5)
B. (3, –2.5)
C. (–2.5, 4)
D. (–4.5, –3)

Answers

The point that lies in the solution set of (x - 2)²/25 + (y + 3)²/4 < 1 is B. (3, –2.5)

How to determine the point that lies in the solution set?

From the question, we have the following inequality expression that can be used in our computation:

(x - 2)²/25 + (y + 3)²/4 < 1

Also, we have

A. (4, –0.5)

B. (3, –2.5)

C. (–2.5, 4)

D. (–4.5, –3)

Next, we test the options as follows

A. (4, –0.5)

(4 - 2)²/25 + (-0.5 + 3)²/4 < 1

1.7225 < 1  -- false

B. (3, –2.5)

(3 - 2)²/25 + (-2.5 + 3)²/4 < 1

0.1025 < 1   -- true

Hence, the point that lies in the solution set is B. (3, –2.5)

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A student has 40 dimes and nickels. Their total value is $2.95. If
de number of dimes and n= number of nickels, this system of equations
represents the situation:
d+n=40
0.10d+0.05n 2.95
How many of each type of coin are there? Solve the system to answer the
question.
A. 10 dimes and 30 nickels
B. 21 dimes and 19 nickels
C. 19 dimes and 21 nickels
D. 20 dimes and 20 nickels

Answers

Answer: C. 19 Dimes and 21 Nickels

19 x .10 = 1.90$
21 x .05 = 1.05$
1.90 + 1.05= 2.95$


1 dime is .10 (10 cents)
1 nickel is .05 (5 cents)

What is the length of side CB to one decimal place?
B
A
10
53°
C

Answers

The length of side CB to one decimal place is 89.3.

To find the length of side CB in the given triangle, we can use the sine rule. The sine rule states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In this case, we have the angle C as 53° and the side opposite to it, side CB, as the unknown. Let's denote the length of side CB as x.

According to the sine rule:

sin(C) / x = sin(A) / AB

We know that angle A is 37° and AB is 120 units. Plugging in the values:

sin(53°) / x = sin(37°) / 120

To find x, we can rearrange the equation:

x = (120 * sin(53°)) / sin(37°)

Calculating this expression gives us:

x ≈ 89.32

Rounding this value to one decimal place, the length of side CB is approximately 89.3.

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Aaron kicked a soccer ball with an initial velocity of 39 feet per second at an angle of 44° with the horizontal. After 0.9 seconds, how far has the ball traveled horizontally? A. 11.4 ft B. 24.4 ft C. 12.3 ft D. 25.2 ft

Answers

The ball has traveled approximately 25.24 feet Horizontally.The correct answer is D. 25.2 ft.

The horizontal distance traveled by the soccer ball after 0.9 seconds, we can use the equation:

horizontal distance = initial velocity * time * cos(angle)

Substituting the given values:

initial velocity = 39 ft/s

time = 0.9 s

angle = 44°

horizontal distance = 39 ft/s * 0.9 s * cos(44°)

Calculating:

horizontal distance ≈ 39 ft/s * 0.9 s * 0.71934 ≈ 25.24 ft

Therefore, after 0.9 seconds, the ball has traveled approximately 25.24 feet horizontally.

The correct answer is D. 25.2 ft.

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Under ideal conditions, the population of a certain species doubles every nine years. If the
population starts with 100 individuals, which of the following expressions would give the
population of the species t years after the start, assuming that the population is living
under ideal conditions?

Answers

P= 2T+ 100

T= years
P=population

can someone please help me on this algebra 13 homework! PLS QUICK!

Answers

The function y=x+3 has the greatest y intercept.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The given function is y=x, it has y intercept which is zero

The given function is y=-x, it has y intercept which is zero

Function is y=x+3, it has y intercept which is three

Function is y=2x, it has y intercept which is zero

Hence, the function y=x+3 has the greatest y intercept.

