For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1? f (x) = StartFraction 2 x Superscript m Baseline Over x a EndFraction a = –1, m = 0 a = 1, m = 0 a = –1, m = 1 a = 1, m = 1.

Answers

Answer 1

Answer:

C. a= -1, m=1

Step-by-step explanation:

hope i helped, have a great day :)

Answer 2

For the function f(x) = [tex]\frac{2x^m}{ x + a}[/tex], if the horizontal asymptote is at y = 2 and vertical asymptote is at x = 1, then a = -1 and m = 1.

What are Asymptotes of a Function?

There are asymptotes like horizontal, vertical and oblique asymptotes.

Horizontal asymptote is the value of the function f(x) as x goes to ±∞, as long as this value is not infinity.

Vertical asymptotes are the values of x which are not in the domain of the function f(x). For a fractional expression it is found by letting the denominator equals zero.

The given function is,

f(x) =  [tex]\frac{2x^m}{ x + a}[/tex]

Horizontal asymptote of this function is at y = 2.

lim x → ∞ f(x) = 2

lim x → ∞  [tex]\frac{2x^m}{ x + a}[/tex] = 2

Eliminate 'a' in the denominator, because as x tends to infinity a + x also tends to infinity.

lim x → ∞  [tex]\frac{2x^m}{ x }[/tex] = 2

For the left hand side to become 2, [tex]x^m[/tex] in the numerator and x in the denominator should get cancelled.

⇒ [tex]x^m[/tex] = [tex]x[/tex]

⇒ m = 1

Vertical asymptote of the function is at x = 1.

Let x + a = 0

⇒ 1 + a = 0

⇒ a = -1

Hence we get the values a = -1 and m = 1 for the function f(x) =  [tex]\frac{2x^m}{ x + a}[/tex] to have the horizontal asymptote at y = 2 and vertical asymptote at x = 1.

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Related Questions

Guided Practice

Type your answer and then click or tap Done.
Use the ^ symbol (Shift+6 on the keyboard) to signify an exponent. For example, for 2 to the third power, enter 2^3.

Identify the quadratic term in the function.

f(x)=2x^2−3x+5

Answers

Answer:

2x^2

Step-by-step explanation:

Q:

identify the quadratic term in the function f(x)=2x^2-3x+5

A:

The quadratic term is 2x^2.

Answer:

2x2-3x-5=0

Step-by-step explanation:

(2x2 -  3x) -  5  = 0

Answer:

The quadratic term in the function is  

Step-by-step explanation:

Given : Function  

To find : Identify the quadratic term in the function ?

Solution :

The quadratic  form of the function is  

Where,  is quadratic term.

On comparing with given function,  

is the quadratic term.

Therefore, the quadratic term in the function is

i need help on i ready what is the length of the breathing tube

Answers

Answer:

The average size of the tube for an adult male is 8.0, and an adult female is 7.0,

The typical depth of the endotracheal tube is 23 cm for men and 21 cm for women

please help with statistic 20

Answers

Part A

p = 0.32 = probability of someone voting by internet

n = 13 = sample size

x = 10 = number of people who voted by internet

Apply the binomial probability formula.

[tex]P(x) = (_n C _x)*(p)^{x}*(1-p)^{n-x}\\\\P(10) = (_{13} C _{10})*(0.32)^{10}*(1-0.32)^{13-10}\\\\P(10) = (286)*(0.32)^{10}*(0.68)^{3}\\\\P(10) \approx 0.0010124942242\\\\P(10) \approx \textbf{0.00101}\\\\[/tex]

Note: the [tex]_n C_x[/tex] refers to the combination formula.

Answer:   0.00101

=============================================================

Part B

We could apply the binomial theorem for the following values of x: {10,11,12,13}. Then would add up the results.

However, such a task is fairly tedious and it's more efficient to use computer software (or a graphing calculator). Also, there's the element of limited time that you'll need to consider. I showed the steps for part A above because your teacher may have wanted you to list them. Usually it's better to rely on software for that task as well. At the very least, it's useful to have software to check your answer.

Whichever method you use, you should find the following:

P(10) = 0.00101P(11) = 0.00013P(12) = 0.00001P(13) = 0

The last value isn't exactly 0, but it's so small that it's effectively zero. This is because we only have 5 decimal places to work with.

