Question 5 of 10
Which of the following rational functions is graphed below?
10 H
10
10
O A. F(x) =
FIX) *-*
X5
X1
B. Fx) = 6-14-5
(x - 1)(x-5)
c. F(X) = 1
D. F(X) = x+5
-
x + 1
Answers
We want to find the equation for the graphed rational function. Notice that the options are not given, so I will try to find the function only from the graph.
The function is:
[tex]f(x) = \frac{(x - 5)}{x - 1}[/tex]
How to analyze the graph of a rational function?The first thing that we can see in the graph is that we have vertical asymptotes at x = 1.
The one in the positive side (of the x range) goes to negative infinity, while the other goes to positive infinity, then the equation will be something like:
[tex]f(x) = \frac{something}{x - 1}[/tex]
Such that the asymptotes are caused when the denominator is equal to zero.
We can see that we also have a horizontal asymptote at y = 1.
This means that, as x tends to infinity, our function will tend to 1, so we have something like:
[tex]f(x) = \frac{(x + b)}{x - 1}[/tex]
The horizontal asymptote is equal to the ratio of the leading coefficients when both polynomials have the same degree, like here, so we can take the two leading coefficients equal to 1, such that:
y = 1/1 = 1
To find the value of b, we evaluate the function in 0:
[tex]f(0) = \frac{b}{-1} = -b[/tex]
And if you look at the graph, you can see that at x = 0 we have:
f(0) = 5
then b = -5
So the function is:
[tex]f(x) = \frac{(x - 5)}{x - 1}[/tex]
If you want to learn more about rational functions, you can read:
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Related Questions
amy is building a house. the basement floor is at -15 feet, The roof of the house is above the ground 25 feet. Write an inequality to compare the heights.
Answers
Answer:
25/15
Step-by-step explanation:
Find the value of x that makes the equation true.
2 = -x
Answers
9514 1404 393
Answer:
x = -2
Step-by-step explanation:
Multiply both sides of the equation by -1.
(-1)(2) = (-1)(-x)
-2 = x
The value of x that makes the equation true is x = -2.
Hello Good morning/evening/afternoon !
Pls Help ?!
Answers
Answer: y = 3/5x + 6
Step-by-step explanation: Slope intercept form is y = mx + b
We must convert your problem into this.
3x - 5y = -30
-5y = -30 - 3x
-5y = -3x - 30
y = (-3x - 30)/-5
y = 3/5x + 6
Would appreciate brainly <3
a. What is the probability that this couple spends 45 dollars or more?
b. Suppose that the restaurant is currently running a promotion with a 10% discount if the total amount spent by a table is 45 dollars or more. What is expected total amount the couple actually has to pay?
Answers
Using the probability table, it is found that:
a) There is a 0.25 = 25% probability that this couple spends 45 dollars or more. b) The expected amount the couple actually has to pay is $36.85.Item a:
To find the probabilities involving the total cost, we have to add the variables X and Y from the table, then:
[tex]P(X = 30) = P(X = 15|Y = 15) = 0.2[/tex]
[tex]P(X = 35) = P(X = 15|Y = 20) + P(X = 20|Y = 15) = 0.15 + 0.15 = 0.3[/tex]
[tex]P(X = 40) = P(X = 15|Y = 25) + P(X = 20|Y = 20) + P(X = 25|Y = 15) = 0.05 + 0.15 + 0.05 = 0.25[/tex]
[tex]P(X = 45) = P(X = 20|Y = 25) + P(X = 25|Y = 20) = 0.1 + 0.1 = 0.2[/tex]
[tex]P(X = 50) = P(X = 25|Y = 25) = 0.05[/tex]
The probability involving values of 45 or more is:
[tex]P(X \geq 45) = P(X = 45) + P(X = 50) = 0.2 + 0.05 = 0.25[/tex]
0.25 = 25% probability that this couple spends 45 dollars or more.
