Answers
The vertical asymptote is at x = -2
The horizontal asymptotes are at y =0.
How to get the asymptotes?First, the vertical asymptote, it happens when the denominator becomes zero, then we need to solve:
-x - 2 = 0
x = -2
The vertical asymptote is at x = -2
For the horyzontal asymptotes we need to check the limit as x tends to ±∞, in both cases because x is only in the denominator, the function will tend to zero.
So we have two horizontal asymptotes at y = 0.
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Related Questions
Which function is the inverse of g (z) = (²-1)³ — 3?
Of(1) = √2+6+1
Of(1) = 2√2+3+1
O f(1) = 2√1+1+3
O f(1) = √21+2+3
Answers
The inverse of function is f(x) = (x - 4)³/8 + 3
What is inverse function?A function that reverses the results of another function is known as an inverse function. If y = f(x), then x = g(y), then a function g is the opposite of a function f. To put it another way, applying f and then g is equivalent to doing nothing. This can be expressed as g(f(x)) = x in terms of how f and g are made up.
Given g(x) = 2(∛x-3)+4
let g(x) = y
y = 2(∛x-3)+4
change the variables since options are in form of x
x = 2(∛y-3)+4
simplify for y
subtract 4 from both side
x - 4 = 2(∛y-3)+4 - 4
x - 4 = 2(∛y-3)
divide both side by 2
(x - 4)/2 = (2(∛y-3))/2
(x - 4)/2 = (∛y-3)
cube both side
((x - 4)/2)³ = ((∛y-3))³
(x - 4)³/8 = y - 3
(x - 4)³/8 + 3 = y
Hence the value f(x) = (x - 4)³/8 + 3 .
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What is the simplest form of the radical expression?
√2+√5/√2-√5
Answers
what is convergence radius calculator
Answers
A convergence radius calculator is a tool used in calculus to calculate the radius of convergence for a power series using the ratio test.
To calculate the convergence radius of a power series, one can use a formula known as the "ratio test". The ratio test involves taking the limit of the absolute value of the ratio of successive terms in the series, as n approaches infinity. If this limit exists and is less than 1, then the series converges absolutely. The convergence radius can then be found as the reciprocal of this limit.
For example, given the power series:
∑(n=0 to infinity) [tex](x-2)^n / n^2[/tex]
we can use the ratio test to find the convergence radius as follows:
[tex]|(x-2)^(n+1) / (n+1)^2| / |(x-2)^n / n^2|[/tex]
= [tex]|(x-2) / (n+1)|^2 * (n^2 / (x-2)^2)[/tex]
= [tex](n^2 / (n+1)^2) * (1 / (x-2)^2)[/tex]
= [tex]n^2 / ((n+1)^2 * (x-2)^2)[/tex]
Taking the limit of this expression as n approaches infinity, we get:
[tex]lim(n- > ∞) (n^2 / ((n+1)^2 * (x-2)^2))[/tex]
= [tex]1 / (x-2)^2[/tex]
Since this limit exists and is less than 1 for all x except x=2, the power series converges absolutely for all values of x within a radius of [tex]1/(x-2)^2[/tex] centered at x=2. Therefore, the convergence radius of the power series is 1.
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Match the following to their correct classification
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
4x+20
4x+20>40
4x+20=40
The option " Inequality " (3 of 3) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.
Answers
The correct classification of the terms is:
Expression; 4x+20
Inequality: 4x+20 > 40
Equation: 4x+20 = 40
What is an expression?
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
Here, we have
Given: 4x+20
4x+20>40
4x+20=40
We have to find their correct classification.
We concluded from an expression that
When an expression has the "=", then the expression is an equation.
When an expression has any of the following signs">, <, >=, <= or != ", then the expression is an inequality.
When the expression is neither an equation nor an inequality, then it is just an expression.
Hence, the correct classifications are:
Expression; 4x+20
Inequality: 4x+20 > 40
Equation: 4x+20 = 40
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How do you find the two largest numbers in an array in Matlab?
Answers
To find the two largest numbers in an array in Matlab, you can use the sort function and indexing to access the two largest elements.