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Suppose that 15% of all American use CNN as their primary source of news. A random sample of 200 Americans is selected. What is the probability that is your sample of 200 Americans that proportion that us CNN as their primary news source is at least 0.21?

Answers

The probability that in a sample of 200 Americans, the proportion that uses CNN as their primary news source is at least 0.21 is 49.6%.

What is the probability?

The probability is determined using the normal approximation to the binomial distribution.

Given that the sample size is large (n = 200) and the probability of success (p = 0.15) is not too close to 0 or 1, the mean (μ) and standard deviation (σ) of the binomial distribution, will be:

μ = n * p

μ = 200 * 0.15

μ = 30

σ = √(n * p * (1 - p))

σ = √(200 * 0.15 * (1 - 0.15))

σ ≈ 4.29

Then, the z-score corresponding to the proportion of 0.21 is:

z = (x - μ) / σ

z = (0.21 - 0.15) / 4.29

z ≈ 0.014

Using a calculator, the probability of a z-score of 0.014 is approximately 0.504.

Hence, the probability of obtaining a proportion at least 0.21, is:

Probability = 1 - 0.504

Probability ≈ 0.496

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A school asks students what type of sports they play. Complete the two-way table for the survey data. Find the answer for the missing letters and show your work as to how you arrived at each answer.

Answers

Answer: b: 58-22=36

A=37 68-22-9

d=99 37+62

c=29 34-9

Step-by-step explanation:

A square has an area of 56 units, find the length of the side in simplest form. Has to be an Improper fraction.

Answers

The length of the side of the square in simplest form is 2sqrt(14).

The area of a square is given by the formula [tex]A = s^2[/tex], where A is the area and s is the length of a side.

We are given that the area of the square is 56 units, so we can set up the equation:

[tex]56 = s^2[/tex]

To solve for s, we can take the square root of both sides of the equation:

sqrt(56) = [tex]sqrt(s^2)[/tex]

We can simplify the square root of 56 by factoring it:

sqrt(56) = sqrt(222*7) = 2sqrt(14)

So, we have:

2sqrt(14) = s

This is an improper fraction because the numerator is larger than the denominator. Therefore, the length of the side of the square in simplest form is 2sqrt(14).

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A family drove 592 miles during their trip this summer. In the winter they drove 376 miles during their trip . How many more miles did the family drive over the summer than over the winter . Explain !

Answers

Answer: 216

Step-by-step explanation:

592-376

592-300= 292

292-70= 222

222-6= 216

A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 30% 30 % of this population prefers the color green. If 20 20 buyers are randomly selected, what is the probability that exactly 1 1 buyer would prefer green? Round your answer to four decimal places.

Answers

The probability that exactly 1 buyer would prefer green P ( A ) = 0.1854

Given data ,

A researcher wishes to conduct a study of the color preferences of new car buyers

And , 30 % of this population prefers the color green

where 20 buyers are randomly selected

Now , binomial distribution problem with n = 20, p = 0.30 and we want to find the probability of exactly 1 buyer preferring green.

The formula for the probability mass function of a binomial distribution is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) = n! / (k! * (n-k)!)

Plugging in the values, we get:

P(X = 1) = (20 choose 1) * 0.30¹ * 0.70¹⁹

= 20 * 0.30 * 0.70¹⁹

= 0.1854 (rounded to four decimal places)

Hence , the probability that exactly 1 buyer would prefer green is 0.1854

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determine what type of model bets fits the given situation: A $500 raise in salary each year

Answers

Answer:A linear model

Explanation:

The type of model that best fits the situation of a $500 raise in salary each year is a linear model.

In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.

In the given case, the dependent variable is the salary and the independent variable is the year.

You may build a table to show that for increments of 1 year the increments of the salary is $500:

Year         Salary        Change in year         Change in salary

2010           A                           -                                       -

2011           A + 500     2011 - 2010 = 1          A + 500 - 500 = 500

2012          A + 1,000   2012 - 2011 = 1          A + 1,000 - (A + 500) = 500

So, you can see that every year the salary increases the same amount ($500).

