Graph the rational function f(x)=(3x-1)/(x-5)
Answers
To graph the rational function f(x) = (3x - 1) / (x - 5), follow these steps. Find the vertical asymptote(s) by setting the denominator equal to zero and solving for x.
x - 5 = 0
x = 5
The vertical asymptote of the function is x = 5.
Step 1: Find the horizontal asymptote by comparing the degrees of the numerator and denominator polynomials. Since the degree of the numerator (3x - 1) is 1, and the degree of the denominator (x - 5) is also 1, the horizontal asymptote is given by the ratio of the leading coefficients:
Horizontal asymptote: y = 3/1
Horizontal asymptote: y = 3
Step 2: Find the x-intercept by setting the numerator equal to zero and solving for x:
3x - 1 = 0
3x = 1
x = 1/3
The x-intercept is (1/3, 0).
Step 3: Find the y-intercept by setting x to zero and evaluating the function:
f(0) = (3 * 0 - 1) / (0 - 5)
f(0) = -1 / -5
f(0) = 1/5
The y-intercept is (0, 1/5).
Step 4: Find additional points to sketch the graph. Choose some x-values around the vertical asymptote (x = 5) and calculate the corresponding y-values. For example, you can use x = 4, x = 6, and x = 8.
x = 4:
f(4) = (3 * 4 - 1) / (4 - 5)
= 11 / -1
= -11
x = 6:
f(6) = (3 * 6 - 1) / (6 - 5)
= 17 / 1
= 17
x = 8:
f(8) = (3 * 8 - 1) / (8 - 5)
= 23 / 3
≈ 7.67
Step 5: Plot the points obtained from Steps 2 to 5 and draw the graph. The graph should approach the horizontal asymptote (y = 3) as it approaches the vertical asymptote (x = 5).
The graph of the rational function f(x) = (3x - 1) / (x - 5) should look like this:
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Related Questions
Ben bought 2 shirts for $16 each, 3 pairs of socks for $2.50 a pair, and a pair of jeans for $37.75. If the sales tax rate is 6.5%, how much did he pay for his items, including tax?
$127.46
$92.81
$82.27
$59.91
Answers
Answer:92.81
Step-by-step explanation:
Answer:
$82.27
Step-by-step explanation:
First, figure out how much it would be without tax.
(2*16=32) + (3*2.50=7.50) + 37.75 = 77.25
Then, multiply this number by your tax rate.
77.25*6.5 = 5.02
Lastly, add your original total with this tax amount for your answer.
77.25+5.02= 82.27
Ethan’s cookie recipe uses 3 cups of sugar to make 21 cookies. Mia’s recipe uses 4 cups of sugar to make 24 cookies. Who's recipe has more sugar per cookie?
Answers
Then Mias cookies are 24 cookies per 4 cups of sugar. You would do 24/4 to get 6, so 6 cookies per cup of sugar.
Mia’s cookies make less cookies per cup of sugar, so they’d have more sugar in them.
Mia- 6:1
Ethan- 7:1
Create your own scenario for a system of equations and solve it. Please do not just write two equations, but apply what you have learned and write your own possible real-world situation.
Answers
Answer:
Dr. Potter provides vaccinations against polio and measles.
Each polio vaccination consists of 444 doses, and each measles vaccination consists of 222 doses. Last year, Dr. Potter gave a total of 606060 vaccinations that consisted of a total of 184184184 doses.
How many polio vaccinations and how many measles vaccinations did Dr. Potter give last year?
Step-by-step explanation:
Answer:
Dr. Potter provides vaccinations against polio and measles.
Each polio vaccination consists of 444 doses, and each measles vaccination consists of 222 doses. Last year, Dr. Potter gave a total of 606060 vaccinations that consisted of a total of 184184184 doses.
How many polio vaccinations and how many measles vaccinations did Dr. Potter give last year?
a car drives at a rate of 65 mi/hr. what is the speed of the car in ft/s? note: 1 mi = 5280 ft
Answers
Answer:. 95.33 ft/sec
Multiply 65 by 5280 to get 343200 feet per hour. Then Divide by 3600. There are 60 minutes in an hour, and 60 seconds in a minute.
343200 ÷ 3600 = 95.333
Step-by-step explanation:
Answer:. 95.33 ft/sec
Multiply 65 by 5280 to get 343200 feet per hour. Then Divide by 3600. There are 60 minutes in an hour, and 60 seconds in a minute.