Item b:
For a discrete distribution, the expected value is the sum of each outcome multiplied by it's respective probability, hence, involving the 10% discount for prices above $45:
[tex]E(X) = 0.2(30) + 0.3(35) + 0.25(40) + 0.9[0.2(45) + 0.05(50)] = 36.85[/tex]
The expected amount the couple actually has to pay is $36.85
A similar problem is given at https://brainly.com/question/25782059
Will the answer to the addition problem below be odd or even?
2156 +992 = ?
Answers
Answer:
Even
Step-by-step explanation:
When two even numbers are added there will be an even result. To check this adding 2156 and 992 gets 3148 which is an even number.
find the area of a circle when the radius is 10cm. Take the value of pi as 3.14
Answers
Answer:
314.16 cm squared
Step-by-step explanation:
Mrs. sanders is bringing colored marshmallows to school so her students can do a graphing experiment. she has 25 students. if she gives each student 1/2 cup of marshmallows , how many cups of marshmallows will she need to bring to class?
Answers
Answer:
25 x 1/2 = 12.5
12 1/2 cups
In 9 minutes, Teresa can type 72 words. What is her rate in words per minute?
Answers
Answer:
8 words per min
Step-by-step explanation:
72/9 words = 9/9 minutes
8 words = 1 minute
which letter onthe diagram below represents a diameter of the circle.
Answers
Solve for B -(12 x 2) x (-6) = -12 x (2 x b)
A. -6
B. 6
C. -12
D. 12
Answers
Answer:
Option A
Step-by-step explanation:
-(12 x 2) x (-6) = -12 x (2 x b)
=> -24 x -6 = -12 x 2b
=> 144 = -24b
=> b = -6
Hoped this helped.
There are 13 pieces of chicken at the dinner table. After dinner, only 3 pieces are left. How many pieces were eaten at dinner?
16
8
7
10
Answers
Answer:
10
Step-by-step explanation:
13 pieses - 3 pieces = 10 pieces that are eaten
Answer:
10
Step-by-step explanation:
HELP ME OUT PLEASE!!!
Answers
Answer:
I think it is the second one.
Step-by-step explanation:
It might be right.
Hope this helps! :)
the price of 10 chairs is equal to that of 4 tables. the price of 15 chairs and two tables together is 4000$ the total price ( in $) of a chair and table is?
Answers
Answer:
$700 for a chair and a table
Step-by-step explanation:
Let t and c represent the price of a table and a chair, respectively. The given relations are ...
10c = 4t
15c +2t = $4000
Divide the first equation by 2 and substitute for 2t:
5c = 2t
15c +5c = $4000
20c = $4000
c = $200
t = 5c/2 = 5($200)/2 = $500
The total price of a chair and a table is ...
$200 +500 = $700 . . . . price of a chair and a table
15 mm
4. You are decorating the Red Cross logo
shown for a float in a parade.
a) The Red Cross logo consists of 5 congruent
squares. Find the area of the Red Cross logo.
+
b) You estimate that on average a red carnation
will cover 2 square inches and a red rose will cover
3 square inches. How many roses do you need to
cover the logo on the float?
36 in
c) You are on a budget. Carnations cost $1.00 and
roses cost $1.50. Should you cover the logo with
carnations or roses? Justify your answer.
Answers
Subtract.
7 1/5−(−3/5)
Enter your answer in the box as mixed number in simplest form.
Answers
Cause I’m smort
Answer:
7 4/5
Step-by-step explanation:
when you subtract, keep the first value then change subtract to addition and, finally, change the sign of the second value
this problem, 7 1/5 -(-3/5) is the same as this addition problem:
7 1/5 + 3/5
this equals 7 4/5
Lara made the table below of the predicted values for h(t), the height, in meters, of a penny t seconds after it is dropped off of the back of the bleachers.
A 2-column table with 9 rows titled Height of Penny over Time. The first column is labeled t with entries 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8. The second column is labeled h(t) with entries 2, 1.951, 1.804, 1.559, 1.216, 0.775, 0.236, negative 0.401, negative 1.136.
To the nearest tenth of a second, how much time would it take the penny to hit the ground?
