Show all work to identify the asymptotes and state the end behavior of the function f of x is equal to 5x divided by the quantity of x minus 25 end quantity.
Answers
The vertical asymptotes is x = 5 and the horizontal asymptotes is y = 5 and as x reaches to positive infinity f(x) reaches to 5
What is hyperbola?It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.
It is given that:
The equation of the function:
f(x) = 5x/(x - 1)
If we plot the above function on a coordinate plane we will see the above equation of the function represents a hyperbola.
The vertical asymptoes: x = 5
The horizontal asymptotes: y = 5
From the graph,
As x reaches to positive infinity f(x) reaches to 5
As x reaches to negative infinity f(x) reaches to 5
Thus, the vertical asymptotes is x = 5 and the horizontal asymptotes is y = 5 and as x reaches to positive infinity f(x) reaches to 5
Learn more about the hyperbola here:
brainly.com/question/12919612
#SPJ2
Answer:
Asymptotes
x = 25, y = 5
End behavior
\(\textsf{As }x \rightarrow - \infty, \text{f}(x) \rightarrow 5\)
\(\textsf{As }x \rightarrow \infty, \text{f}(x) \rightarrow 5\)
Step-by-step explanation:
Given rational function:
\(\text{f}(x)=\dfrac{5x}{x-25}\)
AsymptotesAn asymptote is a line that the curve gets infinitely close to, but never touches.
Vertical Asymptotes
To find the vertical asymptote(s) of a rational function, set the denominator to zero and solve for x.
\(\implies x-25=0\)
\(\implies x=25\)
Horizontal Asymptotes
If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.
If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote (but there is a slant asymptote).
If the degree of the numerator is equal to the degree of the denominator, divide the highest degree term of the numerator by the highest degree term of the denominator.
As the degree of the numerator of the given function is equal to the degree of the denominator of the given function, the horizontal asymptote is:
\(\implies y=\dfrac{5x}{x}\)
\(\implies y=5\)
End BehaviorThe end behavior of a function describes the behavior of the curve as x approaches positive and negative infinity.
As the given function has a horizontal asymptote at y = 5, this is the end behavior of the function. So as x approaches both positive and negative infinity, the function approaches the horizontal asymptote y = 5.
\(\textsf{As }x \rightarrow - \infty, \text{f}(x) \rightarrow 5\)
\(\textsf{As }x \rightarrow \infty, \text{f}(x) \rightarrow 5\)
Related Questions
using the line of best fit
Answers
The monthly cell phone bill when shared data equals zero is given as follows:
$26.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The intercept of the line in this problem is given as follows:
b = 26.
Hence $26 is the monthly cell phone bill when shared data equals zero.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Use the expression (5.3x+4)+(−4.7x+7). a. Find the sum. b. Explain how you know when to combine terms with variables.
Answers
The sum (5.3x+4)+(−4.7x+7) is 0.6x+11.
The sum of two or more numbers, magnitudes, quantities, or specifics as established by or as if determined by the mathematical addition process: 14 is the result of the combination of 6 and 8. a specific sum, particularly when referring to money: The costs were a huge amount. The outcome of adding two or more numbers or phrases is known as the sum in mathematics. As a result, the sum serves as a means of bringing everything together. To put it another way, combining two or more numbers yields a new outcome or sum.
(5.3x+4)+(-4.7x+7)
Determine the sign.
5.3x+4-4.7x+7
Combine like terms.
0.6x+11
Learn more about sum here
https://brainly.com/question/28421287
#SPJ1
Where does 1/6 land on a number line
Answers
Answer:
On a number line, 1/6 would land in the exact middle between 0 and 2/6
Step-by-step explanation:
Not too sure what your question meant, but I hope my answer helped!
If it wasn't what you were looking for, please let me know and elaborate on your question and I'll be happy to help out! :)
1. The sum of 6 and the quotient of a number and 4 is 10.
Answers
Step-by-step explanation:
20÷4=20/4=5 is the quotient I'm pretty sure
Answer:
34 Sorry if im kinda late
Step-by-step explanation
The equation is 6+x/4=10. now we figure out what x=? there are a lot of ways to figure out the answer this is what im gonna do first figure out what divided by 4 equals 10. multiply 10 times 4 you get 40 which means 40 divided by 4 equals 10 now subtract 6 from 40 and you get 34.
