The girl's basketball team won 75 games and the boy's basketball team won 151 games.
Let's assume the number of games the girl's basketball team won "g," and the number of games the boy's basketball team won "b."
We know that the total number of games won by both teams is 226, so we can set up our first equation as follows:
g + b = 226
We also know that the boy's basketball team won one more than twice as many games as the girl's basketball team. We can represent this as follows:
b = 2g + 1
Now we have two equations and two unknown values, so we can solve for g and b using algebra. Let's substitute the second equation into the first equation to eliminate one of the unknowns:
g + (2g + 1) = 226
This simplifies to:
3g + 1 = 226
Subtracting 1 from both sides gives us:
3g = 225
Dividing both sides by 3 gives us:
g = 75
Now that we know the value of g, we can substitute it back into the second equation to solve for b:
b = 2 x 75 + 1 = 151
Therefore, the girl's basketball team won 75 games and the boy's basketball team won 151 games.
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a rectangular field will be bounded by a wall on one side and by fencing on the other three sides. what is the largest area you can enclose with 120 feet of fencing?
The largest area you can enclose with 120 feet of fencing is 900 square feet.
To find the maximum area you can enclose with 120 feet of fencing, you can use the formula for the area of a rectangle, which is A = lw, where A is the area, l is the length, and w is the width. Since the length of the rectangle is bounded by a wall and cannot be changed, the width will be the variable we seek to maximize.
Since the perimeter of the rectangle is fixed at 120 feet, we can set up the following equation:
2l + 2w = 120
This equation represents the total length of the fence needed to enclose the rectangular field. We can solve for w in terms of l by rearranging the equation as follows:
2w = 120 - 2l
w = (120 - 2l)/2
To maximize the area of the rectangle, we want to maximize the value of w. We can do this by making l as small as possible, since this will make w as large as possible. Therefore, we can set l equal to the minimum possible value, which is the length of the wall.
Let's say the length of the wall is x feet. Then, we can substitute x for l in the equation for w to find the maximum possible width:
w = (120 - 2x)/2
To find the maximum area, we can then substitute this value for w back into the formula for the area of a rectangle:
A = lw
= x((120 - 2x)/2)
= (120x - 2x^2)/2
This is a quadratic function, and we can use the techniques for maximizing quadratic functions to find the maximum value of A. To do this, we take the derivative of the function and set it equal to zero:
A' = (120 - 4x)/2 = 0
120 - 4x = 0
x = 30
Substituting this value back into the equation for A, we find that the maximum possible area is:
A = (120 * 30 - 2 * 30^2)/2
= (3600 - 1800)/2
= 1800/2
= 900 square feet
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The equation of a parabola is y=5x^2+15x–25. Write the equation in vertex form.
Write any numbers as integers or simplified proper or improper fractions
The equation of the parabola y = 5 · x² + 15 · x - 25 in vertex form is y + 145 / 4 = 5 · (x + 3 / 2)².
How to find the vertex form of a quadratic equation
Herein we find the equation of a parabola in standard form, that is, an equation of the form:
y = a · x² + b · x + c
Where:
a, b, c - Real coefficientsx - Independent variabley - Dependent variableFrom this equation we must derive the vertex form, whose definition is shown below:
y - k = C · (x - h)²
Where:
C - Vertex constant(h, k) - Coordinates of the center.The vertex form is found by algebra properties. First, write the equation of the parabola:
y = 5 · x² + 15 · x - 25
Second, use algebra properties until the vertex form is found:
y + 25 = 5 · x² + 15 · x
y + 25 = 5 · (x² + 3 · x)
y + 25 + 45 / 4 = 5 · (x² + 3 · x + 9 / 4)
y + 145 / 4 = 5 · (x + 3 / 2)²
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Please help me respond this question
Answer:
y=0
Step-by-step explanation:
Based on the boxplot, the top 25 percent of the cars have a typical gas mileage of at least how many miles per gallon? responses.