Here's an example:
array = [3, 8, 2, 10, 5];
sorted_array = sort(array, 'descend');
largest_number = sorted_array(1);
second_largest_number = sorted_array(2);
In this example, we have an array of numbers called array. We use the sort function to sort the array in descending order, which means that the largest numbers will be at the beginning of the array. The resulting sorted array is assigned to a new variable called sorted_array.
We then use indexing to access the first and second elements of the sorted array, which will be the two largest numbers. These numbers are assigned to the variables largest_number and second_largest_number, respectively.
It's important to note that if the array contains duplicate values, this method will return the two largest unique values. If you want to find the two largest values including duplicates, you can use the max function twice with the 'omitnan' parameter to handle any NaN values in the array:
array = [3, 8, 2, 10, 5, 10];
largest_number = max(array, [], 'omitnan');
array_without_largest_number = array(array < largest_number);
second_largest_number = max(array_without_largest_number, [], 'omitnan');
In this example, we first find the largest number in the array using the max function with the 'omitnan' parameter to ignore any NaN values. We then create a new array that excludes the largest number, and use the max function again to find the second largest number in the new array.
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The image of a trapezoid is shown.
An isosceles trapezoid with a short base of 3 meters and a height of 5 meters. The portion of the large base from the left vertex to the perpendicular is 4 meters. The portion of the large base from the right vertex to the perpendicular is 7 meters.
What is the area of the trapezoid?
70 m2
38 m2
35 m2
19 m2
Answers
Answer: 35m2
Step-by-step explanation:took the test and i got it right
An isosceles trapezoid with a short base of 3 meters and a height of 5 meters then the area of the trapezoid is 35 m²
What is the area of the trapezoid?
To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.
We can start by finding the length of the long base. Since the trapezoid is isosceles, we know that the length of the portion of the large base from the left vertex to the perpendicular is equal to the length of the portion from the right vertex to the perpendicular. Let's call the length of the long base "x":
x = 4 + 7 = 11 meters
Now we can use the formula for the area of a trapezoid:
Area = (1/2) * (short base + long base) * height
Substituting the values we have:
Area = (1/2) * (3 + 11) * 5
Area = 7 * 5
Area = 35 m²
Therefore, the area of the trapezoid is 35 m².
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A loan of $25,000 has an annual simple interest rate of 5.5%. The total cost of the loan is $38,750. How much total interest will you pay?
Answers
The solution is, total interest will you pay is $13750.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
given that,
A loan of $25,000 has an annual simple interest rate of 5.5%.
The total cost of the loan is $38,750.
so, total interest will you pay = $(38750 - 25000)
= $13750
Hence, The solution is, total interest will you pay is $13750.
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What is 200 Micrograms (mcg) in Milligrams (mg)?
Answers
To convert 200 micrograms (mcg) to milligrams (mg), we need to use the conversion factor that 1 milligram is equal to 1000 micrograms, 200 micrograms (mcg) is equal to 0.2 milligrams (mg).
When we want to convert a unit of measurement to another unit of measurement, we use conversion factors to make the conversion. In the case of converting micrograms (mcg) to milligrams (mg), we need to know that 1 milligram is equal to 1000 micrograms. This means that to convert any value from micrograms to milligrams, we need to divide by 1000.
To convert 200 micrograms (mcg) to milligrams (mg), we need to use the conversion factor that 1 milligram is equal to 1000 micrograms.
So, to convert 200 mcg to mg, we divide 200 by 1000:
200 mcg ÷ 1000 = 0.2 mg
Therefore, 200 micrograms (mcg) is equal to 0.2 milligrams (mg)
It is important to understand the concept of unit conversions because it is a crucial aspect of many scientific and engineering calculations. Knowing how to convert units of measurement allows us to work with data that is expressed in different units and compare results from different experiments. In addition, being able to convert units is a valuable skill for everyday life, such as when reading nutrition labels or measuring medication dosages.
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Use the drop-down menus to order the decimals from greatest to least.
8.31, 8.296, 8.06, 8.3
Answers
Answer:
8.31, 8.3, 8.296, 8.06
Step-by-step explanation:
8.31, 8.296, 8.06, 8.3
The order of decimals from greatest to least is
8.31, 8.3, 8.296, 8.06
can yall help me with this question immediately pls?