Please mark brainliest.
2.2.PS-16
Challenge Schools A and B are competing in an academic contest. Correct answers earn 9 points.
Incorrect answers lose 2 points. In the final round, School A gives the same number of correct and
incorrect answers. School B gives no incorrect answers and the same number of correct answers as
School A. School A started the final round with 62 points. School B started with 24. The game ends
with the two schools tied. Let x represent the number of correct answers given by School A in the final
round. Write an equation that models the outcome of the contest. Then find the number of answers
that each school got correct in the final round.
Which equation models the scoring in the final round and the outcome of the contest?
OA. 9x + 2x - 62 = - 9x + 24
OB. 2x-9x + 62 = 9x + 24
OC. 9x - 2x - 62 = 9x + 24
OD. 9x - 2x + 62 = 9x + 24
Answers
Answer:
9x - 2x + 62 = 9x + 24
Number of correct answer each obtained = 19
Step-by-step explanation:
Given that:
Number of correct answers = x
POINTS for correct answers = 9
POINTS for incorrect answers = - 2
SCHOOL A:
Number of correct answers = x
Number of incorrect answers = x
Initial point = 62
Initial point + 9(number of correct answers) + - 2(number of incorrect answers)
62 + 9x - 2x
SCHOOL B :
Number of correct answers = x
Number of incorrect answers = 0
Initial point = 24
Initial point + 9(number of correct answers) + - 2(number of incorrect answers
24 + 9x
Since they end up tied :
School A = School B
62 + 9x - 2x = 24 + 9x
9x - 2x + 62 = 9x + 24
Number of correct answers gotten :
9x - 2x + 62 = 9x + 24
7x + 62 = 9x + 24
7x - 9x = 24 - 62
-2x = - 38
x = 19
Hence, Number of correct answers each obtained = 19
find the inverse of each function
Answers
Answer:
c
Step-by-step explanation:
assume base 10
-logy = x
\( \frac{1}{ log(y) } = x\)
log base x y = 5 turns into the format x^ 5 = y
implement that to get c
(a) The perimeter of a rectangular field is 328 m.If the length of the field is 95 m, what is its width?Width of the field:
Answers
The rule of the perimeter of a rectangle is
\(P=2(L+W)\)L is the length
W is the width
Since the length of the field is 95 m
The perimeter of the field is 328 m
Substitute them in the rule
\(2(95+W)=328\)Divide both sides by 2
\(95+W=164\)Subtract 95 from both sides
\(\begin{gathered} 95-95+W=164-95 \\ W=69 \end{gathered}\)The width of the field is 69 m
bala has 18 meters of fabric. she uses 1/3 of the fabric to make curtains. she uses 3/8 of the remaining fabric to make a tablecloth. how much fabric does she have left?
Answers
Joanna created a triangular shaped vegetable garden and needs to put down fertilizer to cover the space. If the garden has a base of 1.4 m and a height of 2.6 m, what is the area of the garden?
Answers
Answer:
triangle
A=1/2 bh A=1/2 .1.4 . 2.6 A=1.82 m^2
Step-by-step explanation:
HELP ASAPPPPPPPPPPP!!!
The legs of an isosceles right triangle are 3 feet long. How long is the hypotenuse?
Answers
Answer:
Step-by-step explanation:
Since its isosceles right triangle, then 2 sides are going to be the same. There are 2 legs that are in any triangle, they give us 1 leg so now we know what the other leg is. Now the formula for finding hypotenuse is a2+b2=c2.
\(3^{2}+3x^{2} =c^{2}\) 3 squared is 9, so 9+9=18
now we have c but we arent done so now we find the square root, \(\sqrt{18}\). Which is \(3\sqrt{2}\) or 4.24.