343200 ÷ 3600 = 95.333
Can you help me get this done by tonight pwitty pweeez... with a chewwy on top
Answers
Answer:
Step-by-step explanation:
try desmos calculator
Alyssa bought a dress for $52 and 3 pairs of jeans. She paid a total of $125. Write an equation to represent this word problem
(PLS ANSWER SERIOUSLY, I WILL GIVE A BRAINLY CROWN TO WHOEVER ANSWERS RIGHT)
Answers
Answer:
..
Step-by-step explanation:
If the dress is $52 all you have to do I subtract the total ($125)from the amount the dress was, which is 76
Answer:
125-52/3
Step-by-step explanation:
1. 125 -52 = 73
2. 73/3 = 24.3
If for triangle ABC and triangle PQR, the correspondence BCA to QRP is a congruence, which of the following are true.
a} Angle B is congruent to Angle Q
b} Angle P is congruent to Angle C
c} Angle C congruent to Angle Q
d} line segment AB is congruent to
line segment PQ
e] line segment BC is congruent to line segment RP
f] line segement AC is congruent
to line segment RP
Answers
Answer:
a d f
Step-by-step explanation:
hope this helps you :)
237,421 rounded to the nearest thousandth
324.3472 rounded to the nearest hundredth
129.9521 roundeded to the nearest tenth
Answers
Answer:
1. 237.40
2. 324.35
3. 130.0
Step-by-step explanation:
remember when the number next to the number BEING rounded,, 5 or more let it soar(goes to the next number) 4 or less let it rest (means it will be a 0)
2. Is 324.35
3. Is 130.0000
10x-(8 + 7x)
SIMPLIFY IT ASAP PLEASE
Answers
Answer:
10x - 15x
Step-by-step explanation:
Do what's in the parentheses and then write the rest out.
Hope this helps :)
Answer:
3 x− 8
Step-by-step explanation:1. Rearrange:
1 0 x− 1 ( 8 + 7 x)
1 0 x− 1 ( 7 x + 8 )
2. Combine Like Terms:
1 0 x − 7 x − 8
10x−7x−8 3 x − 8
3. Then Answer:3 − 8
Which expression best estimates Negative 18 and one-fourth divided by 2 and two-thirds?
18 divided by 3
Negative 18 divided by 3
Negative 18 divided by (negative 3)
18 divided by (negative 3)
Answers
Option (B) Negative 18 divided by 3
ILL GIVE BRAINLIEST PLZ HELP IM BEGGING
I NEED THE 2 QUESTIONS ASAP
Answers
Answer:
Step-by-step explanation:
question 1: options 2 and 5 have negative slopes
question 2: option 3
Please help! I will give brainliest!
Answers
Answer:
A
Step-by-step explanation:
trust me brother
subtracting a negative number is the same as adding the number
A cell phone company charges $60 a month for up to 1 gigabyte of data. The cost of individual data is $0.35 per megabyte. If d represents the number of additional gigabytes, and c represents total charges at the end of the month, which linear equation can be used to determine a users monthly bill?
Answers
c=60+0.05d
Hope this helps :)
Kayla is given a monthly allowance. She uses 40% of this allowance to purchase a designer bag, and then donates $15 to a charity. If she ends up with $155, which of the equations below can be used to determine what her monthly allowance was?
a. 0.40 X -15 = 155
b. 40 X + 15 = 155
c. 0.60 X - 15 = 155
d. 60 X -15 = 155
Answers
Answer:
A. 0.40x - 15=155
Step-by-step explanation:
40% can be written as 0.40
x = total money earned
-15 from that total
The expression which can be used to calculate her monthly allowance is 0.6X - 15 = 155
Let :
monthly allowance = X Designer bag purchase = 40% of X = 0.4X Donation to charity = $15Total amount left = $155Percentage left after bag purchase :
1 - 0.4X = 0.6X0.6X - charity = amount left
Therefore, the required expression is 0.6X - 15 = 155
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if the answer to a system of equations is x = 4 y = 0, if you were to graph the solution at what point(X,Y) would you expect to see the two lines intersecting. Explain your answer.
Answers
Answer:
Step-by-step explanation:
We can find the solution to a system of equations by graphing the equations. Let's do this with the following systems of equations:
\goldD{y=\dfrac{1}{2}x+3}y=
2
1
x+3start color #e07d10, y, equals, start fraction, 1, divided by, 2, end fraction, x, plus, 3, end color #e07d10
\greenE{y=x+1}y=x+1start color #0d923f, y, equals, x, plus, 1, end color #0d923f
First, let's graph the first equation \goldD{y=\dfrac{1}{2}x+3}y=
2
1
x+3start color #e07d10, y, equals, start fraction, 1, divided by, 2, end fraction, x, plus, 3, end color #e07d10. Notice that the equation is already in yyy-intercept form so we can graph it by starting at the yyy-intercept of 333, and then going up 111 and to the right 222 from there.
