Mathematics College

Find the horizontal or oblique asymptote of f(x) = negative 3 x squared plus 7 x plus 1, all over x minus 2

Answers

Answer 1
Find the horizontal or oblique asymptote of f(x) = negative 3 x squared plus 7 x plus 1, all over x minus 2

Finding the horizontal and oblique asymptote of
f(x)= (-3x^2+7x+1)/(x-2)

Solution:

For Horizontal Asymptote:
Line y=L is a horizontal asymptote of the function y=f(x), if either limx→∞f(x)=Llimx→∞f(x)=L or limx→−∞f(x)=Llimx→−∞f(x)=L, and LL is finite.

Calulate limits:

limx→∞(1x−2(−3x2+7x+1))=−∞

limx→−∞(1x−2(−3x2+7x+1))=∞

Thus, there are no horizontal asymptotes.

For Oblique Asymptote:

Do polynomial long division (−3x2+7x+1)/(x-2)=−3x+1+3/(x−2)

The rational term approaches 0 as the variable approaches infinity.

Thus, the slant asymptote is y=−3x+1y=−3x+1.


Related Questions

hey can you please help me posted picture of question

Answers

The correct answer is option B

(5 + 3i)(4+ 2i)

= 5(4+2i) + 3i(4+2i)

= 20 +10i + 12i +6i²

= 20 +22i +6(-1)

= 20 + 22i - 6

= 14 + 22i

an organization surveyed a random sample of their employees about their new vacation policy. Out of the employees surveyed, 83% rated the vacation policy as "delightful" with a margin of error of ±2% and a confidence interval of 95%. What does the margin of error imply?

Answers

Margin of error implies that the number of those who rated the vacation as delightful ranges between 81% (that is, 83-2) and 85% (that is, 83+2) of the population at a 95% confidence interval.

Answer:

Given is:

Out of the employees surveyed, 83% rated the vacation policy as "delightful" with a margin of error of ±2% and a confidence interval of 95%.

±2% means plus 2% from 83% and minus 2% from 83%, making the interval between 81% and 85%.

In general the margin of error tells that, how many percentage points the results will differ from the real population value. A small margin of error shows trustworthy results whereas a large margin of error means the results are not accurate.

Therefore, it can be concluded, with 95% confidence, that between 81% and 85% of all employees will rate the vacation policy as "delightful."

when is periodic data useful? give examples to support your answer please

Answers

It's useful in following conditions:

(i) when you want to know the valency to male compounds
for example :
when H2 and O2 react in normal conditions they form H2O, amd here we needed crossmultiplication of their valencies.

(ii) To know masses while calculating mass number.
For example In case you wanna find mass of 100 molecules of H2O.

(iii) To find electronegativity (to determine type of bond formed).
For example: which kind of bond Hydrogen and Clorine will form.



what is sqrt p^5 q^10 expressed in simplified form?

Answers

The simplified form of the expression [tex]\sqrt{p^5q^{10}}[/tex] is p²q⁵√p, obtained by separating and simplifying the square roots of the individual factors.

The expression [tex]\sqrt{p^5q^{10}}[/tex] can be simplified by separating the square roots of the individual factors and simplifying each one individually.

First, let's rewrite the square root of the entire expression:

[tex]\sqrt{p^5}[/tex] = p²√p because we are taking the square root of p to the fifth power which results in p squared and the square root of p remaining.[tex]\sqrt{q^{10}}[/tex] = q⁵ because q to the tenth power is a perfect square, and taking the square root gives us q to the fifth power.

Therefore, the simplified form of [tex]\sqrt{p^5q^{10}}[/tex] is p²q⁵√p.

The table below shows a correct representation that 15 pounds (lb) of sugar cost $3: lb lb lb lb lb lb lb lb lb lb lb lb lb lb lb $1 $1 $1

Answers

by the way you are saying it the answer would be 0.20

Answer:

true

Step-by-step explanation:

2,5,11,20 32,47 what is the next number in the series

Answers

it is easy 2,  5, 11,   20,  32,  47,   65
              +3,+6, +9,+12,+15,+18, +21, 

The next number in the series is 65. To identify the pattern in the given series and find the next number, let's look at the differences between consecutive terms.