Each of the following functions f,g,h, and h represents the amount of money in a bank account in dollars as a function of time x, in years they are each written in form m(x)= a•b
Answers
Answer:
f(x) : exponential growth
g(x); exponential growth
h(x): exponential growth
j(x): exponential decay
Step-by-step explanation:
In an exponential function such as
\(m(x) = a \cdot b^x\)
the factor that determines whether it is a growth or decay function depends entirely on the value of b since x cannot be negative
If b > 1, it is a growth function
If b < 1 then it is a decay function
If b = 1 neither growth or decay function values are constant
In this context
f(x) has b = 2 > 1 . Hence it is a growth function
g(x) has b = 3 > 1 hence growth function
h(x) has be = 3/2 > 1; hence growth function
j(x) has be = 0.5 < 1 hence decay function
Answer:
O f(x) : exponential growth
O g(x); exponential growth
O h(x): exponential growth
O j(x): exponential decay
Step-by-step explanation: I used to do this before :)
Find the arc length of the following problem:
Answers
Answer:
\(61.261 {ft}^{2} \)
Step-by-step explanation:
\( \frac{270}{360} \times 2\pi \: r \\ \frac{270}{360} \times 2 \times \pi \times 13 \\ = 61.261 {ft}^{2} \)
Can I have the brainliest please?Write an equation of a line that
represents the situation below:
sally bought 3 apples for $2
and 9 apples for $6.
Equation:
Answers
Answer:
(3 times 2)+(9 times 6)
Step-by-step explanation:
The total will equal 60 but also the 6 and 3 represents the money so if u have to put the $ sign u can
I really need help on this question. I have attached it thx. Do all the questions I have put on it so the answer and units.
Answers
Answer:
14 cm
Step-by-step explanation:
The formula for circumference of a circle is 2πr, where r is the radius. In this problem, the circumference would be 2π * 7cm = 14 cm
Skylar went shopping for a new video game. To find the total plus tax, she multiplied the price of the video game by 1.0775. What percent tax did she pay?
Answers
Answer:A topic sentence is used to bring
to a paragraph.
Step-by-step explanation:
A topic sentence is used to bring
to a paragraph.
4 siblings are weeding a flower bed with an area of 9 square yards. If they share the job equally, how many square yards of the flower bed will each child need to weed? Each child will need to weed ____ yards. (Write fraction answers like this, 1 1/2) *
Answers
Answer:
i think its 2 1\4
Step-by-step explanation:
i divided 9 by 4 on a mixed number caculator
Solve the following equation for x (in degrees).
Rounded to four places.
cos(x)=5/11
Answers
The solution for x in the equation cos(x)=5/11 is x = 62.9643
How to determine the solution for xFrom the question, we have the following parameters that can be used in our computation:
cos(x)=5/11
Evaluate the quotient of 5 and 11
So, we have the following representation
cos(x)=0.4545
Take the arccos of both sides
So, we have the following representation
x = 62.9643
Hence, the value of x is 62.9643 degrees
Read more about trigonometry function
https://brainly.com/question/24349828
#SPJ1
AB and AD are tangent to circle C. Find the length of AB, if AB = 8x and AD = x + 9. Round your answer to 2 decimal places.
Answers
When a line is tangent to a circle, it forms a right angle with the radius drawn to the point of tangency. This means that triangle ABD is a right triangle with AB as the hypotenuse.
We can use the Pythagorean theorem to find the length of AB:
AB^2 = AD^2 + BD^2
Since AD = x + 9 and BD = 8x - (x + 9) = 8x - x - 9 = 7x - 9, we can substitute these values into the equation:
(8x)^2 = (x + 9)^2 + (7x - 9)^2
64x^2 = x^2 + 18x + 81 + 49x^2 - 126x + 81
64x^2 = 50x^2 - 108x + 162
14x^2 + 108x - 162 = 0
Dividing the equation by 2, we get:
7x^2 + 54x - 81 = 0
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
a = 7, b = 54, c = -81
x = (-54 ± √(54^2 - 4 * 7 * -81)) / (2 * 7)
x = (-54 ± √(2916 + 2268)) / 14
x = (-54 ± √5184) / 14
x = (-54 ± 72) / 14
Now we solve for x:
Case 1: x = (-54 + 72) / 14 = 18 / 14 = 9 / 7
Case 2: x = (-54 - 72) / 14 = -126 / 14 = -9
Since the length of a segment cannot be negative, we discard the second case and focus on the positive solution.
Therefore, x = 9/7.