Answers
The diameter of the Ferris wheel will be the difference between two consecutive maximum height and minimum height of the ferris wheel.
What is diameter?Diameter is the line jwhich passes through the center of a circle and joins two points on the circumference of the circle.
To find the diameter of the Ferris wheel which is a circle, we see that the grpah gives the height of a passenger on the Ferris wheel as a function of the number of complete cycles since the ride started.
Now, the diameter of the Ferris wheel will be the difference between two consecutive maximum height and minimum height of the ferris wheel.
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Bonnie bakes a pan of brownies and cut them into 12 equal pieces after lunch 8/12 of the brownies are left her friends eat half of those brownies with dinner what fraction of the whole pan of brownies do they eat with dinner
Answers
Answer:
4/12
Step-by-step explanation:
8/12 ÷ 2 = 4/12
Answer: 1/3
Step-by-step explanation:
8/12 divided by 2 is 1/3
What is the LCM of 3 and 5 and 3?
Answers
Answer:15
Step-by-step explanation:
Analyze the linear inequalities and determine if the solution set is the shaded region above or below the boundary
line.
Warm-Up
y> -1.4x +7
y> 3x-2
y <19-5x
y>-x-42
y < 3x
y<-3.5x+2.8
Solution Set Shaded Above
Solution Set Shaded Below
Answers
Answer:
The graph in the attached figure
we have
----> inequality A
The solution of the inequality A is the shaded area below the dashed line
The slope of the dashed line A is positive m=2
The y-intercept of the dashed line A is (0,-5)
The x-intercept of the dashed line A is (2.5,0)
----> inequality B
The solution of the inequality B is the shaded area above the dashed line
The slope of the dashed line B is negative m=-3
The y-intercept of the dashed line B is (0,1)
The x-intercept of the dashed line B is (1/3,0)
The solution of the system of inequalities is the shaded area between the two dashed lines
using a graphing tool
The graph in the attached figure
GIVE ME BRAINLIEST IF IM CORRECT :)
properties of rectangles assignment
Answers
The properties of a rectangle are;
A rectangle is seen as a type of quadrilateralThe opposite sides are parallel and also equal to each otherEach interior angle is equivalent to 90 degreesThe sum of all the interior angles is 360 degreesWhat is a rectangle?A rectangle is described as a quadrilateral shape with only two pairs of its sides equal.
The properties of a rectangle are given as;
A rectangle is seen as a type of quadrilateralThe opposite sides are parallel and also equal to each otherEach interior angle is equivalent to 90 degreesThe sum of all the interior angles is 360 degreesThe diagonals bisect each other at right angleBoth the diagonals are of the same lengthA rectangle with side lengths a and b has the perimeter that is equal to 2a+2b unitsA rectangle with side lengths a and b has the area that is given as ab sin 90 = ab square unitsA diagonal of a rectangle is also the diameter of its circumcircleLearn about rectangles at:
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The properties of a rectangle is listed below;
A rectangle is referred to as a quadrilateral
The diagram of a rectangle is attached
What are the properties of a rectangle?A rectangle is a 4 sided shape and also four vertices
A rectangle is referred to as a quadrilateral
The opposite sides of a rectangle is opposite and equal to each other
The diagonals of a rectangle are equal
The diagonals of a rectangle bisects each other
Each interior angle of a rectangle is equal to 90°
The sum of all the interior angles is equal to 360°
Therefore, a four sided quadrilateral with two opposite sides equal is a rectangle.
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Vector u = (-3, 8), and vector v = (-14, 6). Match each vector operation with the magnitude of its resultant vector
Answers
The magnitude of given operations of vectors are found.
What are Vectors?Quantities with the independent characteristics of magnitude and direction are called vectors.
Given:
u = (-3, 8) and v = (-14, 6)
So, 3u = (-9, 24) and 2v = (-28, 12)
3u - 2v = (-9+28, 24-12)
3u - 2v = (19, 12)
Magnitude of 3u - 2v = √19² + 12² = √505 units
2u = (-6, 16) and 3v = (-42, 18)
2u - 3v = (36, -2)
Magnitude = √36² + (-2)² = √1300 units
u = (-3, 8) and 4v = (-56, 24)
u + 4v = (-59, 32)
Magnitude = √(-59)² + 32² = √4505 units
5u = (-15, 40) and v = (-14, 6)
5u - v = (-1, 34)
Magnitude = √1157 units
7u = (-21, 56) and 2v = (-28, 12)
7u - 2v = (7, 44)
Magnitude = √1985 units.