5 - 2 = 3

11 - 5 = 6

20 - 11 = 9

32 - 20 = 12

47 - 32 = 15

As we observe, the differences between consecutive terms are increasing by 3 each time. So, to find the next difference, we add 3 to the last difference:

15 + 3 = 18

Now, to find the next number in the series, we add this difference to the last number in the series:

47 + 18 = 65

Therefore, the next number in the series is 65.

To know more about series:

https://brainly.com/question/30241975

#SPJ6

Q # 17 , Find the slope

Answers

In order to find the slope we need to find two points on the line.

From the above graph we can see that the points (-4,-1) and (0, -3) lie on the line. So using these two points we can find the slope.

[tex]Slope=m= \frac{-3-(-1)}{0-(-4)} \\ \\ m= \frac{-3+1}{0+4} \\ \\ m= \frac{-2}{4} \\ \\ m= \frac{-1}{2} [/tex]

So, first option is the correct answer
The slope is given by:
 m = (y2-y1) / (x2-x1)
 Substituting values we have:
 m = (- 4 - (- 3)) / (2-0)
 Rewriting we have:
 m = (- 4 + 3) / (2-0)
 m = (- 1) / (2)
 m = -1 / 2
 Answer:
 The slope is given by:
 m = -1 / 2
 option 1

Solve the system using the substituiton method
branliest offered
3x-7y=10
x-4y=5

Answers

Hi there!

To solve this problem using substitution, we need to set x equal to a value and substitute it into the other equation.

Since
x - 4y = 5,
x = 5 + 4y

3x - 7y = 10
3(5 + 4y) - 7y = 10
15 + 12y - 7y = 10
15 + 5y = 10
5y = -5
y = -1

Now that we know y is -1, we can substitute it back into the equation to find x:

y = -1
x - 4y = 5
x - 4(-1) = 5
x - (-4) = 5
x + 4 = 5
x = 1

So, your answers are x = 1 and y = -1.

Hope this helps!

hey can you please help me posted picture of question

Answers

The discriminant can be determined from the number of roots of the graph.

If Disc> 0, the function has two distinct roots
If Disc = 0, the function has a repeated root
If Disc < 0, the function has no real root.

Since the given graph has no real root, i.e. it does not cross x-axis at any point, so we can say that the discriminant of the given function is negative.

So the answer to this question is option C

Ken started saving for retirement at age 35 with plans to retire at age 70. He invested an average of $600 per month in various securities, with an average annual return of 5% adjusted for inflation. Assuming monthly compounding, how much has Kent saved at the start of retirement

A: $54,192.18
B: $825,655.45
C: $499,355.18
D: $681,655.46

Answers

The answer is C $499,355.18

What are a) the ratio of the perimeter’s b) and the ratio of areas of the larger figure to the smaller figure?

Answers

did you get the answers?

a) We have been given two similar figures and we have to find ratio of perimeters of these figures.

Let a be given side of larger figure and b be the given side of smaller figure. Let [tex]p_{1} \text{ and } p_{2}[/tex] be the perimeters of two figures and [tex]A_{1} \text{ and } A_{2}[/tex] be the areas of the two figures.

We know that perimeters of two similar figures are in the ratio of corresponding sides.

[tex]\frac{p_{1}}{p_{2}}=\frac{a}{b}[/tex]

We have been given, [tex]a=26\text{ and }b=6[/tex]

Therefore, upon substituting these values in the above equation, we get

[tex]\frac{p_{1}}{p_{2}}=\frac{26}{6}[/tex]

[tex]\frac{p_{1}}{p_{2}}=\frac{13}{3}[/tex]

(b)

Further we know that areas of two similar figures are in the ratio of squares of corresponding sides.

[tex]\frac{A_{1}}{A_{2}}=\frac{a^{2}}{b^{2}}\\ \frac{A_{1}}{A_{2}}=\frac{26^{2}}{6^{2}}\\ \frac{A_{1}}{A_{2}}=\frac{676}{36}\\ \frac{A_{1}}{A_{2}}=\frac{169}{9}\\[/tex]

Therefore, first option is the correct answer.


