Answers
The horizontal asymptote is at y=4, shown by the green dashed line. This indicates the behavior of the function as x becomes very large in magnitude.
The blue dot marks the y-intercept at (0,6).
To find the graph that represents the function [tex]\( f(x) = \frac{2}{x-1} + 4 \)[/tex], let's analyze its characteristics step by step:
1. Identify the Type of Function
The function [tex]\( f(x) = \frac{2}{x-1} + 4 \)[/tex] is a rational function, specifically a transformed version of the reciprocal function.
2. Vertical Asymptote
The denominator [tex]\( x - 1 = 0 \)[/tex] gives the vertical asymptote, which is [tex]\( x = 1 \)[/tex]. This means the graph will approach but never touch the line [tex]\( x = 1 \)[/tex].
3. Horizontal Asymptote
For large values of x, the term [tex]\( \frac{2}{x-1} \)[/tex] approaches zero. Thus, the horizontal asymptote is determined by the constant term, which is [tex]\( y = 4 \)[/tex].
4. Y-Intercept
To find the y-intercept, set [tex]\( x = 0 \)[/tex]:
[tex]\[ f(0) = \frac{2}{0-1} + 4 = 2 + 4 = 6 \][/tex]
So, the y-intercept is at (0, 6).
5. Behavior around Asymptotes
As x approaches 1 from the left, [tex]\( f(x) \)[/tex] goes to negative infinity.As x approaches 1 from the right, [tex]\( f(x) \)[/tex] goes to positive infinity.6. Additional Points
It might be helpful to calculate the function's value at a couple of additional points for a more accurate graph. For instance, calculate [tex]\( f(2) \)[/tex] and [tex]\( f(-1) \)[/tex].
7. Sketching the Graph
Considering these characteristics, the graph:
Has a vertical asymptote at [tex]\( x = 1 \)[/tex].Has a horizontal asymptote at [tex]\( y = 4 \)[/tex].Passes through the y-intercept at (0, 6).Shows the function going to negative infinity as x approaches 1 from the left and to positive infinity as x approaches 1 from the right.Here is the graph of the function [tex]\( f(x) = \frac{2}{x-1} + 4 \)[/tex]. As analyzed:
(Graph is give below)
It has a vertical asymptote at x=1, represented by the red dashed line. The function goes to negative infinity as x approaches 1 from the left and to positive infinity as x approaches 1 from the right.
The complete question is here:
Which graph represents the function [tex]$f(x)=\frac{2}{x-1}+4$[/tex] ?
Related Questions
If m = 35 cm and n = 37 cm, what is the length of l?
A. 15 cm
B. 13 cm
C. 12 cm
D. 2 cm
Answers
So the right answer is 12cm.
Look at the attached picture ⤴
Hope it will help u..
Answer:
12
Step-by-step explanation:
What is the m in 45m - 900 = 90m
Answers
Step-by-step explanation:
[tex]45m - 900 = 90m \: [/tex]
[tex]45m - 90m = 900[/tex]
[tex] - 45m = 900[/tex]
[tex]m = \frac{900}{ - 45} = - 20[/tex]
Answer:
m=-20
Step-by-step explanation:
45m -900=90m
-900=45m
-900/45=45m/45
m=-20
Which fraction has the greatest value 1/3 2/3 2/9 2/9
Answers
Answer:
2/3
Step-by-step explanation:
Gavin is starting a running plan to train for a race. In the first week of his running plan, Gavin will run 5 miles. The plan calls for Gavin to increase his weekly milage by 3.5 miles every week. If Gavin sticks to the plan, how many miles would he be expected to run during his 11th week of the training plan? Round to the nearest tenth (if necessary).
Answers
Step-by-step explanation:
In the first week of his running plan,the number of miles covered = 5 miles
Weekly mileage will increase by 3.5 miles every week.
At the end of second week, the number of miles covered = 5 + 3.5 = 8.5
At the end of third week, the number of miles covered = 8.5 + 3.5 = 12
The series is 5, 8.5, 12, ...
Consider this as an AP, where a = 5, d = 3.5
By formula,
[tex]a_{n} = a + (n-1)d[/tex]
Substituting the values in the above equation, we get
[tex]a_{11} = 5 + (10-1) 3.5[/tex]
= 5 +(9)3.5
= 5 + 31.5
=36.5 miles.