Next, let's graph the second equation \greenE{y=x+1}y=x+1start color #0d923f, y, equals, x, plus, 1, end color #0d923f as well.
The Hendersons went on a driving vacation. They decided to travel 1/3 of the distance on the first day. Owing to bad weather, they had to stop for the night having gone only 1/4 of the distance to the one-third point.
What fraction of the total distance did they travel the first day? Show your work and reduce to lowest terms.
Howie works at a petting zoo. He fed a piglet 1/5 of a bottle of milk, then gave 3/4 of what was left to a calf.
How much of the bottle of milk did the calf drink? Show your work and reduce to lowest terms.
Nathan used 2(5/6) loaves of bread to make sandwiches for a lunch. He made equal numbers of 4 different types of sandwiches.
What fraction of a loaf of bread did Nathan use for each type of sandwich?
Answers
Answer:
A)
[tex]\displaystyle \frac{1}{12}[/tex]
B)
[tex]\displaystyle \frac{3}{5}[/tex]
C)
[tex]\displaystyle \frac{17}{24}[/tex]
Step-by-step explanation:
Part A)
The Hendersons were traveling 1/3 of the distance on the first day.
However, they had to stop, having only traveled 1/4 of the 1/3 distance.
So, we can multiply the two fractions together.
Therefore, the fraction of the total distance they traveled is given by:
[tex]\displaystyle \frac{1}{4}\times\frac{1}{3}=\frac{1}{12}[/tex]
The Hendersons traveled 1/12 of the total distance.
Part B)
We are assuming the bottle of milk was full at the beginning.
So, at the beginning, there were 1/1 bottle of milk left.
Howie fed a piglet 1/5 of the bottle. So, there is now:
[tex]\displaystyle 1-\frac{1}{5}[/tex]
Of the bottle left.
Making common denominators and subtracting yields:
[tex]\displaystyle =\frac{5}{5}-\frac{1}{5}=\frac{4}{5}[/tex]
So, after feeding the piglet, 4/5 of the bottle of milk was still there.
3/4 of the remainder was fed to a calf.
So, the amount that was fed to the calf is 3/4 times 4/5. Therefore:
[tex]\displaystyle \frac{3}{4}\times\frac{4}{5}[/tex]
Multiply:
[tex]\displaystyle =\frac{12}{20}=\frac{3}{5}[/tex]
So, the calf drank 3/5 of the bottle of milk.
Part C)
Nathan used 2 (5/6) loaves of bread to make 4 sandwiches.
First, convert 2 (5/6) to an improper fraction. So:
[tex]\displaystyle 2\frac{5}{6}=\frac{12+5}{6}=\frac{17}{6}[/tex]
Nathan made 4 sandwiches using this. So, we will divide this by 4. Note that this is the same as multiplying by 1/4. Therefore:
[tex]\displaystyle \frac{17}{6}\times\frac{1}{4}=\frac{17}{24}[/tex]
So, Nathan used 17/24 loaves of bread per sandwich.
Plsss helppp i rlly need help with this math!!!
Answers
Answer:
13.150
14. 11.2
Step-by-step explanation:
Have a good day :)
9.
Daryll is given $30 and spends $1.25 per day on basketball cards. On the same day, Larry is given $2 and saves $1.25 per day. The graph shows the amount of money each boy has compared to the number of days that have passed.
How much money will each boy have on the day that the boys have the same amount of money?
$11.20
$30.00
$2.00
$16.00
Answers
The boys have $16 on 11th day.
What is Graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
Following the creation of a research question, data is continuously gathered through observation. The information is subsequently arranged, condensed, categorised, and visually portrayed.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Usually, data that varies over time is represented with a line graph.
Given:
Daryll is given $30 and spends $1.25 per day on basketball cards.
Larry is given $2 and saves $1.25 per day.
So, to find the same day for both from the graph.
We have to focus on where the lines for two persons intersects, it will the on same day how much money they have.
Hence, the boys have $16 on 11th day.
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Write an addition expression using integers to describe this situation. Then find the sum.
Roger owes his mom $5. He borrows another $6 from her.
Answers
Answer:
-5+6=
Sep-by-step explanation:
For each babysitting job, Adam charges a fee for his bus fare plus an hourly rate.
The graph shows how he calculates the cost of a babysitting job.
Drag numbers to complete a linear function in terms of x and y to model the situation.
Numbers may be used once, more than once, or not at all.
PLEASE I NEED HELP ASAP!!!!