In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).              

In this case, m = $500 and b is the starting salary: y = 500x + b.

ONLY NEED PT 2 1st blank is: -1.5,-1.07,=0.70,-0.67,0.67,0.70,1.07,1.5,4,27,33.
2nd blank is:Means, Medians, modes, Standard deviatins, Ranges.
3rd blakn is Below, Above
4th blank is: Means, Medians, modes, Standard deviatins, Ranges.

Answers

The z-score is calculated as z-score.

The score x = 33 is 1.5 standard deviations above the mean of 27.

How to Calculate the z-score?

To find the z-score for x = 33 in a normal distribution with a mean of 27 and a standard deviation of 4, we can use the formula for calculating the z-score:

z = (x - μ) / σ

where in this case, x = 33, μ = 27, and σ = 4. Plugging these values into the formula, we can calculate the z-score:

z = (33 - 27) / 4

z = 6 / 4

z = 1.5

The z-score for x = 33 is 1.5.

The z-score represents the number of standard deviations that a given value (x) is away from the mean (μ) in a normal distribution. It indicates how many standard deviations a data point is above or below the mean.

In this context, a z-score of 1.5 for x = 33 means that the value 33 is 1.5 standard deviations above the mean of 27.

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What’s the value of x?

Answers

Answer:

The answer is 8

Step-by-step explanation:

/x/ // /8/

x=8

Find the equation of the line passing through the point (–1, 5) and perpendicular to the line y = – 3x + 4.

A) 3y = –x + 16

B) y = –3x + 8

C) y = –3x + 2

D) 3y = x + 16

Answers

Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 4 ← is in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (- 1, 5 ) into the partial equation

5 = - [tex]\frac{1}{3}[/tex] + c ( add [tex]\frac{1}{3}[/tex] to both sides )

5 [tex]\frac{1}{3}[/tex] = c ⇒ c = [tex]\frac{16}{3}[/tex]

y = [tex]\frac{1}{3}[/tex] x + [tex]\frac{16}{3}[/tex] ( multiply through by 3 to clear the fractions )

3y = x + 16

1. The population of a town was 112 in 2014. The population doubles every year.
(a) Use the exponential growth model to write an equation that estimates the population tyears after
2014.
(b) Estimate the population of the town in 2023. Show your work.
Answer:

Answers

The estimated population of the town in 2023 is 57,344.

(a) Let P be the population in t years after 2014.

Since the population doubles every year, we can use the formula :

P = P₀(2)ⁿ, where P₀ is the initial population in 2014.

We have P₀= 112, so the equation is P = 112(2)ⁿ.

(b) To find the population in 2023, we need to find t when t + 2014 = 2023.

So t = 2023 - 2014 = 9.

Substituting t = 9 into the equation from part (a), we get:

P = 112(2)⁹

P ≈ 57,344

Therefore, the estimated population of the town in 2023 is 57,344.

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x=1
x=3
z=x-25y
print(z)

Answers

The output of the program for the variable z is -22 or it returns an error if z = x - 25y

Evaluating the output of the program

From the question, we have the following parameters that can be used in our computation:

x = 1

x = 3

z = x - 25y

print(z)

The value of the variable y is not given

So, the program would return an error

However, if the complete program is as follows (removing the variable y)

x = 1

x = 3

z = x - 25

print(z)

Using the above as a guide, we have the following:

The final value of x is 3

So, we have

z = 3 - 25

Evaluate

z = -22

This means that the output of the program for z is -22

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3. In a data set, the mode, median, and mean are all equal. Which data set below fits this description? A. 26, 39, 39, 39, 52 B. 26, 27, 28, 28, 39 C. 15.0, 15.5, 16.0, 16.0, 21.5 105, 110, 110, 116, 120​

Answers

A. 39, In Order of Least to Greatest 39 is in Middle, Which is Median. Mean Equals to Add All Numbers and Then Divide By How Many are Left. Mode is the Most Frequent Number.