Gavin would be expected to run during 36.5 miles during his 11th week of the training plan
Kenny and Kylee's music players have the same capacity for music. Kenny's music player is full with 320 songs. His songs have an average length of four minutes. Kylee has fewer songs, but the average length of her songs is five minutes. Assuming both music players are at full capacity, how many songs does Kylee have?
224
200
128
256
Answers
Given that both players have the same capacity, we first calculate the total time in minutes for Kenny's music player by multiplying the number of Kenny's songs (320) by the average length per song (4 minutes). The result is 1280 minutes. We then take this number and divide by the average length of Kylee's songs (5 minutes) to find that Kylee's music player holds 256 songs.
Explanation:In this problem, we are given that Kenny and Kylee's music players have the same capacity, but Kylee's songs are longer on average. We are asked to find out how many songs Kylee has on her player assuming it is at full capacity. To do this correctly, we first need to understand that we're dealing with an issue of equal music player capacities, but the time a song occupies on each player is different.
Let's calculate the total capacity of the music player in minutes, we multiply the number of Kenny's songs (320) by the average length of each song (4 minutes), giving us 1280 minutes.
Because both players have the same capacity, Kylee's player can also hold 1280 minutes of music. However, since Kylee's songs are longer on average (5 minutes each), she will have fewer songs on her player. So, dividing the total capacity in minutes (1280) by the length of Kylee's songs (5 minutes) gives us 256 songs. That is the number of songs on Kylee's music player.
Learn more about Problem Solving here:https://brainly.com/question/31606357
#SPJ12
Mai's water bottle had 24 ounces in it. After she drank x ounces of water, there were 10 ounces left. Select all the equations that represent this situation.
Answers
Answer:
x+10=24
Step-by-step explanation:
the actual equation would give you 14
To represent the situation, you can use the equation x = 24 - 10 or the proportion x/24 = 10/24.
Explanation:To represent the situation, we can use the equation: x = 24 - 10, where x represents the amount of water Mai drank. This equation represents the fact that the initial amount of water in the bottle (24 ounces) minus the amount of water that Mai drank (x ounces) equals the remaining amount of water (10 ounces).
Alternatively, we can also use the proportion x/24 = 10/24 to represent the situation. This proportion shows that the ratio of the amount of water Mai drank to the initial amount of water in the bottle is equal to the ratio of the remaining amount of water to the initial amount of water.
The points in the table lie on a line. What is the slope of the line?
Answers
To find the slope(m), use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] And plug in two points on the line. I will use
(-2, 1) = (x₁, y₁)
(4, -6) = (x₂, y₂)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{4-(-2)}{-6-1}[/tex] (two negative signs cancel each other out and become positive)
[tex]m=\frac{4+2}{-6-1}[/tex]
[tex]m=\frac{6}{-7}[/tex]
To calculate the slope of the line passing through the points (-8, -2) and (4, 10), use the formula m = (y2 - y1) / (x2 - x1), which gives a slope of 1.
The question pertains to finding the slope of a line that passes through certain points with given x and y coordinates. The slope of a line is the ratio of the change in y (the rise) to the change in x (the run). To calculate it, we can use any two points on the line. Let's use the points (-8, -2) and (4, 10) as an example.
We calculate the slope (m) using the formula:m = (y2 - y1) / (x2 - x1)
Substituting the values:m = (10 - (-2)) / (4 - (-8))
m = (12) / (12)
The slope m equals 1.This means for every increase of 1 on the horizontal axis, there is a rise of 1 on the vertical axis.
Please help me with the following question.
Answers
I am pretty sure x is 9 because if you divide 14 by 2 you get 7. 18 divided by 2 is 9.
Answer:
x=9
Step-by-step explanation:
the word similar means the same shape but different sizes. That means that you can think of this problem as ratios. The ratio for the first triangle would be 14:14:18. Since the second ones ratio is 7:7:x we know that the seven was found by dividing 14 by two so we do that with the rest of the of the number to find x you divide 18 by two and get 9. So x=9.
(a) Find the GCF of 18 and 8
(b) use the GCF to factor 18-8
18 - 8 = blank x (blank - blank)
Answers
b) 2*(9-4). You divide both 18 and 8 by their GCF. You can check this- 18-8 is 10 and 2*5 is 10. (I got the 5 from 9-4.)
The Greatest Common Factor (GCF) of 18 and 8 is 2. Using this GCF, 18 - 8 can be factored as 2 × (9 - 4).
(a) To find the GCF (Greatest Common Factor), we need to determine the largest number that divides both 18 and 8 without leaving a remainder.