The top 25% of cars have a typical gas mileage of at least 33.5 miles per gallon.
To calculate this, you need to use the interquartile range (IQR) formula.
The IQR is calculated by subtracting the 25th percentile (Q1) from the 75th percentile (Q3).
IQR = Q3 - Q1
In this case, the 25th percentile (Q1) is 28.4, and the 75th percentile (Q3) is 37.9. So:
IQR = 37.9 - 28.4 = 9.5
The top 25% of cars have a gas mileage of 33.5 miles per gallon, which is Q3 + 1.5*IQR.
33.5 = Q3 + 1.5*IQR
33.5 = 37.9 + 1.5*9.5
33.5 = 37.9 + 14.25
33.5 = 52.15
Therefore, the top 25 percent of cars have a typical gas mileage of at least 33.5 miles per gallon.
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The graph represents a quadratic function. Write an equation of the function in standard form.
The equation for the quadratic function in standard form is f(x) = x² - 11x + 24
Writing Quadratic equationFrom the question, we are to write an equation for the quadratic function in standard form.
From the given quadratic graph,
The roots of the function are 3 and 8.
That is,
x = 3 and x = 8
Then,
The factors of the quadratic function are (x -3) and (x - 8)
Thus,
We can write that
(x - 3)(x - 8) = 0
x² - 8x - 3x + 24 = 0
Simplify
x² - 11x + 24 = 0
Hence, the equation is f(x) = x² - 11x + 24
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Use elimination method to solve the following system of equations
6x+y=-4
6x+5y=4
Answer:(-1,2)
Step-by-step explanation:
-(6x+y=-4)
6x+5y=4
------------------
-6x-y=4
6x+5y=4
--------------
4y=8
y=2
6x+2=-4
6x=-6
x=-1
Please help and show work, will give lots of points!
Lourdes is reading a biography for her history class. She reads 30 pages each day. After 9 days, Lourdes has read 3/5 of the biography. Write a linear equation to represent the number of pages Lourdes still has to read after x days.
y = []x + []
(Use above format to write the equation.)
What does the y-intercept of this linear equation represent?
A. Pages already read
B. Pages in book
C. Pages read each day
D. Days to finish
Answer:
The linear equation is y = 450 - 30 x, where y is the number of pages
Lourdes has left to read after x days
Step-by-step explanation:
Each day, Lourdes reads 30 pages of a 450-page book
- We need to write a linear equation to represent the number of pages
Lourdes has left to read after x days
∵ Lourdes reads 30 pages each day
∵ Lourdes will read for x days
∴ The number of pages Lourdes will read in x day = 30 x
- The left pages will be the difference between the total pages of the
book and the pages Lourdes read
∵ The book has 450 pages
∵ Loured will read 30 x in x days
∴ The number of pages left = 450 - 30 x
- Assume that y represents the number of pages Lourdes has left
to read after x days
∴ y = 450 - 30 x
The linear equation is y = 450 - 30 x, where y is the number of
pages Lourdes has left to read after x days
What are two ways sequences can be defined?
The two ways that sequences can be defined include the following: Arithmetic Sequences and Geometric Sequences.
What is a sequence in mathematics?A sequence is defined as the collection of items in such a way that repetitions can be observed.
There are two major ways the sequence can be defined in arithmetics and this includes the following:
Arithmetic Sequences: This is the type of sequence whereby every term is created by adding or subtracting a definite number to the preceding numberGeometric Sequences: This is the type of sequence whereby every term is obtained by multiplying or dividing a definite number with the preceding number.Learn more about sequence here:
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Characterize observational study with respect to nature of the sample and treatment.
An observational study is used to answer a research question based purely on what the researcher observes.
What Is an Observational Study?An observational study is a statistical study that does not have any treatment or intervention done by the researchers.
Observational research allows the researcher to see what their subjects really do when confronted with various choices or situations. The term refers to the study of non-experimental situations in which behaviour is observed and recorded.