Add up those four values to get:

[tex]P(x \ge 10) = P(10)+P(11)+P(12)+P(13)\\\\P(x \ge 10) \approx 0.00101+0.00013+0.00001+0\\\\P(x \ge 10) \approx 0.00115\\\\[/tex]

A faster shortcut is to use your calculator's binomCDF function.

This result of 0.00115 is fairly small. The usual distinction we make between whether a probability is small or not is to set up some kind of threshold. This threshold is known as the significance level. By default, it's set to 0.05 unless your teacher specifies otherwise. Another common significance level is 0.01, but it's usually mentioned.

Since 0.00115 is smaller than 0.05, and even 0.01, we consider the probability of getting 10 or more internet voters to be a significant event. It's fairly unusual to get 10 or more people voting by internet in this sample of n = 13 people.

Answer: Choice A) Yes, because the probability of 10 or more is 0.00115, which is low.

=============================================================

Part C

Like with part B, we could find the binomial probability values for x = {1,2,3,...,11,12,13}. We could add up the values like I did, or use the binomCDF function which is faster.

Another approach is to use the complement of the event "at least 1". If x is some number in the set {0,1,2,..,12,13}, then either [tex]x = 0[/tex] or [tex]x \ge 1[/tex]

From this, we can say

[tex]P(x=0) + P(x \ge 1) = 1\\\\P(x \ge 1) = 1-P(x=0)\\\\P(x \ge 1) \approx 1-0.00665\\\\P(x \ge 1) \approx 0.99335\\\\[/tex]

This then rounds to 0.993

Answer:  0.993

Please help me with this homework

Answers

answers: 1)208 2)284 3)405 4)210
1. 52 x 4 = 208
2. 71 x 4 = 284
3. 81 x 5 = 405
4. 42 x 5 = 210

Hope this helps

Brainliest is appreciated :)

4 2/3 + 6 1/5
1 13 /15

10 13/15

13 5/10

Answers

HOPE IT IS HELPFUL TO YOU ☺️

Answer:

4+6+ (10/15+3/15):10 13/15

given g(x)=-2x+1 solve for x when g (x)=5

Answers

Answer:

x = -2

Step-by-step explanation:

g(x) = 5

-2x + 1 = 5

-2x  = 5 - 1

-2x = 4

x = 4/-2

x = -2

>> Answer

_________

[tex]\:[/tex]

g(x) = 5

5 = -2x + 1

5 - 1 = -2x

4 = -2x

x = -2

can someone help me 5/4/7 + 1/3/4

Answers

Please check the attached image for the steps.

Answer = 11/42 = 0.261

____

RainbowSalt2222 ☔

Your above-ground pool has sprung a leak, and you do not have a way to fix it. At 12 noon, the water in the pool is 5 feet deep (in other words, the water level is 5 feet above the ground). You are not sure how quickly the pool level is falling, so you check again after 40 minutes and see that the height of the water level is now feet. You notice that there is a relationship between the time that has passed to the height of the water level in the pool.

Answers

Answer:

Step-by-step explanation:



Sully built a shelf 8 5/8 inches wide for his DVD collection. If each DVD is 3/8 inches
wide, how many can he fit on the new shelf?

Answers

Answer:

23

Step-by-step explanation:

8 5/8 = 69/8

Each DVD is 3/8 inches

Ignore the denominators

We have 69 and 3

69 is 23 times bigger than 3, so 23 DVD's can fit

.Learning Task 2: Get the quotient of each item up to the nearest ten thousandths place. Then, round the decimals to their nearest thousandths. Number 1 is done for you.