Prime factors of 18: 2 × 3 × 3
Prime factors of 8: 2 × 2 × 2
The only common prime factor is 2.
So, the GCF of 18 and 8 is 2.
(b) We know that 18 - 8 = 10. To factor this expression using the GCF, we rewrite 10 as a product involving the GCF.
Factor out the GCF (2) from 18 - 8:
10 = 2 × (9 - 4)
So, 18 - 8 = 2 × (9 - 4).
y=−7x+8 y=−7x−8 Choose 1 answer: Choose 1 answer: (Choice A) A Exactly one solution (Choice B) B No solutions (Choice C) C Infinitely many solutions
Answers
Answer:
I THINK ITS A ;-;
Step-by-step explanation:
Answer:
no solution
Step-by-step explanation:
the ordered pair is not a solution to the equation
Please help me ASAP i give brainliests and thanks :)
Answers
Answer:
Positive
Step-by-step explanation:
Since there are two x-intercepts, -2 and 2, there is a positive discriminant. If the parabola was below the x axis and opened downwards, the discriminant would be negative.
Answer:
positive
Step-by-step explanation:
The length of a rectangle is 1 meter less than its
width. The area of the rectangle is 42 square
meters. Find the dimensions of the rectangle.
Answers
If the length of the rectangle is x, then we know the width is x + 1.
The area of a rectangle is length · width, so we can substitute as x · (x + 1)
Now, we now x · (x + 1) = 42
Expand
x² + x = 42
Solve
x² + x - 42 = 0
(x + 7)(x - 6) = 0
So, x = 6
That means the length is 6 meters and the width is 7 meters.
The dimensions of the rectangle are:
Width, W = 7 meters
Length, L = 6 meters
Let's denote:
L = the length of the rectangle
W = the width of the rectangle
Given that the length of the rectangle is 1 meter less than its width, we can write the equation:
L = W - 1
We're also given that the area of the rectangle is 42 square meters. The formula for the area A of a rectangle is:
A = length × width
Substituting the given values, we have:
42 = (W - 1) × W
Now, let's solve this equation for W to find the width of the rectangle.
42 = [tex]W^2[/tex] - W
Rearranging terms, we get a quadratic equation:
[tex]W^2[/tex] - W - 42 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula. Factoring seems simpler in this case:
Product = 1 × -42 = -42
Sum = -1
Required numbers: 6 × -7
[tex]W^2[/tex] - W - 42 = 0
[tex]W^2[/tex] + 6W - 7W - 42 = 0
W (W + 6) - 7 (W + 6) = 0
(W - 7) (W + 6) = 0
Setting each factor equal to zero gives us two possible values for W:
W - 7 = 0 or W + 6 = 0
Solving each equation:
W - 7 = 0W = 7
W + 6 = 0W = -6
Since the width of the rectangle cannot be negative, we discard W = -6.
So, the width of the rectangle is W = 7 meters.
Now, to find the length L, we can use the equation L = W - 1:
L = 7 - 1
L = 6
The question is:
The length of a rectangle is 1 meter less than its width. The area of the rectangle is 42 square meters. Find the dimensions of the rectangle.
When two pipes fill a pool together, they can finish in 4 hours. If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 9 hours. How long will it take each pipe to fill the pool if it were working alone?
Answers
The faster pipe will fill the pool in 6 hours and the slower pipe will fill the pool in 12 hours.
What is time and work for commercial mathematics?Work Done = Time Taken × Rate of Work. Rate of Work = 1 / Time Taken. Time Taken = 1 / Rate of Work. If a piece of work is done in x number of days, then the work done in one day = 1/x.
Given here, two pipes fill the pool in 4 hours if they work together and If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 9 hours.
Let volume of the pool be LCM(9,4)= 36 unit³ and their efficiencies be E₁ and E₂ respectively then we have E₁+E₂ = 36/4
=9 units
Also 18/ E₁ +18/E₂ = 9
putting E₁=9-E₂ we get
18₁/ 9-E₂ +18/E₂ = 9
E²₂ -9E₂ +18 =0
(E₂ +3) (E₂ -6) =0
Therefore E₂ =6 units as efficiency cannot be negative and consequently E₁ =3 units
Hence, if they are working alone they finish the work in 36/3 =12 hours and 36/6=6 hours respectively.