0.5 seconds
0.6 seconds
0.7 seconds
0.8 seconds
Answers
Answer:
Step-by-step explanation:
as the chart is broken into steps with the same precision we're looking for. Just choose the one where height is closest to zero or 0.6 s
To do it mathematically
The equation is
h = 2 - ½gt²
to find g, plug in a time and height
0.236 = 2 - ½g(0.6²)
g = 9.8 m/s
check another one just to be sure
1.559 = 2 - ½(9.8)0.3²
1.559 = 1.559
now plug in zero elevation with an unknown time
0 = 2 - ½(9.8)(t²)
-2 = - ½(9.8)(t²)
t² = 4/9.8
t = 0.6388765...
t = 0.6 s
The time it takes for the penny to hit the ground is about 0.6 seconds.
Option B is the correct answer.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
To determine the time it takes for the penny to hit the ground, we need to find the point where the height of the penny is equal to zero.
Looking at the table,
We can see that the height of the penny is negative when t = 0.7 and becomes more negative for larger values of t.
So the penny must hit the ground between t = 0.6 and t = 0.7 seconds.
Now,
We can use linear interpolation to estimate the time at which the height of the penny is zero by finding the equation of the line that passes through the two points closest to zero on the table, namely (0.6, 0.775) and (0.7, -0.401).
So,
The slope of the line passing through these points.
= (change in height) / (change in time)
= (-0.401 - 0.775) / (0.7 - 0.6)
= -1.176
The equation of the line passing through these points.
y - 0.775 = -1.176(x - 0.6)
Simplifying
y = -1.176x + 1.438
Setting y to zero and solving for x.
0 = -1.176x + 1.438
x = 1.438 / 1.176
x ≈ 1.22
Therefore,
To the nearest tenth of a second, the time it takes for the penny to hit the ground is about 0.6 seconds.
Learn more about equation of a line here:
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Use the GCF and the distributive property to find each sum 15 + 57
Answers
Answer:
(3*5)+(19*3)
Step-by-step explanation:
both numbers GCF is 3.
(3*5)=15
(19*3)=57
15+57=72
Hope that helps
Find the equation of this line.
Answers
y=3/4x+1/4
I hope this helped :)
Answer:
Step-by-step explanation:
two points on the line are (-3,-2) and (5,4)
slope=(4-(-2))/(5-(-3)=(4+2)/(5+3)=6/8=3/4
eq. of line is
y+2=3/4(x+3)
4y+8=3x+9
4y=3x+9-8
4y=3x+1
y=3/4 x+1/4
Please take a look at the picture
Answers
Answer:
B) [tex]-\frac{a}{-b}[/tex]
Step-by-step explanation:
The value [tex]-\frac{-a}{b}[/tex] is the same as [tex]\frac{a}{b}[/tex] since the negatives cancel out to make a positive.
Option A is incorrect since the overall value of the term would be negative. Option B however is correct since there will not be a negative value in the denominator of a fraction and thus it cancels out with the negative in front of the fraction to produce the value of [tex]\frac{a}{b}[/tex] which is the same as the expression given in the question, thus it is option B.
Are the following polynomial sets open or closed?
6. (x ^ 2 + x - 4) - (x ^ 2 + x + 8)
7. (2 - x)(1 + 3x)
8. (5b - 3c)(7b - 3c)
Answers
Answer:
All closed.
Addition, subtraction as well as multiplication of polynomials result into another polynomial. Therefore, the set of polynomials is closed under addition, subtraction and multiplication.
Open polynomial set is (x² + x - 4) - (x² + x + 8)
Closed polynomial sets are (2 - x)(1 + 3x) and (5b - 3c)(7b - 3c)
What is polynomial?A polynomial is an expression consisting of variables and their coefficients, operations of addition, subtraction, multiplication, and positive-integer powers of variables are involved in polynomial. If the result of a polynomial set applying different operations is polynomial then it is closed under that operation.