Substituting this value back into AB = 8x:
AB = 8 * (9/7) = 72/7 ≈ 10.29
Rounding to 2 decimal places, the length of AB is approximately 10.29 units.
Answer:
To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:
8x = x + 9
Solving for x, we get:
x = 1.5
Therefore, AB = 8x = 8(1.5) = 12.
To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:
AB^2 + BD^2 = AD^2
Substituting the values, we get:
12^2 + BD^2 = (1.5 + 9)^2
Simplifying, we get:
BD^2 = 56.25
Taking the square root of both sides, we get:
BD = 7.5
Hence, the length of AB is 12 and the length of BD is 7.5.
MARK AS BRAINLIEST!!!
share 560 in a ratio of 3 : 5 among two people, how much does each get
Answers
Step-by-step explanation:
Let the ratio constant be 'x'
Sum of the ratios=3x+5x=8x
First person gets:-
3/8 x 560 = 210
Second person gets:-
5/8 x 560 = 350
12,34761 (a) What is this number called? (b) How are the digits after the comma represented? (c) How many decimal places does the number have? (d) What can you say about the denominator of each digit after the comma?
Answers
This is a seven digits number that includes five decimal places. Moreover, the first digit after the comma is considered to be 1/10.
What is this number called?This number is twelve three four seven six one.
How many decimal numbers does it have?All numbers after the comma are decimal, therefore there are 5 decimal numbers.
How are the decimal numbers represented?The first decimal number is represented as 3/10, the second one is 4/100, the third one is 7/1000, the fourth one is 6/10000, and the last one is equivalent to 1/100000.
Learn more about decimal numbers in: https://brainly.com/question/4708407
#SPJ1
30.16=17.56+5x
What is the answer?
Answers
Answer:
2.52= x
Step-by-step explanation:
What' the mean 3,2,2,12 6,5,14,4
Answers
Answer: 6
Explanation: The mean of a data set is the sum of the numbers in the data set divided by however many numbers are in the data set.
So, let's begin by adding the numbers.
So we have 3 + 2 + 2 + 12 + 6 + 5 + 14 + 4 which is 48.
Now we divide 48 by the number of numbers in the set which is 8.
48 ÷ 8 is 6.
So the mean of the given data set is 6.
How many solutions are there to the equation below?|x| = -4
A 0
B 2
C 4
D 1
Answers
Answer:
There are 0
Step-by-step explanation:
Absolute value is the positive distance a number is away from 0, so no value of x will make the equation true
Answer:
A 0
Step-by-step explanation:
There are no solutions. Because the absolute value always returns a positive value, there are no solutions to this equation.
If x is negative, the answer will be positive. If x is positive the answer will still be positive. No value of x will give a value of -4. So there is no solution.
4−(3−5)=.
does anyone know what this is ??
Answers
4-(-2)
Two negatives equal one positive so it would be:
4+2
And 4 plus 2 is of course 6.
If -10 is subtracted from a number, the result is 6.
What is the number?
A. -16
B.-4
C. O
D. 4
Answers
Answer:
B.) -4
Step-by-step explanation:
-4-(-10)
-4+10
6
Match each equation with its graph. y = 5x + 2, y = 3x + 3, y = 2x + 3
Answers
Answer:
Green line: y = 5x + 2
Red line: y = 3x + 3
Purple line: y = 2x + 3
Step-by-step explanation:
1) All the given equations are in slope-intercept form, or \(y = mx + b\) format. When an equation is written in this form, the constant on the right side of the equation, or the \(b\), represents the y-intercept. The y-intercept is the point at which the line crosses the y-axis.
Knowing this, the y-intercept of \(y = 5x + 2\) must be (0,2). The only graph in which the line crosses the y-axis at the point (0,2) is the one with the green line, thus the graph of \(y = 5x + 2\) is the green one.
2) Now, since the other two equations share the same y-intercept, we have two graphs left. We can find out which graph belongs to which equation by taking a look at the slope of the line. The number in place of \(m\), or the coefficient of the x-term in an equation in slope-intercept format represents the slope. Thus, the slope of \(y = 3x +3\) is 3 and the slope of \(y = 2x + 3\) is 2.