1.45÷8= 5.6250 -5.625------- example

4.93÷9 = _____ - ______

2. 77÷9 = _____ - ______

5.88 ÷7= _____ - ______

3.81÷7= _____ - ______

6.55÷8=_____ - ______​

sorry if the numbers is a bit confusing

Answers

The responses for the quotient given to the nearest thousandths are

presented in the order of the of the questions as follows;

[tex]Question \ 4) \ \displaystyle \underline{\frac{93}{9} = 10.3333 \approx 10.333}}[/tex]

[tex]Question \ 2) \ \displaystyle \underline{\frac{77}{9} = 8.5555 \approx 8.556}[/tex]

[tex]Question \ 5) \ \displaystyle \underline{\frac{88}{7} = 12.4285 \approx 12.429}[/tex]

[tex]Question \ 3) \ \displaystyle \underline{\frac{81}{7} = 11.5714\approx 11.571}[/tex]

[tex]Question \ 6) \ \displaystyle \underline{\frac{55}{8} = 6.8750\approx 6.875}[/tex]

Reasons:

4. The division is presented as follows;

[tex]\displaystyle \mathbf{\frac{93}{9}}= \frac{90 + 3}{9} = 10 + \frac{1}{3} = 10.\overline 3[/tex]

Given that we have;

[tex]\displaystyle \frac{1}{3} = 0.\frac{10}{3} =0.3 \frac{10}{3} = 0.3333[/tex]

Therefore;

[tex]\displaystyle \underline{\frac{93}{9} = 10.3333 \approx 10.333}[/tex]

2. The division is presented as follows;

[tex]\displaystyle \mathbf{\frac{77}{9}} = \frac{72 + 5}{9} = 8 + \frac{5}{9} = 8. \frac{50}{9} = 8.5\frac{50}{9} = 8.55\frac{50}{9} = 8.555\frac{50}{9} = 8.5555[/tex]

Therefore;

[tex]\displaystyle \underline{\frac{77}{9} = 8.5555 \approx 8.556}[/tex]

5. The division is presented as follows;

[tex]\displaystyle \mathbf{\frac{88}{7}} = \frac{85 + 3}{7} = 12 + \frac{3}{7} = 12. \frac{30}{7} = 12.4\frac{20}{7} = 12.42\frac{60}{7} = 12.428\frac{40}{7} = 12.4285\frac{5}{7}[/tex]

[tex]\displaystyle \underline{\frac{88}{7} = 12.4285 \approx 12.429}[/tex]

3. The division is presented as follows;

[tex]\displaystyle \mathbf{\frac{81}{7}} = \frac{77 + 4}{7} = 11 + \frac{4}{7} = 11. \frac{40}{7} = 11.5\frac{5}{7} = 11.57\frac{10}{7} = 11.571\frac{30}{7} = 11.5714\frac{20}{7}[/tex]

Therefore;

[tex]\displaystyle \underline{\frac{81}{7} = 11.5714\approx 11.571}[/tex]

6. The division is presented as follows;

[tex]\displaystyle \mathbf{\frac{55}{8}} = \frac{48 + 7}{8} = 6 + \frac{7}{8} = 6. \frac{70}{8} = 6.8\frac{60}{8} = 6.87\frac{40}{8} = 6.875\frac{0}{8} =6.8750[/tex]

Therefore;

[tex]\displaystyle \underline{\frac{55}{8} = 6.8750\approx 6.875}[/tex]

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What is the estimated quotient of 8 455 divided by 17? *.

Answers

Answer:

34.7647058824

Step-by-step explanation:

Finding slope from tables and

Answers

Answer:

m=-5/2 b=2

Step-by-step explanation:

It goes over 2 times ever time it goes down 5 times. and when the y is 0 the x is 2

Find the value of X.

Answers

Answer:

x=28

Step-by-step explanation:

90-33=57

2x+1=57

2x=56

x=28

Simplify.

x2+2x−3/
x−4/
2x2+5x−3/
x^2−16



x2−x−12/2x−3

x2−5x−4/2x−1

x2+3x−4/2x−1

x2+x−12/2x−3

Answers

Answer:

x^2 + 7x- 3/x - 3/x^2 -16

Step-by-step explanation:

Key:  ( ^ ) means exponent

= x^2 + 2x- 3/x -2x^2 + 5x- 3/x^2 -16

= x^2 - 2x^2 + 2x+5x - 3/x- 3/x^2 -16

= x^2 - 2x^2 = -x^2

=  -x^2 + 2x + 5x- 3/x- 3/x^2-16

As you see you add 2x and the 5x and got 7x

= Answer : x^2 + 7x- 3/x - 3/x^2 -16

Answer:

I think the answer is x^2+3x-4/2x-1

What does the A stand for in the star problem solving process

Affect

Agree

Add

Act

Answers

The answer is D. Act.