A marble is drawn at random first from a jar containing four black and four white marbles, and then from a jar containing six black and two white marbles. What is the probability of drawing two black marbles?

Answers

[tex] |\Omega|=8\cdot8=64\\
|A|=4\cdot6=24\\\\
P(A)=\dfrac{24}{64}=\dfrac{3}{8}=37.5\% [/tex]

Answer:

the answer is 37.5% Hope this helps!

A father is giving his child a 30-inch long softball bat for her birthday.He has a rectangular box that has the dimensions of 5 inches by 6 inches by 25 inches. Will the bat fit in the box ? Explain

Answers

I think it will because 5 × 6 × 25 = 750 in.

The bat is 30 in.

So, I think it will fit.

Hope this helped☺☺

Answer:

No, the bat will not fit. Using the Pythagorean theorem, the length of a diagonal of a face of the box is about 24 inches, and the length of the diagonal of the cube is about 29.4 inches. This is less than the length of the bat.

Step-by-step explanation:

Edguenity

At a school for performance art students
2/5

of the girls study music,
3/5

of the girls study dance and
1/6

of the girls study music and dance. What fraction of those who study music also study dance?

Answers

the to the girls studying music and dance the factions is 55

#1. if i have a circle with a radius of 6 in and it is cut into 8 equal slices (like a pie) and the coordinates are (8, 5) then what is the central angle, what is the measure of the arc that 2 pieces together would intercept, and the equation that represents as well as the circumference?

I also need the same answers for these:

#2. radius 10 inches, 14 equal pieces, and points of (3, 7)

#3. radius 25 cm, 16 pieces and 14 and 53

#4. radius 12 inches, 8 pieces and points of (2, 5)

#5. radius 4 inches, 12 equal pieces, and points of (3, 6)

Answers

part 1)
coordinates of the center (8,5)
radius=6 in
is cut into 8 equal slices-----> 360°/8-----> 45° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-8)²+(y-5)²=6²

b) circumference=2*pi*r-----> 2*pi*6---> 37.68 in
if 360° (full circle) has a length of---------> 37.68 in
 90° (2 pieces together)---------> x
x=90*37.68/360-----> x=9.42 in

the measure of the arc that 2 pieces together would intercept is 9.42 in

c)  The central angle of one slice is 45 degrees

Part 2)
coordinates of the center (3,7)
radius=10 in
is cut into 14 equal slices-----> 360°/14-----> 25.71° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-3)²+(y-7)²=10²

b) circumference=2*pi*r-----> 2*pi*10---> 62.8 in
if 360° (full circle) has a length of---------> 62.8 in
 51.42° (2 pieces together)---------> x
x=51.42*62.8/360-----> x=8.97 in

the measure of the arc that 2 pieces together would intercept is 8.97 in

c)  The central angle of one slice is 25.71 degrees

Part 3)
coordinates of the center (14,53)
radius=25 cm
is cut into 16 equal slices-----> 360°/16-----> 22.5° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-14)²+(y-53)²=25²

b) circumference=2*pi*r-----> 2*pi*25---> 157 cm
if 360° (full circle) has a length of---------> 157 cm
 45° (2 pieces together)---------> x
x=45*157/360-----> x=19.63 cm

the measure of the arc that 2 pieces together would intercept is 19.63 cm

c)  The central angle of one slice is 22.5 degrees

Part 4)
coordinates of the center (2,5)
radius=12 in
is cut into 8 equal slices-----> 360°/8-----> 45° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-2)²+(y-5)²=12²

b) circumference=2*pi*r-----> 2*pi*12---> 75.36 in
if 360° (full circle) has a length of---------> 75.36 in
 90° (2 pieces together)---------> x
x=90*75.36/360-----> x=18.84 in

the measure of the arc that 2 pieces together would intercept is 18.84 in

c)  The central angle of one slice is 45 degrees

Part 5)
coordinates of the center (3,6)
radius=4 in
is cut into 12 equal slices-----> 360°/12-----> 30° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-3)²+(y-6)²=4²

b) circumference=2*pi*r-----> 2*pi*4---> 25.12 in
if 360° (full circle) has a length of---------> 25.12 in
 60° (2 pieces together)---------> x
x=60*25.12/360-----> x=4.19 in

the measure of the arc that 2 pieces together would intercept is 4.19 in

c)  The central angle of one slice is 30 degrees


Q9 Q6.) Write an equation for intersection l₂ that keeps traffic moving.

