Show all work to identify the asymptotes and zero of the function f(x)= 5x/x^2-25. Please answer ASAP!!!

Show All Work To Identify The Asymptotes And Zero Of The Function F(x)= 5x/x^2-25. Please Answer ASAP!!!

Answers

Answer 1

Answers:

root: x = 0Vertical asymptotes: x = 5 and x = -5Horizontal asymptote: y = 0

The term "root" is another way of saying "zero of a function"

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

Explanation:

To find the roots, we need to solve f(x) = 0 for x

f(x) = 0

5x/(x^2 - 25) = 0

5x = 0*(x^2-25)

5x = 0

x = 0/5

x = 0

Plugging x = 0 into f(x) leads to f(x) = 0.

The root is x = 0 meaning the x intercept is at 0 on the x axis number line. This is the origin (0,0).

---------------

To find the vertical asymptotes, set the denominator equal to 0 and solve for x

x^2 - 25 = 0

x^2 - 5^2 = 0

(x-5)(x+5) = 0 ... difference of squares rule

x-5 = 0 or x+5 = 0

x = 5 or x = -5

If either x = 5 or x = -5, then then the denominator x^2-25 is zero

We cannot divide by zero, so these values are excluded from the domain, and this produces the vertical asymptotes.

--------------

The horizontal asymptote is y = 0 because the degree of the numerator is 1, while the degree of the denominator is 2. The denominator's degree is larger, which leads to y = 0. The rules for finding the horizontal asymptote are

If m < n, then the horizontal asymptote is y = 0If m = n, then the horizontal asymptote is y = a/bIf m > n, then there is no horizontal asymptote (use polynomial long division to find the oblique asymptote)

For those rules above, m and n are the degrees of the numerator and denominator respectively. The a,b refers to the leading coefficients of the numerator and denominator.

Answer 2

The asymptotes and zero of the function are ±5 and 0 respectively

Given the function below;

[tex]f(x)=\frac{5x}{x^2-25}[/tex]The vertical asymptotes occur at the point where the function goes large that is the denominator is zero.

If the denominator is zero, hence;

x^2 - 25 = 0

x^2 = 25

x = ±√25

x = ±5

Hence the asymptotes of the function is ±5

For the zero of the function;

[tex]\frac{5x}{x^2-25}=0\\5x = 0\\x = 0\\[/tex]

Hence the zero of the function is 0

Learn more on asymptotes here: https://brainly.com/question/25827382


Related Questions

PLS HELP BEST ANSWER GETS BRAINLIEST Find the volume of the rectangular prism with edge lengths of 1/2, 2/3, and 4/3.

Answers

Answer:

  4/9 cubic units

Step-by-step explanation:

The volume of a rectangular prism is the product of its edge lengths:

  V = LWH

  V = (1/2)(2/3)(4/3) = (1·2·4)/(2·3·3) = 4/9 . . . . cubic units

what is. - 3 7/8 × - 4 3/5 help please

Answers

Answer:

713/40 or as mixed fraction of 17 33/40 (see setps below)

Step-by-step explanation:

Simplify the following:

-(3 + 7/8) (-(4 + 3/5))

Hint: | Multiply all instances of -1 in -(3 + 7/8) (-(4 + 3/5)).

(-1)^2 = 1:

(4 + 3/5) (3 + 7/8)

Hint: | Put the fractions in 3 + 7/8 over a common denominator.

Put 3 + 7/8 over the common denominator 8. 3 + 7/8 = (8×3)/8 + 7/8:

(4 + 3/5) (8×3)/8 + 7/8

Hint: | Multiply 8 and 3 together.

8×3 = 24:

(4 + 3/5) (24/8 + 7/8)

Hint: | Add the fractions over a common denominator to a single fraction.

24/8 + 7/8 = (24 + 7)/8:

(4 + 3/5) (24 + 7)/8

Hint: | Evaluate 24 + 7 using long addition.

| 1 |  

| 2 | 4

+ | | 7

| 3 | 1:

(4 + 3/5)×31/8

Hint: | Put the fractions in 4 + 3/5 over a common denominator.

Put 4 + 3/5 over the common denominator 5. 4 + 3/5 = (5×4)/5 + 3/5:

31/8 (5×4)/5 + 3/5

Hint: | Multiply 5 and 4 together.

5×4 = 20:

((20/5 + 3/5)×31)/8

Hint: | Add the fractions over a common denominator to a single fraction.