You get 87 pointss please help meee
Answers
Answer:
Can you add more to it because this does not make sense if they numbers are already on the chart what numbers can we use
Step-by-step explanation:
Answer:
y = 6x + 2
Step-by-step explanation:
I'm a math expert. If I helped you, give me brainliest.
A school is going on a field trip to the zoo. There were s amount of students. The tickets cost $15 each. The school ended up giving the zoo $2,550 for all of the tickets. Write and solve an equation to figure out how many students are going on the trip.
Step by step
Answers
(divide both sides by 15)
S=170
170 students went
Answer:
15 times x which would be the students or you could do 2550 divided by 15 and you get 170 students
Step-by-step explanation:
9. The two figures below have a scale factor of 3 : 2. What is the value of x?
Answers
The value of x can be found by setting up a proportion based on the given scale factor of 3:2 is 16/3 units.
The breadth of the first parallelogram is 8 and the breadth of the second parallelogram is x.
Setting up the proportion, gives:
8/3 = x/2.
To solve for x, cross-multiply:
[tex]8 \times 2 = 3 \times x.[/tex]
Simplifying the equation, gives:
16 = 3x.
Next, divide both sides of the equation by 3 to isolate x:
x = 16/3.
Therefore, the value of x is 16/3.
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Brad has walked 4/9 of his goal distance this month. If his goal is 27 miles, how many miles has Brad walked
Answers
Answer:
12 miles
Step-by-step explanation:
you would multiply 4/9 by 27 and you would get 12 miles in total.
⚠️(Long Math Question!)⚠️ PLEASE HELP! THIS IS A TEST! "Jack compared the number of pink rose buses to the number of yellow rose bushes as part of a school project. Jack counted 3 pink rose bushes to every 8 yellow rose bushes. Later in the year, there was a drought and many rose bushes died. New rose bushes were planted to make sure there were the same number of rose bushes before the drought. The new ratio of the number of pink rose bushes to the number of yellow rose bushes is 5:6. After planting new yellow rose bushes there were 180 yellow rose bushes. How many pink and yellow rose bushes were there before the drought? Explain your answer using a tape diagram."
Answers
The ratio at the beginning of the year was 3:8 then it became 5:6 it says that they planted the rose bushes so there would be the same number as before so that means the ratio was 3:8 with 180 yellow rose bushes, to start solving you have to find out how many yellow rose bushes were represented by a 1 in the ratio, to get that divide 180 by 8 to get 22.5, now you know that a 1 in the ratio is equal to 22.5 bushes, multiply 22.5 by 8 to get the total number of yellow bushes and multiply it by 3 to get the total number of pink bushes so then you get (obviously) 180 total yellow rose bushes and 67.5 total pink rose bushes before the drought, you can check that by simplifying the ratio of 67.5:180 which simplifies into 3:8 which means the numbers check out! This took a super long time so please award brainliest or more points if you can.
it costs $3.45 to buy 3/4 lb of chopped walnuts. how much would it cost to purchase 7.5 lbs of walnuts?
Answers
Answer:
$6.75 I THINK
Step-by-step explanation:
I struggled to figure this out and I'm pretty sure its $6.75 but im not sure :(
:)
2) slope and y-intercept, i need help ASAP plz plz
Answers
Answer:
slope: 8.75 y intercept: 0
Step-by-step explanation:
Im not certain, but i think the equation would be y = 8.75x. I dont think there is a y intercept because she doesnt have any money to start with
Combine like terms to create an equivalent expression.
-1/2(-3y+10)
Answers
Answer: 3/2y - 5
Step-by-step explanation:
Explanation:
-1/2(-3y+10) distribute the -1/2
-1/2(-3y) = 3/2y
-1/2(10) = -5
3/2y - 5
Need helpp fastt plss will give brainliest to who is correct plss helpp
PLSSS HELPP I NEED THE ANSWER CORRECT
Answers
Answer:
below-
Step-by-step explanation:
The reason the reader may say this is because it doesn't add up to 100%
If all the votes were for Smith or Murphy, then 50% plus 20% should equal 100% but it actually equals 70%
Hope this helps dude
HELP ME PLEASE I WILL GIVE BRAINLIEST
Answers
Answer:
Donalds Donut shop
Step-by-step explanation:
There are cheeper because it might be more money but
there is more donuts and it is 0.59 cents per donut at Donald's but it is 0.73 cents per donut at Donut co.
At a book store there are 25 books on the clearance section. 20 of the books are young adult novels and the rest of the books are picture books. Which statement is not true? *
A) For every 4 young adult novels, there is 1 picture book
B) For every 5 books, 4 are young adult novels
C) The ratio of picture books to young adult novels is 1:4
D) There is 1 picture book for every 5 books
E) All statements are true