Learn more about time and work here:
https://brainly.com/question/3854047
#SPJ3
Solve for an angle in right triangles help
Answers
Answer:
71.57
Step-by-step explanation:
Tangent = opposite over adjacent (sides)
TanA = ( 9/3 )
A = [tex]Tan^{-1}[/tex](3)
A = 71.57
Factor and solve: -3p^2 - p - 2 = 0
Please show step by step and how to factor trinomials when the leading coefficient is a negative number.
Answers
Answer:
Step-by-step explanation:
-3p² - p - 2 = 0
a = -3; b = -1 c = -2
[-b ±√(b² - 4ac)]/2a = [1 ± √(1-4*-3*-2) ] /2*-3
=[1 ± √(1-48) ]/-6
= - [1 ±√-47]/6
= - [1 ±√47i]/6
The graph below represents the path of a grasshopper as it jumps which type of function models the data on the graph
Answers
Answer:
Quadratic
Step-by-step explanation:
Given function is a quadratic function.
There are many key features in a quadratic graph such as the zeroes (x-intercepts, also known as the roots), y-intercept, axis of symmetry, and the vertex.
The graph of a quadratic function is a parabola, which has several important properties:
Vertex: The vertex is the point where the parabola changes direction. It is the highest or lowest point on the parabola, depending on whether the parabola opens upward or downward, respectively.
Axis of symmetry: The axis of symmetry is a vertical line that divides the parabola into two symmetrical halves. It passes through the vertex and is perpendicular to the directrix.
Directrix: The directrix is a horizontal line that is located at a distance equal to the distance between the vertex and the focus. It is perpendicular to the axis of symmetry and reflects the parabola onto itself.
Focus: The focus is a point on the axis of symmetry that is located at a distance equal.
As we can see that given graph has two roots and it is symmetric to the line parallel to the y-axis.
From the graph we know this is a quadratic function { a parabola with respect to symmetry and axis symmetry}
Learn more about Quadratic equation here:
https://brainly.com/question/22364785
#SPJ7
The whale swims down 300 feet to feed. What is the whale’s elevation now?
Answers
The elevation of the whale is -300 feet.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the whale swims down 300 feet to feed. The elevation of the whale will be:-
Elevation = -300 feet
Therefore, the elevation of the whale is -300 feet.
To know more about an expression follow
https://brainly.com/question/25230781
#SPJ2
Mark sold 445 tickets for the school play. Student tickets cost $3 and adult tickets
cost $5. Mark's total income for the event was $1871. How any adult tickets did he
sell?
Answers
Answer:
Mark sold 268 adult tickets.
Step-by-step explanation:
We are given the following in the question.
Let x be the number of students ticket sold and y be the number of adult tickets sold.
Total number of tickets sold = 445
Thus, we can write the equation:
[tex]x + y = 445[/tex]
Cost of student ticket = $3
Cost of an adult ticket = $5
Total income = $1871
Thus, we can write the equation:
[tex]3x + 5y = 1871[/tex]
Solving the two equations, we get,
[tex]3x + 5y - (3x+3y) = 1871 - 3(445) \\2y = 536\\\Rightarrow y = 268\\\Rightarrow x = 445 - 268 = 177[/tex]
Thus, Mark sold 268 adult tickets.
Answer:he sold 268 adult tickets at the school play
Step-by-step explanation:
find the product d^j•d^k
Answers
Answer:
d^(j+k)
Step-by-step explanation:
d^j * d^k
We know that a^b * a^c = a^(b+c)
d^(j+k)
Would do anything for the answer to this question
Answers
Given:
The length of the entire rectangle is 10x + 7.
The width of the entire rectangle is 6x.
The length of the unshaded rectangle is 4x - 5.
The width of the unshaded rectangle is 2x.
We need to determine the area of the shaded region of the rectangle.
Area of the entire rectangle:
The area of the entire rectangle can be determined using the formula,
[tex]A=length \times width[/tex]
Substituting the values, we have;
[tex]A_1=(10x+7)(6x)[/tex]
[tex]A_1=60x^2+42x[/tex]
Thus, the area of the entire rectangle is 60x² + 42x
Area of the unshaded rectangle:
The area of the unshaded rectangle can be determined using the formula,
[tex]A=length \times width[/tex]
Substituting the values, we have;
[tex]A_2=(4x-5)(2x)[/tex]
[tex]A_2=8x^2-10x[/tex]
Thus, the area of the unshaded rectangle is 8x² - 10x
Area of the shaded region of the rectangle:
The area of the shaded region of the rectangle can be determined by subtracting the area of the entire rectangle by the area of the unshaded rectangle.