One shirt at H&M cost $7. what is the cost of 40 shirts

Answers

Answer:

$280

Step-by-step explanation:

7•40=$280

Can someone answer and provide an explanation for these problems?

Answers

The equation for each circle is given as follows:

36) (x - 2)² + (y - 15)² = 4.

37) (x + 8)² + (y + 18)² = 25.

38) (x - 11)² + (y + 9)² = 49.

39) (x - 13)² + (y + 8)² = 36.

What is the equation of a circle?

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

For item 36, the center is given as follows:

(-3, 11)

After the translation, the center will be given as follows:

(2, 15)

Hence the equation is given as follows:

(x - 2)² + (y - 15)² = 4.

For item 37, the center is given as follows:

(-3, -14)

After the translation, the center will be given as follows:

(-8, -18)

Hence the equation is given as follows:

(x + 8)² + (y + 18)² = 25.

For item 38, the center is given as follows:

(11, -9).

Hence:

(x - 11)² + (y + 9)² = r².

Point (18, -9) is on the circle, hence the radius squared is obtained as follows:

r² = (18 - 11)² + (-9 + 9)²

r² = 49.

Hence the equation is:

(x - 11)² + (y + 9)² = 49.

For item 39, the center is given as follows:

(13, -8).

Hence the equation is:

(x - 13)² + (y + 8)² = r².

Point (7, -8) is on the circumference of the circle, hence the radius squared is obtained as follows:

r² = (7 - 13)² + (-8 + 8)²

r² = 36.

Hence the equation is given as follows:

(x - 13)² + (y + 8)² = 36.

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Select the correct answer.

Which coefficient matrix represents a system of linear equations that has a unique solution?

Answers

The coefficient matrix A represents a system of linear equations that has a unique solution.

In a system of linear equations, the unique solution exists when the coefficient matrix has full rank and the determinant of the matrix is non-zero.

The other coefficient matrices listed do not have these properties.

1.  [[6, 0, - 2]

     - 2, 0, 6

        1, - 2, 0]

has a determinant of zero, indicating that the system of equations is dependent and does not have a unique solution.

Similarly, the matrices

[5, 10, 5

 4, 1, 4

- 1, - 2, - 1]

and, [2, 0, - 2

        - 7, 1, 5

          4, - 2, 0]

also do not satisfy the conditions for a unique solution.

Therefore, the coefficient matrix A represents a system of linear equations that has a unique solution.

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What is the end behavior of:
(2x ^ 2 - 5) / (x ^ 2 - 1)

A) x -> ∞ : f(x) -> 0

B) x -> ∞ : f(x) -> 2

C) f(x) -> - ∞ : x -> ∞

D) x -> ∞ : f(x) -> ∞

Answers

The given function does not have an end behavior because it is not a polynomial function.

What is the end behavior of a function?

The end behavior of a function refers to how the function behaves or approaches as the input values (x-values) of the function become extremely large (approaching positive infinity) or extremely small (approaching negative infinity).The long term behavior of the function when x moves towards the ends of the coordinate plane can be predicted.

In a polynomial function, the leading coefficient and degree of the function often determine the polynomial function.

The given function is;

f(x) = 2x² - 5 / x² - 1

The end behavior of this function does not exist because this is not a polynomial.

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PLEASE HELP ASAP!!!!!!

Answers

Answer:

A. Using the commutative property

Step-by-step explanation:

Because there is no use of commutative property in the solution process.

Answer:

A) Using Commutative property

Step-by-step explanation:

In step 1, it used distributive property when the number 5 is distributed inside of the equation in the parenthesis.