Answers

The numbers of cars entering the intersection are z and 7. The numbers of cars exiting the intersection are x and 5. To keep traffic moving, ...
  number entering = number exiting
  z + 7 = x + 5

The appropriate selection is ...
  A. z +7 = x +5

Peter is working for an hourly wage of 12$ if he worked for 20 hours last week what is his gross pay

Answers

Hourly wage = $12
Number of hours Peter worked = 20 hours

Gross Pay = Hourly Wage x Number of Hours worked

Using the values, we get:

Gross Pay = 12 x 20 = $240

Thus, the gross pay of Peter was $240 for his work of last week

In a survey conducted in an Office, 60% of the sample respondents agreed that employees should have flexible working hours.
If the margin of error is +-2%, the expected population proportion that wanted flexible working hours is between -------% and------%

Answers

The % margin of error means that the real value is in the range between the mean less the margin error and the mean plus the margin error. This is [ mean - % of error, mean + % of error]. Then, in this case the error of +/- 2% means that the expected population proportion that wants flexible working hours is between 60% - 2% and 60% + 2%, which is between 58% and 62%.

Answer:

Yes, the answer is between 58% and 62%

Step-by-step explanation:

I just did it on Edmentum

identify the slope and Y- intercept of the graph of the equation.Then graph the equation, Y = - 5/4X + 1

Answers

The solution is as shown in the figure.

The slope = -5/4

the slope of the line below is -3. which of the following is the point-slope form of the line? A.) y+2=3(x-2) B.) y+2=-3(x-2) C.) y-2=-3(x+2) D.) y-2=3(x+2)

Answers

The "point-slope" form of the equation of a straight line is:

[tex]y-y_1=m(x-x_1)\\\\(x_1;\ y_1)\ is\ a\ known\ point\\\\m\ is\ the\ slope\ of\ the\ line[/tex]

We have:

[tex]m=-3;\ (x_1;\ y_1)=(2;-2)[/tex]

Substitute

[tex]y-(-2)=-3(x-2)\\\\y+2=-3(x-2)[/tex]

Answer: B. y + 2 = -3(x - 2)

Answer:

B) y + 2 = -3(x - 2)

Step-by-step explanation:

it's what I got

Jack had $80 more than Eric. When Jack spent $30, he found that the amount of money he had left was twice s much as Eric had. How much did the boys have altogether at the beginning?

Answers

First we define variables:
 x: amount of money Jack has
 y: amount of money Eric has
 We write the system of equations:
 x = y + 80
 x - 30 = 2y
 Solving the system we have:
 x = $130 
 y = $ 50
 Therefore, the amount of money they had at the beginning is:
 130 + 50 = $ 180
 Answer:
 the boys had $ 180 altogether at the beginning

a season ticket for bolton f.c. this season cost £410 it is to go up by 34% next season how.much will a season ticket cost next season?

Answers

This should be right if you're doing multipliers -

100 + 34 = 134
÷ 100 = 1.34
1.34 is your multiplier. So if you do 410 x 1.34 you'll have £549.40
I may be wrong, but I'm quite sure this is right!

A rubber ball dropped on a hard surface takes a sequence of bounces, each one 4/5 as high as the preceding one. If this ball is dropped from a height of 10 feet, what is the total vertical distance it has traveled at the time when it hits the surface for its fifth bounce?
A) 28 77/125 feet
B) 49 1/25 feet
C) 57 29/125 feet
D) 59 29/125 feet

Answers

Answer:

The answer is 57 29/125 feet ⇒ answer (C)

Step-by-step explanation:

∵ The ball dropped from a height 10 feet

∴ The vertical distance = 10 feet

∵ It bounces 4/5 as high as the preceding one

∴ 1st bounce = 10 × 4/5 = 8 (move down another 8)