Now, find the slope of one of the lines in the graphs. To do so, use the slope formula, \(m = \frac{y_2-y_1}{x_2-x_1}\). Substitute the x and y values of two points on the chosen line into the formula in order to figure out the line's slope. I chose to find the slope of the red line, using the points (0,3) and (-1,0):
\(m = \frac{(0)-(3)}{(-1)-(0)} \\m = \frac{0-3}{-1-0}\\m = \frac{-3}{-1} \\m = 3\)
So, the slope of the red line is 3. Its equation must be \(y = 3x + 3\) since it has the matching slope. By process of elimination, the purple line must have the equation of \(y = 2x + 3\).
The Matching is:
Green line: y = 5x + 2Red line: y = 3x + 3Purple line: y = 2x + 3What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
We know the slope- intercept form
y= mx+ b
where m is the slope.
For y= 5x+ 2 the slope is 5.
and, for y= 3x+ 3 the slope is 3.
and, for y= 2x+ 3 the slope is 2.
For Graph 1, the slope is 5/1= 5
and, For Graph 2, the slope is 6/2= 3
and, For Graph 3, the slope is 6/3 = 2
Learn more about slope here:
https://brainly.com/question/3605446
#SPJ2
Lincoln Middle School is painting a circle on their playground with a radius of 18 feet. What will be the total area of the circle, in square feet?
Use π = 3.14, and round your answer to the nearest hundredth.
Answers
Answer:
1017.36
Step-by-step explanation:
area = 3.14 (18)square
3.14 (324)
1017.36
50 Points! Multiple choice algebra question. One factor of x^3+4x^2-11x-30=0 is x+2. Find the remaining factors. Photo attached. Thank you!
Answers
The solution to the above algebra question is (b) x-3, x+5.
What is the explanation for the above response?To find the remaining factors of the polynomial x^3+4x^2-11x-30=0, we can use polynomial long division or synthetic division. However, since we are given that x+2 is a factor of the polynomial, we can use synthetic division to simplify the process.
We set up the synthetic division table as follows, using -2 as the divisor:
-2 | 1 4 -11 -30
|____-2__-4___30
| 1 2 -15 0
The bottom row of the table represents the coefficients of the quadratic polynomial obtained by dividing x^3+4x^2-11x-30 by x+2. The last term of the quadratic is 0, which indicates that x+2 is a factor of the polynomial. The remaining quadratic polynomial can be factored as:
x^2 + 2x - 15 = (x - 3)(x + 5)
Therefore, the remaining factors of the polynomial x^3+4x^2-11x-30=0 are x+2, x-3, and x+5.
The correct answer is (b) x-3, x+5.
Learn more about algebra at:
https://brainly.com/question/24875240
#SPJ1
1853
1854
1850
1851
1852
YEAR
1841
1847
1848
1849
8:59
NUMBER
OF IRISH
IMMIGRANTS
37,772
105,536
112,934
159,398
164,004
221,253
159,548
162,649
101,606
Which of the following statements mos
accurately describes patterns of Irish
immigration in the mid-19th century?
O It remained relatively unchanged.
O
It continually increased between
1847 and 1854.
Answers
The statement that most accurately describes patterns of Irish immigration in the mid-19th century is: its peaked in approximately 1851. The Option D is correct.
What was pattern of Irish immigration to US in mid 19th century?Irish immigration to the United States in the mid-19th century was characterized by several factors:
Timing: Irish immigration to the United States peaked in the mid-19th century, particularly in the decades following the Great Famine of 1845-1852. During this time, millions of Irish fled to the United States to escape poverty and famine at home.Destination: Irish immigrants tended to settle in cities, particularly in the Northeast, such as Boston, New York, and Philadelphia. These cities offered employment opportunities and a supportive Irish-American community.Employment: Many Irish immigrants in the mid-19th century worked in manual labor jobs, such as construction, manufacturing, and domestic service. They faced significant discrimination and prejudice from the American-born population, who often considered them to be inferior and less capable.Read more about Irish immigration
brainly.com/question/27970047
#SPJ1
What is the order number of this image?
a) 8
b) 9
c) none
d) 4
Answers
Answer:
a)8
Step-by-step explanation:
kxxxchgddggcgghxdzxttxrt