In Step 4, dividing both sides by 10 to further simplify the equation

In step 2, you combined like terms and it results to the equation in step 3

Adam’s prepaid card charges a one-time opening fee and a monthly fee. The table below shows his total fees after x months.

x # of months y total fees ($)

2 27
3
4
5 60

a. How much is the initial opening fee?

b. How much is the monthly maintenance fee?

c. Write an equation to model Adam’s fees over time.

Answers

Based on a system of equaitons, the initial opening fee (one-time payment) is $5.00, the monthly maintenance fee is $11.00, while an equation that models Adam's fees over time in months, x is y = 11x + 5.

What is a system of equations?

A system of equations or simultaneous equations are two or more equations solved concurrently or at the same time.

An equation is a mathematical statement showing the equality or equivalence of two or more algebraic expressions.

While algebraic expressions combine variables with numbers and mathematical operands, equations use the equal symbol (=).

Total Fees after x months

x = # of months    y = total fees ($)

2                                      27

3                                      38 (11 x 3 + 5)

4                                      49 (11 x 4 + 5)

5                                     60

Let w = the monthly maintenance fee

Let z = the one-time opening fee

Equations:

5w + z = 60 ... Equation 1

2w + z = 27 ... Equation 2

Subtract Equation 2 from Equation 1:

3w = 33

w = 11

b) The monthly maintenance fee is $11.00.

a) The initial (one-time) opening fee is $5.00.

z = 60 - 55

= 5

c) The total fees after x months is y = 11x + 5.

Thus, the one-time opening fee and the monthly maintenance fee can be computed using a system of equations.

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Divide the sum 200 and 300 by the difference 80and 30.​

Answers

Answer:

10

Step-by-step explanation:

300 plus 200 is 500

80 minus 30 is 50

500 divided by 50 is 10

Va rog!! Cineva rapid

Answers

Answer:18

Step-by-step explanation:

Erik has been collecting comic books for the past few years. The number of total comic books in his collection each year is as follows. • 30 comic books the first year • 60 comic books the second year • 90 comic books the third year • 120 comic books the fourth year Write a function that represents the number of comic book as a function of the number of years, t.

Answers

The function that represents the number of comic book as a function of the number of years, t is expressed as y = 30x or f(t) = 30t.

How to Write a Linear Function?

We can use the given data to create a linear equation of the form y = mx + b, where y represents the number of comic books and x represents the number of years.

To find the equation, we can use any two pairs of (x, y) values. Let's use the first and fourth years:

First year: (1, 30)

Fourth year: (4, 120)

The slope, m, of the line can be calculated using the formula:

m = change in y / change in x = (120 - 30) / (4 - 1)

m = 90 / 3

m = 30

The y-intercept, b, can be found by substituting one of the (x, y) values and the slope into the linear equation, y = mx + b:

30 = 30(1) + b

b = 0

Therefore, the equation that represents the number of comic books, y, as a function of the number of years, x, is:

y = 30x

or

f(t) = 30t [where t represents the number of years.]

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find the expected value of the given variable with the following probability distribution

Answers

The expected value of the given variable with the probability distribution is 7

How to find the expected value of the variable

From the question, we have the following parameters that can be used in our computation:

The probability distribution on the table of values

The expected value of the variable is calculated as

Expected value = ∑x * P(x)

Using the above as a guide, we have the following:

Expected value = 2 * 1/36 + 3 * 1/18 + 4 * 1/12 + 5 * 1/9 + 6 * 5/36 + 7 * 1/6 + 8 * 5/36 + 9 * 1/9 + 10 * 1/12 + 11 * 1/18 + 12 * 1/36

Evaluate

Expected value = 7

Hence, the expected value of the variable is 7

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Which expression is equivalent to 4^7/8
4^1/4?