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What is 20% off 250000 ?
Answers
From the given information provided, 20% off 250000 is 50000, and the discounted price is 200000.
The formula for calculating percentage is:
percentage = (part/whole) x 100
Here's an example:
Let's say you got 35 out of 50 questions correct on a test. To calculate the percentage of questions you answered correctly, you would use the formula as follows:
percentage = (35/50) x 100
percentage = 0.7 x 100
percentage = 70%
To calculate 20% off 250000, you can multiply 250000 by 20% (which is 0.20 in decimal form) and then subtract the result from 250000:
250000 - (0.20 x 250000) = 250000 - 50000 = 200000
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An ice cream store charges 75 cents for each scoop of ice cream and 25 cents for each cone. The formula c=0.75x+0.25
can be used to determine c, the total cost for an ice cream cone with x scoops of ice cream. According to the formula, how much should it cost to buy an ice cream cone with 4 scoops of ice cream?
Responses
Answers
You substitute the variable x for 4 and you solve the equation after.
c=0.75(4)+0.25
c=3+0.25
c=3.25
What is the value of x, given that the two prisms are similar?
Answers
Answer:
A. 10
Step-by-step explanation:
2/4 = x/20
1/2 = x/20
2x = 20
x = 10
Answer: 10
the population of a school is 800 students and is increasing at a rate of 2%per year.
Answers
Answer: Increases by 16 students per year
Step-by-step explanation:
100% = 800
2% = x
So between 100% and 2%, the scale factor would be 50 since 100 / 2 = 50
Then 800 / 50 would be 16
So..
1 Year = 816 students
2 Years = 832 students
3 Years = 848 students
4 Years = 864
And so on..
Which number has 57 as a multiple?
Answers
Answer:
What are the multiples of 57? The first 10 multiples of 57 are 57, 114, 171, 228, 285, 342, 399, 456, 513 and 570
Step-by-step explanation:
have great day
2.
(5x-2)(2x
+ 7)
= (5x)(2x) - 2(7)
= 10x² - 14
A.10x14
B.10x² +31x 14
C.7x + 5
D.10x + 5
Answers
The resultant of the given expression (5x-2)(2x+7) is 10x² + 31x - 14
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that contains variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent mathematical relationships and can be used to solve equations and perform calculations.
For example, the expression "3x + 2" is an algebraic expression that contains the variable "x", the numbers "3" and "2", and the mathematical operations of addition and multiplication.
Given expression ,
(5x-2)(2x+7)
= (5x-2)(2x+7) = 5x(2x) + 5x(7) - 2(2x) - 2(7)
= 10x² + 35x - 4x - 14
= 10x² + 31x - 14
Therefore, The resultant of the given expression (5x-2)(2x+7) is 10x² + 31x - 14
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HELP ME PLEASE!!!!! FAST ASAP HELP
PICTURE ATTACHED
A company logo is made up of a desire and two identical triangles as shown in this image
What is the area of the logo
Answers
The area of the logo is given as 139 cm
How to solve for the areaIn order to get the area of the shape, i would have to get the area of the triangles first
area of a triangle = 1/2 b * h
base = 9 / 2 = 4.5
h = 6
area = 1/2 * 9 * 6
= 27
Area of 2 triangle = 2 x 27
= 58
The are aof the square = a * a
= 9 * 9
= 81
The total area of the logo is given as 81 + 58
= 139 cm
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What are the math topics covered in the grade 6 math worksheets?
Answers
The math topics covered in the grade 6 math worksheets are algebra,geometry,measurement, number operation.
1. Number sense and operations: This includes understanding numbers, fractions, decimals, and integers, as well as performing operations with them.
2. Algebra: This includes understanding algebraic expressions and equations, and using them to solve problems.
3. Geometry: This includes understanding basic geometric concepts, such as lines, angles, and shapes, and using them to solve problems.