Thus, we have;
[tex]A=A_1-A_2[/tex]
Thus, we have;
[tex]A=60x^2+42x-(8x^2-10x)[/tex]
[tex]A=60x^2+42x-8x^2+10x[/tex]
[tex]A=52x^2+52x[/tex]
[tex]A=52x(x+1)[/tex]
Thus, the area of the shaded region of the rectangle is 52x(x + 1)
The domain of F(x) is the set of all numbers greater than or equal to 0 and
less than or equal to 2.
A. True
B. False
Answers
Answer:
Frue
Step-by-step explanation:
HELP ASAP !!!
Please explain why
Answers
Option 4: if you’ll insert (0,0) in the equation then you’ll get 0>-2 which is true so (0,0) is a solution. Another way to check is if (0,0) is in the shaded region of the graph
Option 5: in the equation-2 is the y-intercept which proves it intersects at (0,-2) on the y-axis
Easy 50 points, one multi choice question
Answers
Answer:
A
Step-by-step explanation:
but it prob doesnt help tho
Answer:
B is the correct answer
Step-by-step explanation:
What is the factor pair for the multiplication sentence below?
11 x 9 = 99
A. 9,99
B. 11.99
c. 11,9
Answers
Find the circumference of the circle.r=9in
56.52 inches
14.13 inches
63.59 inches
254.34 inches
28.26 inches
Answers
Answer:56.52
Step-by-step explanation: I just did it
Use the table to work out the values of
a
,
b
,
c
, and
d
.
x
y
=
x
2
+
2
x
−
4
−
3
−
1
−
2
a
−
1
b
0
−
4
1
−
1
2
c
3
d
a
=
b
=
c
=
d
=
Answers
By substituting the given x-values from the table into the equation y = x² + 2x - 4, we found that a=-4, b=-5, c=4, and d=11.
Explanation:The values of a, b, c, and d can be found by substituting the given x-values from the table into the formula y = x2 + 2x - 4.
For a, place -2 in the equation so we get y = (-2)2 + 2*(-2) - 4 = 4 - 4 - 4 = -4.
For b, place -1 in the equation, and it results y = (-1)2 + 2*(-1) - 4 = 1 - 2 - 4 = -5.
The third value, c, is computed by substituting 2 for x to obtain y = (2)2 + 2*2 - 4 = 4 + 4 - 4 = 4.
Lastly, for d, the y-value when x is equal to 3 is y = (3)2 + 2*3 - 4 = 9 + 6 - 4 = 11.
So, the solutions are a=-4, b=-5, c=4, and d=11.
Learn more about Solving equations here:https://brainly.com/question/17595716
#SPJ12
Air Jordan’s are manufactured in China and reportedly cost Nike a bit more then $16 a pair in 2014. The Air Jordan 10s are listed on Amazon for $240. What is the percent increase for Air Jordan’s sold in the US to the nearest tenth?
Answers
Answer: That would be a massive 1500% increase from 16 to 240
In a scale drawing, the height of a tree is 3 inches. In real life, the height of the tree is 6 feet. What is the scale factor?
A. 1/24
B. 24
C. 3 in : 6 ft
D. 6 in : 3 ft
Answers
Answer:
The answer is A 1/24
12(6)=72
72/3=24
2) What is 8% of 24.52? Round your answer to the nearest hundredth.
Answers
What is 8% of 24.52= 1.9616
just round up
Answer:
What is 8% of 24.52= 1.9616
Step-by-step explanation:
round it
A landscaper planted 10 cattails by a new pond. The number of cattails double each month over a period of time. Write a function f(x) to model the number of cattails in the pond after x months. f(x)=?
Answers
Answer:
[tex]\large \boxed{f(x) = 10(2)^{ x}}[/tex]
Step-by-step explanation:
Write a table giving the number of cattails for the first few months
[tex]\begin{array}{lr}\mathbf{x} & \mathbf{f(x)}\qquad \qquad\quad \\0 & 10 = 2^{0}(10) = 10(2)^{0}\\1 & 2(10) = 2^{1}(10)= 10(2)^{1} \\2 & 2\times2(10) = 2^{2}(10)= 10(2)^{2} \\3 & 2\times 2^{2}(10) = 2^{3}(10)= 10(2)^{3}\\4 & 2\times 2^{3}(10) = 2^{4}(10)= 10(2)^{4}\\\end{array}\\\text{The pattern appears to be $\large \boxed{\mathbf{f(x) = 10(2)^{\mathbf{x}}}}$}[/tex]