Given, polynomial sets
(x² + x - 4) - (x² + x + 8)
Applying subtraction operation
x² + x - 4 - x² - x - 8
Subtracting like terms
-12
The result is integer, it is open polynomial set
(2 - x)(1 + 3x)
Applying multiplication operation
2 - x - x - 3x²
= 2 - 2x - 3x²
The result is polynomial, it is closed polynomial set
(5b - 3c)(7b - 3c)
Applying multiplication operation
35b² - 15bc - 21bc + 9c²
= 35b² - 36bc + 9c²
The result is polynomial, it is closed polynomial set
Hence, (x² + x - 4) - (x² + x + 8) is an open polynomial set
(2 - x)(1 + 3x) and (5b - 3c)(7b - 3c) are closed polynomial sets.
Learn more about polynomials here:
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The picture below shows the graph of which inequality?
Answers
Answer A is correct.
Step-by-step explanation:
Negative one is less than one.
(X-2)(5x+6)
Multiply using Distributive property
Answers
[tex](x-2)(5x+6)\\\\=x(5x+6) -2(5x+6)\\\\= 5x^2 +6x -10x -12 \\\\=5x^2 -4x-12[/tex]
5x-10x+6x-12
-`9x-12
i believe so
Solve the equation: c + -22 = 16
Answers
Answer:
c=38
Step-by-step explanation:
Answer:
c = 38
Step-by-step explanation:
c+(-22) = 16c-22 = 16c = 16+22c = 3812x3y2z3 - 8x2y2z2 + 20xy2z3
Answers
1/4 of students in a class play a musical instrument of those students 2/5 also speak a second language. What fraction of the whole class plays a musical instrument and speak a second language
Answers
Answer:
Step-by-step explanation:
Say the class has 20 students
20(1/4) = 5 play instruments
5(2/5) = 2 speak a second language
2 / 20 = 1/10
pls help i need it.
You are the Parish Youth Ministry treasurer Every year your organization conducts a fundraising activity to help the poor school-children in your parish. This year, your organization aimed to help 500 school-children by providing them school supplies. You have been tasked by the Parish Priest to lead this year's fundraising activity. Together with your co-officers, you go to Divisoria which is known to be the place where the cheapest prices for school supplies can be found. Here is the list of the items that you need and their prices. what is the total amount of this price per item? make a clear and accurate computation of the trial amount needed to buy all the school supplies that you need. present it to the praish priest who will approve budget. guide questions:
1. how much money does your organization need for this project?
2. if you already have a an existing fund of php 1,200.00, do you still need to raise a fund or not? why?
3. are you also a member/officer of an organization in your parish? if yes, write one among your remarkable experience for being a member of the organization.
Answers
Step-by-step explanation:
each child gets a certain amount of items costing the specified price by item.
so, we need to multiply the number of children with the number of items with the price per item to get the total cost.
500×3×3.5 for pencils = 5,250
500×5×7.5 for notebooks = 18,750
500×1×21.75 for crayons = 10,875
500×2×9.26 for pad paper = 9,260
total 44,135
since we have only 1,200 available in the existing fund, we need a new one to cover the remaining
44,135 - 1,200 = 42,935
4.
Which of the following equations has
both -1 and 4 as solutions?
A) x²+4x+4 B) x2-4x+3
C) x2-3x-4 D) x2+3x-4
Answers
A flight from Boston to London took only 5 hours because of a strong tailwind. The flight back to Boston against the same wind took 6 hours. What was the speed of the wind if the speed of the plane in still air is 550 mph?
Answers
Step-by-step explanation:
let v is the speed of the wind,
the equation of the speed:
(550 + v ) × 5 = (550 - v) × 6
2750 +5v = 3300 - 6v
11v = 3300 - 2750
11v = 550
v = 550/11
v = 50
therefore, the speed of the wind =
50 mph
Step-by-step explanation:
v = speed of the wind5(550 + v) = 6(550 - v)
2.750 + 5v = 3.330 - 6v
5v + 6v = 3.300 - 2.750
11v = 550
v = 550 ÷ 11
v = 50mph
if you get it right ill mark brainliest
Answers
Answer:
Step-by-step explanation:
? i cant see what the page is
solve pls brainliest