STAR stands for Situation, Task, Action, Result.

Answer:

act

Step-by-step explanation:

A stands for act. Act on your plan and work the problem out.

Alybia was making 115 cookies for a Valentine’s Day party. They were each either red or purple. Forty percent of the cookies were red. How many cookies were purple?

Answers

Answer:

69 purple cookies!

Step-by-step explanation:

b. (a+b)x 1= (a+b)
What property is this?

Answers

commutative property
Identity property of multiplication

what is the solution to the system of equations​

Answers

Here the answer hope this help

Which number is a rational number? OA √15 OB. 2.6457513110... O c. 17.156 OD. 3√85​

Answers

Answer:

"O c. 17.156"

Step-by-step explanation:

    A is not a rational number because it cannot be written as a fraction [with two integers] or an integer (the square root of 15 is equal too 3.87298334...)

   B is not a rational number because it also goes on forever, just like A.

    C is a rational number because it does not go on forever.

    D is like A and B, it goes on forever.

Have a nice day!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

If A(2, 3) and B(-4, -6), find AB.--

Answers

[tex] \huge \bf༆ Answer ༄[/tex]

The distance between points can be solved using Distance formula (similar to Pythagoras theorem)

[tex] \boxed { \sf D = \sqrt{(x2 - x1) {}^{2} + {(y2 - y1) {}^{2} } }}[/tex]

Put the values : -

[tex] \sf D = \sqrt{ (2 - ( - 4)) {}^{2} + (3 - ( - 6)) {}^{2} } [/tex]

[tex] \sf \: D = \sqrt{ {(6)}^{2} + (9) {}^{2} } [/tex]

[tex] \sf D = \sqrt{36 + 81} [/tex]

[tex] \sf D = \sqrt{117} [/tex]

[tex] \sf D = 3 \sqrt{13} [/tex]

Distance between the points = 3√13 units

[tex]꧁ \: \large \frak{Eternal \: Being } \: ꧂[/tex]

Answer:

If you are trying to find the line, simply use a graph.

Step-by-step explanation:

ACCURATE ANSWER=BRAINLIST
The first four terms of a sequence are shown.

7, 25, 43, 61, ...
Which of the following expressions can be used to find the nth term of the sequence?

Question 3 options:

7+18n

18+7n

18+7(n−1)

7+18(n−1)

Answers

Answer:

7+18n

might be the answer sorry if I am wrong

It’ be 7 + 18(n-1)

I plugged in the fourth term for n, and only that expression gave the correct answer of 61

please help me with this math problem

Answers

Step-by-step explanation:

the group of x friends is SPLITTING the cost of $50. Therefore to find the amount each person pays after the split, you will divide 50 by the amount fo friends (x). Each person is also paying an extra $5 for dessert. Therefore, you will be adding that 5 to everyone's total after splitting.

So the equation you will get is

[tex]a(x) = \frac{50}{x} + 5[/tex]

Answer:

A(x)= (50/x)+5

Step-by-step explanation:

50 bucks divided by the number of people in the group which is X and each must also pay 5 bucks for dessert.


A 8th grade student has 5 years
to save up enough money to
pay for her 4 years of college.
She is estimating each year will
cost $7,500. If she has $5,000
to start a savings account, then
based on the table, what is her
minimum monthly deposit
needed to reach her goal?
Initial Balance
(dollars)
$5,000
$5,000
$5,000
$5,000
Monthly Deposit
(dollars)
$100
$200
$300
$400
Account Value in
Five Years
(dollars)
$12,273
$18,737
$25,202
$31,667

Answers

Answer:

$400

Step-by-step explanation:

If college costs $7,500 per year, and she's going to go for 4 years, then she needs to save 4 x $7,500  = $30,000 total.  From the table, she would need to deposit $400 per month in order to have $31,667 in time for college.

Answer: $200

Step-by-step explanation:

Because in the table the minimum number is in the month when she save $200.