20/5 + 3/5 = (20 + 3)/5:

31/8 (20 + 3)/5

Hint: | Evaluate 20 + 3.

20 + 3 = 23:

23/5×31/8

Hint: | Express 23/5×31/8 as a single fraction.

23/5×31/8 = (23×31)/(5×8):

(23×31)/(5×8)

Hint: | Multiply 5 and 8 together.

5×8 = 40:

(23×31)/40

Hint: | Multiply 23 and 31 together.

| 3 | 1

× | 2 | 3

| 9 | 3

6 | 2 | 0

7 | 1 | 3:

Answer: 713/40

________________________________________

Convert to a mixed number:

713/40

Hint: | Use long division to get a quotient and remainder.

Divide 713 by 40:

4 | 0 | 7 | 1 | 3

Hint: | How many times does 40 go into 71?

40 goes into 71 at most one time:

| | | 1 | |  

4 | 0 | 7 | 1 | 3 |  

| - | 4 | 0 | |  

| | 3 | 1 | 3 |  

Hint: | How many times does 40 go into 313?

40 goes into 313 at most 7 times:

| | | 1 | 7 |  

4 | 0 | 7 | 1 | 3 |  

| - | 4 | 0 | |  

| | 3 | 1 | 3 |  

| - | 2 | 8 | 0 |  

| | | 3 | 3 |  

Hint: | Summarize the results.

Read off the results. The quotient is the number at the top and the remainder is the number at the bottom:

| | | 1 | 7 | (quotient)

4 | 0 | 7 | 1 | 3 |  

| - | 4 | 0 | |  

| | 3 | 1 | 3 |  

| - | 2 | 8 | 0 |  

| | | 3 | 3 | (remainder)

Hint: | In the equivalent mixed fraction, the quotient becomes the whole number part, the remainder becomes the numerator part, and the divisor (denominator) remains the denominator.

The quotient of 713/40 is 17 with remainder 33, so:

Answer: 17 33/40

Write the mixed number as a decimal. 4 9/20

Answers

answer : 89/20 = 4.45

multiply 20 & 4 to get 80, then add 9.

89 divided by 20 is: 4.45

120 = -5 (2m - 7) + 5 Multi - Step

Answers

Answer:

Step-by-step explanation:

-10m + 35 + 5 = 120

-10m + 40 = 120

-10m = 80

m = -8

Simplify (2+3)^2+8/2

Answers

Answer:

Exact Form: − 29 30 Decimal Form: − 0.9 ¯ 6

Hoped I helped

The average temperature in a northern Canadian city is 1 degree Fahrenheit. The actual temperature in January differs by 10 degrees. (use x as the variable |x(+or-)#|=# | -------- | = ----------

Answers

Answer:

x+10

Step-by-step explanation:

what is thirty two percent of fifty six

Answers

Answer: 17.92

Step-by-step explanation:

32% of 56  

Change to fraction

32 /100 x 56

Change to decimal

0.32 x 56

= 17.92

If -7(y-3)= -14. What is the value of x?

Answers

Answer:

none

Step-by-step explanation:

no x because (y-3)=14 so the x wouldnt repeat

Answer:

y = 5

Step-by-step explanation:

-7(y-3)= -14

Divide each side by -7

-7/-7(y-3)= -14/-7

y-3 = 2

Add 3 to each side

y-3+3 = 2+3

y = 5

What is the distance between (-1, -2) and (2, 2)?

Answers

Answer: The distance would be, (3, 4)

Solve 12x + 4y = 20 for y.
A. y=-3x+ 20
B. y = -12x+ 20
C. y= 12x+ 5
D. y=-3x+ 5

Answers

Answer:

D. y= -3x+ 5

Step-by-step explanation:

[tex]12x + 4y = 20[/tex]

Move 12x to the right and change its sign

[tex]4y =20-12x[/tex]

Divide through by 4

[tex]\frac{4y}{4} = \frac{20}{4} -\frac{12x}{4} \\\\Simplify\\y = 5-3x\\y =-3x+5[/tex]

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{y = - 3x + 5}}}}}[/tex]

Option D is the correct option.

Step-by-step explanation:

[tex] \sf{12x + 4y = 20}[/tex]

Move 12x to right hand side and change it's sign

⇒[tex] \sf{4y = - 12x + 20}[/tex]

Divide both sides of the equation by 4

⇒[tex] \sf{ \frac{4y}{y} = \frac{ - 12x + 20}{4} }[/tex]

⇒[tex] \sf{y = \frac{ - 12x}{4} + \frac{20}{4} }[/tex]

Divide -12x by 4 . Also divide 20 by 4

⇒[tex] \sf{y = - 3x + 5}[/tex]

Hope I helped!