4. Measurement: This includes understanding measurement concepts, such as length, area, and volume, and using them to solve problems.
5. Data analysis and probability: This includes understanding basic concepts of statistics, such as mean, median, and mode, and using them to analyze data and make predictions.
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A 2020 study showed that the presence of male pattern baldness and a severe reaction to COVID-19 had a strong association, so some suggested that having male pattern baldness might somehow cause a person to have a severe reaction to COVID-19 (since they had been bald before catching COVID-19, so that the disease could not have caused their baldness). Which option below was most likely a lurking variable?
Age
Diet
Height
Weight
Answers
If a 2020 study showed that the presence of male pattern baldness and a severe reaction to COVID-19 had a strong association: A. Age is the most likely lurking variable in this scenario.
What is a lurking variable?In this case, the relationship between male pattern baldness and severe COVID-19 reactions may be influenced by age, as older individuals are more likely to experience both male pattern baldness and severe COVID-19 symptoms.
Age could also affect other factors such as overall health and immune system function, which may contribute to the severity of COVID-19 symptoms.
Diet, height, and weight may also be related to overall health and immune system function, but they are less likely to be related specifically to male pattern baldness
Therefore, age is the most likely lurking variable in this scenario.
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F(x)=4x+2 FIND THE INVERS SHOW WORK
Answers
Given To find Solution: First, we replace with and with : Now, we finally replace with Therefore, the inverse of is
Answer:y=(x-2)/4
Step-by-step explanation:
y=4x+2
4x=y-2
x=(y-2)/4
y=(x-2)/4
A letter in the word ACCEL is
chosen 50 times. results are
shown in the table below.
What is the theoretical probability of
choosing a C?
Answers
probability is calculated from the number of times an event happens, divided by the total number of trials in an actual experiment.
probability for choosing C = 7/50
Solve for x
Show proofs
Help
Answers
The length of the rise x is 25.5
How to determine the value of the side length xFrom the question, we have the following parameters that can be used in our computation:
Length = 17
Angle = 27 degrees
The rise, x is then calculated using the following laws of tangent
tan(27) = 13/x
Make x the subject
So, we have the following representation
x = 13/tan(27)
Evaluate the expression
This gives
x = 25.5
Hence, the value of x is 25.5
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Write the linear equation for the graph below.
Answers
Answer:
y = 6x
Step-by-step explanation:
The line is sloping up at a rate of 6 y units per 1 x unit. So the slope is 6/1 (6x)
If f(1) = 0, what are all the roots of the function ? use the remainder theorem.
Answers
By using synthetic division, we can find all the roots of the function f(x) = x³ + 3x² - x - 3 and determine that the roots are 1, -1, and -3.
A root of a function is a value for x that makes the function equal to zero.
In this case, we have a function f(x) = x³ + 3x² - x - 3 and we know that f(1) = 0. To find all the roots of this function, we can use the remainder theorem.
The remainder theorem states that if we divide a polynomial by a linear expression (such as x - a), the remainder will be equal to the value of the polynomial at that value of x (a). In other words, if we write f(x) = (x - a)q(x) + r, where r is the remainder, then f(a) = r.
So, if we divide our function f(x) by x - 1, the remainder will be equal to f(1), which we know is zero. Therefore, (x - 1) is a factor of f(x), and the function has a root at x = 1.
Next, we can divide f(x) by (x - 1) to get a quotient, q(x), and a new remainder, r. We can repeat this process, dividing q(x) by another linear expression until we have no more remainders.
The roots of f(x) will be the values of x that we used as factors in each step of the division process.
This process of dividing a polynomial by a linear expression to find its roots is called synthetic division.
Complete Question
If f(1) = 0, what are all the roots of the function f(x) = x³ + 3x² - x - 3. Use the remainder theorem.
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Write the equation of the line that passes through the points (4, -3) and (8,5). Put
your answer in fully simplified point-slope form, unless it is a vertical or horizontal
line.
Answers
An equation of the line that passes through the points (4, -3) and (8,5) is y + 3 = 2(x - 4).
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At data points (4, -3), a linear equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - (-3) = (5 - (-3))/(8 - 4)(x - 4)
y + 3 = 8/4(x - 4)
y + 3 = 2(x - 4)
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