∴ The vertical distance = 8 + 8 = 16 feet

∴ 2nd bounce = 8 × 4/5 = 6.4 (move down another 6.4)

∴ The vertical distance = 6.4 + 6.4 = 12.8 feet

∴ 3rd bounce = 6.4 × 4/5 = 5.12 (move down another 5.12)

∴ The vertical distance = 5.12 + 5.12 = 10.24 feet

∴ 4th bounce = 5.12 × 4/5 = 4.096 (move down another 4.096)

∴ The vertical distance = 4.096 + 4.096 = 8.192 feet

∵ The ball will hit the surface to make the 5th bounce

∴ The total vertical distance is :

   10 + 16 + 12.8 + 10.24 + 8.192 = 57.232 = 57 29/125

Another way:

* We can use the formula of geometric sequence with

  1st bounce distance (a) = 8 + 8 = 16 and ratio (r) = 4/5

  and number of bounces (n) = 4 (hit the surface for its 5th bounce)

∵ [tex]S_{n}=\frac{a(1-(r^{n}))}{1-r}[/tex]

∴ [tex]S_{4}=\frac{16(1-(\frac{4}{5})^{4})}{1-\frac{4}{5}}=47\frac{29}{125}[/tex]

* Then we must to add the 10 feet

  (the ball dropped from height 10 feet)

∴ The total vertical distance = 10 + 47 29/125 = 57 29/125 feet

Hey can you please help me posted picture of question

Answers

The correct option is: Option (D) 7

Explanation:
These type of questions can easily be solved using the Venn diagram. Below is the image attached that shows the Venn diagram and the solution. 
THere are seven patrons that dont like any of these coffee drinks

so the answer for your question is D.7

I hope I can show the solution but I cant post the picture right now :(

Hope  Ihelped

A batch of cookies requires 3/8 cup of butter. Butter can be purchased in boxes, each containing 4 sticks, with 1 stick equivalent to 1/2 cup of butter. If Monica is to bake 15 batches of cookies, which of the following is the best estimate for the total number of boxes of butter she needs to buy?

Answers

Firstly, we need to find how many cups of butter is needed to bake [tex]15[/tex] batches. We will need [tex]15 \cdot \frac{3}{8} = \frac{45}{8}[/tex] cups of butter. This is [tex]5.625[/tex] cups. Since we can only buy butter in boxes with 2 cups of butter in it, we will have to buy 3. This will give us 6 cups of butter, which will be enough. If we only buy 2, then we will only have 4 cups of butter, which won't be enough to bake 15 batches of cookies.
So, the answer is [tex]\boxed{3}.[/tex]

which is an example x-intercept of the graph of the function y=tan(x-(5pi/6))

Answers

Answer: x = 5π/6

Explanation:

1) Given function:

[tex]y=tan(x- \frac{5 \pi }{6} )[/tex]

2) x-intercept are the roots of the function, i.e. the solution to y = 0

3) to find when y = 0, you can either solve the equation or look at the graph.

4) Solving the equation you get:

y = 0 ⇒ tan(x - 5π/6) = 0 ⇒ x - 5π/6 = arctan(0)

arctan(0) is the angle whose tangent is zero,so this is 0

⇒ x - 5π/6 = 0 ⇒ x = 5π/6.

Then, one example of an x-intercept is x = 5π/6, which means that when x = 5π/6, the value of the function is 0.

Since, the tangent function is a periodic function, there are infinite x-intecepts, that is why the questions asks for one example and not all the values.

You can verify by replacing the value x = 5π/6 in the given function:

y = tan (5π/6 - 5π/6) = tan(0) = 0.

Answer:

D?

Step-by-step explanation:

what is 103.468 rounded to the nearest liter

Answers

Rounded to the nearest liter: 103

Hope this helps!
This question is asking you to round a number, the number will be rounded up if 1 digit below them is a value of 5 or more and if the number below them is 4 or less. In this question you have to round to the nearest liter which means the nearest one. The number in this question is 103.368, one digit below one will be the 0.4. Since the value is 4, which is lower than 5, then the number is rounded down. So your answer would be 103.