Initial balance is $5000

Account in value in five years is $18,737

if 5/6 of the 30 motorcycles were new, how many motorcycles were used​

Answers

Answer:

5 Motorcycles are used

30÷6= 5

5×5= 25

30-24=5

so the answer is 5

Answer:

5 out of the 30 motorcycles are used

Step-by-step explanation:

First, we should look at what we know. We know that there are 30 motorcycles in total. As a fraction, that'd be 30/30. We also know that of that 30, the equivalent of 5/6 are brand new.

Our next step is to figure out how much 5/6 is out of 30. Since we know that in total there 30/30 motorcycles, we need to convert 5/6 to have a denominator of 30. So what times 6 equals 30.

30 ÷ 6 = ?    opposite of 6 x ? = 30

5                   divide

So now we now that 6 times 5 equals 30. What we do to the denominator we must do to the numerator.

[tex]\frac{5}{6}[/tex] × [tex]\frac{5}{5}[/tex]    

[tex]\frac{25}{30}[/tex]

Now we know that 25 of the 30 motorcycles are new and all we need to do is subtract that 25 from the total 30 to get 5. This tells us that 5 of the total motorcycles are used.

I hope this helped :)

What number is furthest from 0 on a number line? 16 or 18?

Answers

18. _______________________________________

Mary has 2 1/5 hours before she needs to meet her friend. She needs to take care of 7 chores before then. How much time can she allocate to each chore?

Answers

around 19 minutes ^^

(18.85 minutes)

Mary can allocate to each chore around 18.85 minutes.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

It is given that Mary has 2 1/5 hours before she needs to meet her friend. She needs to take care of 7 chores before then.

Hence, we get

2 and 1/5 hours = 132 minutes (120 + 12)

thus, Mary will have 132/7 = 18.85714285714286 minutes for each chore.

Or around 18.85 minutes for each chore

Therefore, she can allocate to each chore around 18.85 minutes.

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Write the equation of the following parabolae in their canonical form and hence find their vertices, foci and directrix.
1.
[tex] {y}^{2} - 6y - 2x + 19 = 0[/tex]
2.
[tex] {x}^{2} + 4x + 4y + 16 = 0[/tex]

Answers

#1

Given:

y² - 6y - 2x + 19 = 0

This is a horizontal parabola.

Canonical form of horizontal parabola is:

4a(x - h) = (y - k)², where (h, k) is vertex

Focus is:

F(h + a, k)

Directrix is:

x = h - a

Convert the equation:

y² - 6y - 2x + 19 = 0y² - 6y  + 9 - 2x + 10 = 0(y - 3)² = 2x - 10(y - 3)² = 4(1/2)(x - 5)

We got:

h = 5, k = 3, a = 1/2

Focus is:

F(5 + 1/2, 3) = F(5.5, 3)

Directrix is:

x = 5 - 1/2 = 4.5#2

Given:

x² +4x + 4y + 16 = 0

This is a vertical parabola.

Canonical form of vertical parabola is:

4a(y - k) = (x - h)², where (h, k) is vertex

Focus is:

(h, k + a)

Directrix is:

y = k - a

Convert the equation:

x² + 4x + 4y + 16 = 0x² +4x + 4 + 4y + 12 = 0(x + 2)² = -4y - 12(x + 2)² = 4(-1) (y + 3)

We got:

h = - 2, k = -3, a = - 1

Focus is:

F(-2, -3 - 1) = F(-2, - 4)

Directrix is:

y = -3 - (-1) = - 2

Em uma avaliação que vale até 5 pontos, João tirou 4,2 pontos. Quanto João teria tirado caso a prova valesse 10 pontos?

Answers

Answer:

8.4 pontos

Step-by-step explanation:

4.2/5

multiplique o numerador e o denominador por 2

8.4/10

A) (2x-10)(3x+1)
B) (3x+2)(2x-5)
C) (2x+5)(3×+1)
D) (2x+1)(3×+5)
E) None of the above. The quadratic f(x) = 6x] + 11X - 10
would have which of the following
factors?

Answers

Answer:

B

Step-by-step explanation:

(3x+2)(2x-5)

Brainliest?

A store owner has 65.5 pounds of candy. If he splits the candy equally into 5 boxes, how many pounds of candy will each box contain?

Answers

Answer: Each box of candy would contain 13.1 pounds of candy.

Step-by-step explanation:

Divide 65.5 by 5. Hope this helps!

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