Statistics is the process of collecting data about a group of objects to draw conclusions about populations of those objects. For example, a statistician may take a sample group of workers from company XYZ and have them rate their job satisfaction with the company. Based on the results of that sample, the statistician can make educated assumptions about all the employees of company XYZ and their job satisfaction.
However, observational studies can only establish that significant associations exist between predictor and outcome variables. Observational studies cannot establish that the associations identified represent cause-and-effect relationships.
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A bag contains 3 basketballs, 10 baseballs, 7 golf balls, and 5 footballs. A ball is chosen at random,not replaced, then another is chosen. Find each probability
17. P(a football, then a baseball)
18.P(two baseballs)
This is based on Conditional Probability.
P(a football, then a baseball) is 0.08333 and P(two baseballs)
is 0.15
What is Conditional Probability?The chance of an event happening given that another event has already occurred (via assumption, supposition, statement, or evidence) is known as conditional probability in the field of probability theory. This particular approach depends on event B happening in some way connected to another event A. In this case, a conditional probability analysis with respect to event B is possible. The probability of A under the condition B is typically expressed as P(A|B) or PB if the event of interest is A and the event B is known to have occurred or is assumed to have done so (A). This can alternatively be thought of as the percentage of probability that B crosses A:
P(A|B)=P(A∩B)/P(B)
Calculation:1) P(a football, then a baseball)= ([tex]\frac{5}{25}[/tex])×([tex]\frac{10}{24}[/tex]) =0.08333
2) P(2 Baseballs) = ([tex]\frac{10}{25}[/tex])×([tex]\frac{9}{24}[/tex]) = 0.15
This is based on Conditional Probability.
P(a football, then a baseball) is 0.08333 and P(two baseballs)
is 0.15
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How do you add rational expressions examples?
The Example of addition of Rational Expressions is "Add 2/3 and 6/7" .
The Rational Expression is defined as the expression , that is represented in the form of p/q , where q ≠ 0 .
Example of Addition of Rational Expression is
Add 2/3 + 6/7 .
In order to add the above two rational expression , we first make the denominator of both the terms same by taking LCM ,
the LCM of denominators 3 and 7 is 21 .
So , the expression becomes ⇒ 14/21 + 18/21 .
⇒ (14 + 18)/21
Simplifying further ,
we get ;
⇒ 32/21
Therefore , the example of addition of rational expressions is explained above .
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which of the following sets of transformations could be used to prove that the line segments are congruent?
A transition of AB6 units to the right followed by a transition 6 unit down this transformations could be used to prove that the line segments are congruent.
How do you know if a line segment is congruent?Line segments of the same length are known as congruent segments. Congruent refers to equality. The standard method for identifying congruent line segments is to draw the same number of tiny, perpendicular tic lines in the middle of each section. By placing a line over the two endpoints of a line segment, we can identify it.A line segment is a section of a straight line that is enclosed by two clearly defined end points and contains every point on the line located within. The Euclidean distance between two ends of a line segment determines its length.Half-open line segments contain exactly one of the endpoints, while closed line segments have both of the endpoints. Open line segments do not contain either of the endpoints.To learn more about line segment refer :
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Why is it called linear?
Because the equation depicts a straight line in the Cartesian plane, it is called a linear equation.
Does linear mean straight?A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.
Why differential is called linear?In the variable separation if the unknown function and its derivatives have no exponent larger than one and there are no cross-expressions—that is, terms like f f′ or f′f′′ in which the function or its derivatives appear more than once—the partial differential equation is said to be linear.
Because the equation depicts a straight line in the Cartesian plane, it is called a linear equation. Through the use of logical and mathematical tools, it enables us to solve issues in a variety of scientific fields and academic disciplines as well as in real-world circumstances.
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Jing just got a new job. She started at a pay rate of $12.50 per hour and will get a $0.50 raise each year. Max started a job where his salary is found by the equation: f(x) = x + 10 , where x is the number of years.
Interpret the rates of change and initial values of the linear functions in terms of the situations they model. Compare the results and what they mean. How many years must they both work for Max to earn more per hour than Jing?