Choose the correct factorization for the polynomial 21xy+15x+35ry+25r

Answers

(21xy +15x )+ (35ry +25r)
3x(7y+5)+ 5r(7y+5)
(3x+5r)(7y+5)
 
Please rate

the sum of a number and 7 is the same as double the number increased by 3

Answers

So, let’s represent the number as n:
n+7=2n+3
Subtract both sides by 3:
n+4=2n
Now by n:
2n=4
Divide:
n=2
The number is 2
The statement above is the same as the mathematical expression below...

x + 7 = 2x + 3

We want to solve for x in these types of problems. To do so, we must get all of the "x"s on one side of the equal sign and the constants on the other.

7 - 3 = 2x - x
4 = x

Our answer is x = 4.

suppose you toss a fair coin and roll a fair six-sided die. What is the probability your actions result in tails on the coin and 3 on the die

Answers

mines 3 to 6 and use 2 power
Other Questions
One function of the plant cuticle is to increase water uptake by roots true or false If cosine x is approximately.9511 what is the measurement of x to the nearest degree? Approximately what is the sine of the angle that is complementary to x A free bird leapson the back of the windand floats downstreamtill the current endsand dips his wingin the orange sun raysand dares to claim the sky.Read the stanza. What is the figurative meaning of the phrase floats downstream? has no worries likes many things needs few people glides with the waterhas no worrieslikes many thingsneeds few peopleglides with the water Help! WHAT IS THE VALUE OF X, and can you show how you got it please? 4 times x plus 2 is at most 10 The Tran Family drove 1,246 miles during a vacation that lasted 14 days. How many miles on average did they drive each day? :3 N the species selection model, __________ is to macroevolution as __________ is to microevolution. Sally has ncd. her motor control and memory have been impacted, though their impairment is not the most significant symptom of her condition. the most significant symptom is her loss of inhibition, evident in her chronic gambling. sally most likely has _____. what is the icd-10-pcs code for a vasectomy A person whose eye level is 1.5 meters above the ground is standing 75 meters from the base of the jin mao building in shanghai, china. the person estimates the angle of elevation to the top of the building is about 80. what is the approximate height of the building What are three consecutive odd integers that have a sum of 39? Maeve is majoring in dance at a local college. although her weight falls into the normal range, some nights she often goes out and eats large amounts of food at each of the five dining halls on campus. after she is through, she feels very guilty and worries about her weekly "weigh-in" at her ballet class and so returns to her dorm where she vomits. maeve is suffering from Which table represents a direct variation function? x y x y x y -3 -4.5 -5.5 -3 -3 -7.5 -1 -3.0 -5.5 -1 -1 -2.5 2 -1.5 -5.5 2 2 5.0 5 0.0 -5.5 5 5 12.5 10 1.5 -5.5 10 10 25.0 x y -5.5 10 -4.5 8 -3.5 6 -2.5 4 -1.5 2 Which excerpt from the poem best reflects the Romantic fascination with the supernatural? A-- Through caverns measureless to man / Down to a sunless sea.B-- A savage place! As holy and enchanted / As eer beneath a waning moon was haunted / By woman wailing for her demon lover!C--The shadow of the dome of pleasure / Floated midway on the waves; / Where was heard the mingled measure / From the fountain and the caves.D--It was an Abyssinian maid, / And on her dulcimer she played, / Singing of Mount Abora.guys is this not a stupid question?? i mean like what poem is it freaking talking about?!! Someone please help me? what does n6 is?????? Monica is shopping for candy for her wedding and needs lollipops and gummy bears for a display she is making for the reception. Lollipops are $1 per pound and gummy bears are $0.75 per pound. She knows she wants to spend exactly $15 on candy. If she spent $9 on lollipops, which of the following is the number of pounds of gummy bears she purchased?68912 Why did many Civil Rights leaders oppose President Lyndon Johnson on the Vietnam War? They felt that the draft unfairly targeted minorities. They did not support any foreign policy of the United States. They were strong supporters of the communist Vietcong. They objected to the segregation in the U.S. military. Simplify the equation 7.5+N+9.63 In which organelle does photosynthesis take place? stoma vascular bundle mitochondrion chloroplast