Best regards!! :D

Tyra bought 4.5 pounds of strawberries they cost $2.60 a pound how much did she spend

Answers

Answer:

11.70

Step-by-step explanation:

1. A recent study revealed that 45% of business travelers plan their own business trips. The study is to be replicated with a sample of 12 frequent business travels. a. What is the probability exactly 5 travelers plan their own trips

Answers

Answer:

The  probability is  [tex]P(X = 5) = 0.222[/tex]

Step-by-step explanation:

From the question we are told that

   The  proportion of business travelers that plan their own business trip is [tex]p = 0.45[/tex]

   The  sample  size is  n  = 12

    The  random number considered is  x =  5

     

Generally the  proportion of business travelers that do not  plan their own business trip is mathematically evaluated as

      [tex]q = 1- p[/tex]

=>   [tex]q = 1-0.45[/tex]

=>    [tex]q = 0.55[/tex]

 This  can study can be said to follow binomial distribution as there is only two outcomes

So the probability exactly 5 travelers plan their own trips is mathematically represented as

     [tex]P(X = 5) = ^{12} C_5 * p^5 * q^{12- 5 }[/tex]

Generally using a combination calculator  

      [tex]^{12} C_5 = 792[/tex]

So

    [tex]P(X = 5) = 792 * (0.45)^5 * (0.45)^{12- 5 }[/tex]

    [tex]P(X = 5) = 0.222[/tex]

   

   

Xavier is building a triangular fence the length of the second side will be 1 foot longer than the length of the first side the length of the third side will be 1 foot longer than the length of the second side the total perimeter of the triangle will be 63 feet what will the length of the third side B

Answers

Answer:

22

Step-by-step explanation:

Jimmy is putting in tile floors in his living room. He ordered 20 boxes of tiles, but only 16 arrived. What percent of the order is missing?

Answers

Answer:

400%

Step-by-step explanation:

20-16=4

4*100%=400%

If x = 4 tan(θ), find sec(θ) in terms of x

Answers

Answer:

[tex] \sec \theta = \pm \frac{ \sqrt{ {x}^{2} + 16} }{4} [/tex]

Step-by-step explanation:

[tex] \because \: x = 4 \tan \theta \\ \therefore\frac{x}{4} = \tan \theta....(1) \\ \\ \because \: { \sec}^{2} \theta = 1 + { \tan}^{2} \theta \\ \therefore \: \sec \theta = \pm\sqrt{1 + { \tan}^{2} \theta } \\ \therefore \: \sec \theta = \pm\sqrt{1 + { \bigg( \frac{x}{4} \bigg)}^{2} } \\ \therefore \: \sec \theta = \pm\sqrt{1 + { \frac{x^{2}}{16} } } \\ \therefore \: \sec \theta = \pm\sqrt{{ \frac{16 + x^{2}}{16} } } \\ \therefore \: \sec \theta = \pm \frac{ \sqrt{ {x}^{2} + 16} }{4} [/tex]

Number between 17/4 and square root of 20

Answers

Answer: 4.485

Step-by-step explanation:

We need to find the number between [tex]\dfrac {17}{4}[/tex] and [tex]\sqrt{20}[/tex].

For this , we first simplify the above numbers.

[tex]\dfrac{17}{4}= 4.25[/tex]  [divide 17 by 4]

[tex]\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}= 2(2.236)=4.472[/tex]   [ [tex]\sqrt{5}=2.236[/tex] ]

Now, Midpoint of  4.25 and 4.472 = [tex]\dfrac{4.25+4.72}{2}=\dfrac{8.97}{2}=4.485[/tex]

Number between 4.25 and 4.472 =4.485

Or number between [tex]\dfrac {17}{4}[/tex] and [tex]\sqrt{20}[/tex] is 4.485.

my account isnt working can you please look at it s

Answers

For what? Is it a website or is it Brainly?

Answer:

What account are you talking about?

Step-by-step explanation:

In the linear equation 3+2x=13, what is the second step in solving the equation for x?

Answers

Subtract 3 from both sides of the equation (i.e. you'll be left with 2x=10) and then divide both sides by two to isolate x (i.e. you'll get x=5)

3+2x=13

2x=10

x=5

Hope this helps!