Jing
Initial value:
Rate of change:
Max
Initial value:
Rate of change:
Jing's initial pay rate is $12.50 per hour. She will receive a pay raise of $0.50 per hour every year.
Max's initial pay rate is 10 dollars per hour. He will receive a pay raise of 1 dollar per hour every year.
To determine how many years it will take for Max to earn more per hour than Jing, we need to find the point at which the two linear equations intersect. This can be done by setting the two equations equal to each other and solving for x.
Jing's equation is: $12.50 + 0.50x
Max's equation is: x + 10
Setting the equations equal to each other and solving for x, we get:
$12.50 + 0.50x = x + 10
This simplifies to:
$0.50x = -2.50
Dividing both sides by 0.50, we get:
x = -5
Since the value of x cannot be negative, this means that Max will never earn more per hour than Jing.
What is the linear inequality symbol?
The symbol of a linear inequality is: " ≤ " or " ≥ "
What is a linear inequality equation?The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.
It's a line with a shaded side on one side to show which xy pairings are the inequality's solutions.
For example -
Let us take a equation, 4x + 8y ≤ -24
Now, solve the above equation in the form of slope-intercept.
4x + 8y ≤ -24
or, 8y ≤ - 4x - 24
or, y ≤ -(1/2)x - 3
Now, the graph becomes according to the slope-intercept form is:
Here we noticed that,
This side of the inequality is shaded below (instead of above) because y is lower than (or equal to) the other side.
Because working with a "or equal to" inequality, draw a solid line rather than a dashed one. Points on the solid line denote locations where the inequality has been solved.
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What is the discriminant and nature of roots of 2x² 3x 5 0?
The discriminant of the quadratic equation 2x² + 3x - 5 = 0 is 49 and the nature of the roots are -3/4 + 7/4 and -3/4 - 7/4.
The discriminant of the quadratic equation 2x² + 3x - 5 = 0 is b² - 4ac = 9 - 4(2)(-5) = 49.
The nature of the roots of the equation can be determined by the discriminant. If the discriminant is positive, then the roots are real and distinct; if it is zero, then the roots are real and equal; and if it is negative, then the roots are complex and conjugate. In this case, the discriminant is positive, so the roots are real and distinct.
To calculate the roots, we use the quadratic formula:
x = [-b ± √b² - 4ac]/2a.
For this equation, a = 2, b = 3, and c = -5,
so x = [-3 ± √49]/2(2) = [-3 ± 7]/4 = -3/4 ± 7/4.
This means the two roots of the equation are -3/4 + 7/4 and -3/4 - 7/4.
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IN THE FIGURE TRIANGLE ABE IS CONGURENT TO TRIANGLE ACD SHOW THAT TRIANGLE ADE AND TRIANGLE ABC ARE SIMILIAR
The triangle ADE is similar to the triangle ABC.
What are congruent triangles?
The triangles are congruent if two sides and the included angle of one triangle match the corresponding sides and angle of another triangle.
It is given that triangle ABE is congruent to triangle ACD, which can also be written as ΔABE≅ΔACD.
So, according to the Corresponding parts of Congruent triangles (CPCT) property:
AB=AC...........(1)
AE=AD...........(2)
By dividing 2 and 1 we will get:
[tex]\frac{AD}{AB} =\frac{AE}{AC}[/tex]........(3)
In the triangles ADE and ABC, ∠A is the common angle and according to this and 3,
ΔADE is similar to ΔABC by side angle side criterion.
Therefore hence it is proved that ΔADE and ΔABC are similar.
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How do you solve 7 step equations?
To solve a 7 step equation, identify the equation, isolate the variable to one side of the equation, simplify the equation if necessary, divide both sides of the equation by the coefficient of the variable.