Answers

the answer is option A
Other Questions
which of the following is considered to be the most potent neuromodulators? which of the following wireless technologies cannot travel through walls or other obsticles? ______ do not store relationships as perceived in the relational model and generally have no support for join operations. in a monopolistic competitive industry, firms can try to differentiate their prodcuts by' What do you think tom and daisy were saying to each other in the kitchen? a hollow cylindrical copper pipe is 1.40 m long and has an outside diameter of 3.90 cm and an inside diameter of 2.30 cm. How much does it weigh? w=?N you can only add one date vlan to a switch port when configured as an access port. what is the second type of vlan that be added to an access port standardized coefficients are also referred to as: a. alpha coefficients. b. beta coefficients. c. j coefficients. d. y coefficients. Which of the following is the first major step in a typical control process?A. Comparing performance with standardsB. Setting standardsC. Taking corrective actionD. Developing valuesE. Measuring performance Homework:homework 6: chapter 6question 1, 6.1.21part 1 of 7hw score: 0%, 0 of 100 points points: 0 of 50question content area toppart 1a telephone counseling service for adolescents tested whether the length of calls would be affected by a special telephone system that had a better sound quality. over the past several years, the lengths of telephone calls (in minutes) were normally distributed with and . the service arranged to have the special phone system loaned to them for one day. on that day, the mean length of the calls they received was minutes. test whether the length of calls has changed using the 5% significance level. complete parts (a) through (d). A={ multiples of 3 between 10 and 20}. B={Even numbers between 10 and 20}. I. AnBii. AuB Identify each data analysis task as belonging to either descriptive or inferential statistics. Descriptive Statistics Drag appropriate answer(s) here + computing the correlation coefficient between two sets of observations determining whether a difference between two sets of results could be due to chance + using meta-analysis to arrive at a stronger conclusion than any single study permits calculating the standard deviation of a set of data values + determining the median value of a set of measurements Drag appropriate answer(s) here Inferential Statistics A candle is placed 10 cm in front of a concave mirror with a 40 cm radius of curvature. Find the magnification and classify the image: real or virtual; upright or inverted; and enlarged or reduced. A particle moves along a line so that its velocity at time t is v(t) = t^2 - t - 6 (measured in meters per second). (a) Find the displacement of the particle during 1 lessthanorequalto t lessthanorequalto 9. (b) Find the distance traveled during this time period. SOLUTION By this equation, the displacement is s(9) - s(1) = integral_1^9 v(t) dt = integral_1^9 (t^2 - t - 6) dt = [t^3/7 - t^2/2 - 6t]_1^9 = 154.67 This means that the particle moved approximately 154.67 meters to the right. Note that v(t) = t^2 - t - 6 = (t - 3)(t + 2) and so v(t) lessthanorequalto 0 on the interval [1, 3] and v(t) greaterthanorequalto V 0 on [3, 9]. Thus, from this equation, the distance traveled is integral_1^9 |v(t)| dt = integral_1^3 [-v(t)] dt + integral_3^9 v(t) dt = integral_1^3 (-t^2 + t + 6) dt + integral_3^9 (t^2 - t - 6) dt = [______]_1^3 + [______]_3^9 = ______ At 3:00 A.M., 10-year-old Lee gets out of bed and sleepwalks to the kitchen. An EEG of his brain activity is most likely to indicate the presence of What are the four European Nationals who traded on the coast of Sierra Leone before 1800 given the reactant brbr, add curved arrows to show homolytic bond cleavage, then draw the expected product. be sure to add any charges and nonbonding electrons that result from the cleavage. Your mission is to capture, in logical form, enough knowledge to answer a series of questions about the following simple scenario:Yesterday Bob went to the local Stop-n-Shop supermarket and bought two pounds of tomatoes and a pound of ground beef.Start by trying to represent the content of the sentence as a series of assertions.You should write sentences that have straightforward logical structure (e.g., statements that objects have certain properties, that objects are related in certain ways, that all objects satisfying one property satisfy another). how should a complaint message begin? using logical development demanding action details of the situation as emotional appeals Simplify the expression log8x