Sam owns a vegetable stand. He tracks the price of potatoes, p, in dollars per pound
throughout the year. In the beginning of the year, the price of potatoes rose gradually
until it peaked in the third month. After that, the price declined until it bottomed out in
the seventh month of the year. Then, the price of potatoes rose to peak again near the
end of the year.

Answers

Answer:

What's the question, what are you meant to find??

What’s the question??

Fill in the blank. In a​ _______ distribution, the frequency of a class is replaced with a proportion or percent.

Answers

Answer:

Relative frequency

Step-by-step explanation:

In a    relative frequency distribution, the frequency of a class is replaced with a proportion or percent.

A relative frequency distribution displays how the proportion of totality of the observations related to each class is correlated to the probability distribution. A relative frequency distribution shows the proportion of times a value occurs in each class. It can be determined by the division of the frequency with the total number of data values.

joey collects 100 seashells. 45% of them are pink. how many shells are not pink. how many are pink .

Answers

Answer:

45 are pink 55 are not pink

Step-by-step explanation:

a) The number of pink seashells is A = 45

b) The number of seashells that are not pink = 55

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the total number of seashells be = 100

Let the percentage of the seashells that are pink = 45 %

If 45% of the 100 seashells are pink, then the remaining 55% must be not pink. We can find the number of pink shells by multiplying 100 by 45%:

Number of pink shells = 100 x 0.45 = 45

To find the number of shells that are not pink, we can subtract the number of pink shells from the total number of shells:

Number of shells not pink = 100 - 45 = 55

Hence , there are 55 seashells that are not pink and 45 seashells that are pink.

To learn more about percentage click :

https://brainly.com/question/12861068

#SPJ2

What is the volume of the pyramid shown below?

Answers

Step-by-step explanation:

Given:

h=7in

w=9in

l=6in

Required:

v=?

Formula:

v=l*w*h

Solution:

v=l*w*h

v=6in*9in*7in

v=54in^2*7in

v=378in^3

Hope this helps ;) ❤❤❤

Find the area of the triangle whose base is 12 cm and height is 4 cm.

Answers

Answer:

A = 24 cm^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh

A = 1/2 (12)*4

A = 24 cm^2

Answer:

1/2bh.

1/2×12×4= 1/2×48.

=24cm^2

Form the union for the following sets.
M={ }
N = {6, 7, 8, 9, 10)
MUN=

Answers

MUN = {6, 7, 8, 9, 10}

Step-by-step explanation:

M={ }

N = {6, 7, 8, 9, 10)

MUN = {6, 7, 8, 9, 10} .. (because A∪∅=A)

The diagonals of a parallelogram are congruent what is the parellelogram

Answers

Answer:

A parallelogram is a shape with 4 equal sides like a square or a rectangle. I hope this helped!

When we are choosing a random sample and we do not place chosen units back into the population, we are

Answers

You are sampling without replacement

James wrote the number 8,980,000 in
scientific notation. Which number did he
write?
A 8.98 x 10-6
C 89.8 x 105
B 8.98 x 10-5
D 8.98 x 106

Answers

To get 8.98, the decimal point is moved 6 places to the left. This means the exponent is positive 6

The answer is D. 8.98 x 10^6

Answer: the answer is d

Step-by-step explanation:

PLZ ANSWER FAST!! CORRECT ANSWER GETS BRAINLIEST!!

Answers

Answer:

(Weight (lb), Price ($) ) = (0.45,2.3)

That means :

Weight (lb) = 0.45 when Price ($) = 2.3

1) So, if we want to find the price per pound, we'll divide 2.3 by 0.45:

=> [tex]\frac{\$ 2.3}{0.45 \ lb}[/tex] [True]

2) Second Statement: [False]

The weight of every 0.45 lb of bag is 2.3 pounds not for per bag.

3) Third Statement: [False]

2.3 pounds of almonds cost $0.45

This is incorrect according to the graph.

4) Fourth Statement: [False]

Almonds cost $0.45 per pound

Let's check it out

0.45 lb = $2.3

Dividing both sides by 0.45

1 lb = $5.11

It is not $4.5

5) Fifth Statement: [True]

0.45 pounds of almond costs $2.30

For every 0.45 pounds, there are $2.30 . So, this statement is true!

is angle 1 in the diagram of an angle of elevation or an angle of depression?​

Answers

Answer:

Angle one is a angle of depression

Step-by-step explanation:

HELPPPPPP doing a last attempt

Answers

Answer:

irational number, non-repeating

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