1. Identify the equation.
2. Limit the variable to only one side of the problem.
3. Simplify the equation, if necessary.
4. Divide both sides of the equation by the coefficient of the variable, if necessary.
5. Continue carrying out steps 2-4 until the equation is resolved.
6. Check your solution by substituting the solution back into the equation.
7. Write the solution in the form of an equation.
To solve a 7 step equation, identify the equation, isolate the variable to one side of the equation, simplify the equation if necessary, divide both sides of the equation by the coefficient of the variable, repeat steps 2-4 until the equation is solved, check your solution by substituting it back into the equation, and then write the solution in the form of an equation.
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What is the equation in slope-intercept form of the line that passes through the point (2,-2)
and is perpendicular to the line represented by y = 2/5x+ 2?
A y=5/2x-7
в y=5/2x+7
c y=-5/2x-3
D y=-5/2x+3
Answer:
D, [tex]y=\frac{-5}{2x}+3[/tex]
Can in text citations be shortened?
Harvard in-text citations allow for the inclusion of up to three authors. When there are four or more authors, et al. is used to shorten the citation.
What are text citations?In-text citations in APA style are used to quickly describe the sources of your information within the text of your research report.
The reader is directed to more detailed information in the Reference list by succinct in-text citations.
The author's last name and the year of publication are used in APA in-text citations,: (Field, 2005). Include the page number when using direct quotations, as in the following example: (Field, 2005, p. 14).
Reduce the source title or organization name, excluding any articles, to the first word or phrase in the in-text citation if it is longer than four words (a, an, and the).
The alphabetized word for the source in the Works Cited should be the first word in the abbreviated title or organization name.
Therefore, Harvard in-text citations allow for the inclusion of up to three authors. When there are four or more authors, et al. is used to shorten the citation.
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What are the 3 types of forecasting?
The three main types of forecasting are qualitative, quantitative, and time series.
What is forecasting?Forecasting is a predictive tool used to make decisions and plan for the future. It involves analyzing past trends and data to predict future events and outcomes. Forecasting helps businesses and organizations prepare for potential market changes, plan ahead for budgeting, and make informed decisions. It is also an invaluable tool for understanding consumer behavior and market trends.
Qualitative forecasting is a subjective approach that relies on expert opinion, intuition, and past experiences. Quantitative forecasting is a more structured approach that uses statistical techniques and data-driven models to make predictions. Time series forecasting is a form of quantitative forecasting that uses historical data to predict future values. It is especially useful for predicting cyclical trends and seasonal variations. All three approaches can be used together to create a comprehensive forecasting strategy for a business.
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find an equation of the tangent line to the curve at the given point. y = 8ex cos(x), (0, 8)
The equation of the line tangent to the curve at the points , y = 8ex cos(x), (0, 8) as calculated is y' = 0.
We will differentiate y = 4ex cos(x) so as to find the required equation.
we get the differential as ,
y' = - 8eˣsin(x)
given the value of x as 0 and y as 8
y' = -8e⁰sin(0)
Now as we know that the value of sin( 0 ) is 0 , therefore the equation becomes,
y'= 0
Differentiation is a branch of calculus which is used to calculate the rate of change in a given object in a specified time. The other branch of calculus is integration.
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Your friend hides a dollar bill under one of three plastic cups. Under the other
two cups is a paper clip. You get to keep whatever is under the cup you
choose, but you don't know which contains the dollar bill. After you choose,
your friend lifts one of the other cups to reveal a paper clip and then gives you
the option of changing your choice.
Should you switch to the other cup?
Answer:
Yes, you should
Step-by-step explanation:
Because the probability of winning the dollar increases from \frac{1}{3} 3 1 to \frac{2}{3} 3 2 by switching.
Please help me with this question
many thanks
answer :
d÷d = 0
then 10 remain
5(2x + 1) = 50 I am struggling please help
Answer:
x = 4.5
Step-by-step explanation:
To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we need to get rid of the 5 that is multiplying the expression 2x + 1.
One way to do this is to divide both sides of the equation by 5. This gives us:
(5(2x + 1))/5 = 50/5
Simplifying the left side of the equation gives us:
2x + 1 = 10
Now, we just need to get x by itself on one side of the equation. To do this, we can subtract 1 from both sides of the equation. This gives us:
2x = 9
Finally, we can divide both sides of the equation by 2 to solve for x. This gives us:
x = 9/2
Therefore, the solution to the equation is x = 9/2, or x = 4.5.
I hope this helps! Let me know if you have any other questions.
Answer:
x = 9/2 or 4.5
Step-by-step explanation:
5(2x + 1) = 50
10x + 5 = 50
10x = 50 -5
x = 45 /10
x = 9/2 or 4.5
I hope my answer helps you.
i need help please.
Answer: ( x + 5, y + 11)
Step-by-step explanation:
Let's pick point S at ( -9, -9); it changes to point S' at (-4, 2)
We see the x increase by 5 and the y increase by 11, so the answer is
( x + 5, y + 11)
E-loan, an online lending service, recently offered 36-month auto loans at 6% compounded monthly to applicants with good credit ratings. If you have a good credit rating and can afford monthly payments of $539, how much can you borrow from E-loan? What is the total interest you will pay for this loan?
I can borrow $17717.48from E-Loan.
The interest I will pay for the loan is $1,686.52
Now, According to the question:
We know,
The formula of present value is
PV = PMT [tex](\frac{ 1-(1+i)^-^n}{i} )[/tex]
PMT = The monthly payment = $539
i= Rate of interest per period = 6%/12 = 0.005
n = The number of month = 36 months
Therefore,
PV = 539[tex](\frac{ 1-(1+0.005)^-^3^6}{0.005} )[/tex]
≈$17717.48
Therefore I can borrow $17717.48 from E-Loan.
The interest = Paid amount - Loan amount
=$[(539×36)-17717.48]
= $1,686.52
The interest I will pay for the loan is $1,686.52
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What is a parallel class 6?
In geometry, parallel lines are the lines which maintain the same distance apart from each other and never intersect at any point.
What is parallel class 6?
In geometry, parallel lines are the lines which maintain the same distance apart from each other and never intersect at any point.
All rungs are perpendicular to the left post is a line perpendicular to one of a set of parallel lines, it is perpendicular to all parallel lines.
The rungs are parallel
lines that are perpendicular to the same line are parallel.
The rungs are perpendicular to both posts and the posts are parallel to each other.
if a line is perpendicular to one of a set of parallel lines, it is perpendicular to all the parallel lines.
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What is the value of |a-b|+|b-a| if a=b-1/2
The value of the absolute expression |a - b| + |b - a| will be 1.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The equation is given below.
a = b - 1/2
The expression is given as,
⇒ |a - b| + |b - a|
The value of (a - b) is given as,
a = b - 1/2
a - b = - 1/2
And the value of (b - a) is given as,
a = b - 1/2
b - a = 1/2
Then the value of the expression is calculated as,
⇒ |a - b| + |b - a|
⇒ |-1/2| + |1/2|
⇒ 1/2 + 1/2
⇒ 1
The worth of the outright articulation |a - b| + |b - a| will be 1.
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What are the 3 different options for horizontal asymptotes?
The 3 different options for horizontal asymptotes are:
If the degree of the numerator < the degree of the denominator.If the degree of the numerator = degree of the denominator. If the degree of the numerator > the degree of the denominator.What are horizontal asymptotes?This refers to a horizontal line y = b where the graph approaches the line as the inputs approach infinity (∞) or negative infinity (–∞).
The 3 different options for horizontal asymptotes
If the degree of the numerator < the degree of the denominator, y = 0 (x-axis), and If n<m, the x-axis, y=0 is the horizontal asymptote.If the degree of the numerator = degree of the denominator. If n=m, then y=an / bm . That is, the ratio of the leading coefficients.It is the horizontal asymptote. If the degree of the numerator > the degree of the denominator. If n>m, there is no horizontal asymptote.Note: If n=m+1, there is an oblique or slant asymptote.
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