Show all work to identify the asymptotes and zero of the function f of x equals 5 x over quantity x squared minus 25

Answers

Answer 1

Answer: VA: x = {-5, 5), HA: y = 0, Zeros: x = 0

Step-by-step explanation:

[tex]f(x) = \dfrac{5x}{x^2-25}[/tex]

Vertical asymptotes: The denominator cannot equal zero.

x² - 25 = 0  

(x - 5)(x + 5) = 0

x = 5, x = -5

Horizontal Asymptote: Let m represent degree of numerator and n represent the degree of the denominator.

If m > n then NO asymptoteIf m = n, then y = coefficient of m ÷ coefficient of nIf m < n, then y = 0

For the given equation, m = 1 and n = 2 so we use option 3 --> y = 0

Zeros: Set the equation equal to zero and solve for x.

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

Multiply both sides by x²- 25   -->    0 = 5x

Divide both sides by 5       -->          0 = x

Answer 2

Using function concepts, it is found that:

The zero of the function is [tex]x = 0[/tex].The vertical asymptotes are [tex]x = \pm 5[/tex].The horizontal asymptote is [tex]y = 0[/tex].

The function is given by:

[tex]f(x) = \frac{5x}{x^2 - 25}[/tex]

Applying the subtraction of perfect squares, the function will be given by:

[tex]f(x) = \frac{5x}{(x - 5)(x + 5)}[/tex]

The zero is the value of x for which:

[tex]f(x) = 0[/tex]

In a fraction, it is when the numerator is zero, thus:

[tex]5x = 0[/tex]

[tex]x = \frac{0}{5}[/tex]

[tex]x = 0[/tex]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, thus:

[tex](x - 5)(x + 5) = 0[/tex]

[tex]x = \pm 5[/tex]

The horizontal asymptote is:

[tex]y = \lim_{x \rightarrow \infty} f(x)[/tex]

Hence:

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

A similar problem is given at https://brainly.com/question/23690889


Related Questions

A phone plan has a limit of $25 that can be spent on text messages. The base cost of the text plan will cost a user $5. Each text will cost $0.05. How many text messages (t) can a user send without exceeding the plan limits?

Answers

Answer:

400 texts

Step-by-step explanation:

Answer:

The answer is A)

Step-by-step explanation:

If £25 = 850 rubles, how many £ are in 1,088 rubles?

Answers

Answer:

There are £32.64 are in 1,088 rubles.

Step-by-step explanation:

To solve this

step 1: find cost of 1 rubble

step 2: multiply number of rubble with cost of one rubble.

cost of 850 rubles = £25

we need to find cost of 1 rubles, for that we divide lHS and RHS with 850

cost of 850/850 rubles = £25/850 = £0.03

cost of 1 rubles = £0.03

Therefore cost of 1088 rubles = 1088* cost of 1 rubles

                                                  = 1088 * £0.03 = £32.64.

Thus, there are £32.64 are in 1,088 rubles.

(100 POINTS & BRAINLIEST!!! HURRY) A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue. Landing on the blue sector will give 3 points, landing on a yellow sector will give 1 point, landing on a purple sector will give 0 points, and landing on a red sector will give –1 point.
If you take one spin, what is your expected value?
What changes could you make to values assigned to outcomes to make the game fair?
Prove that the game would be fair using expected values.

Answers

Answer:

The game is not fair

Step-by-step explanation:

A wheel with seven sectors:

Red Sectors  = 2   |  Probability  = 2/7

Purple sectors  = 2  |  Probability  = 2/7

Yellow sectors  = 2 |   Probability  = 2/7

Blue sectors  = 1  |  Probability  = 1/7

Landing on the blue sector will give 3 points,  => 3 * 1/7  = 3/7    points

landing on a yellow sector will give 1 point => 1 * 2/7 = 2/7   points

landing on a purple sector will give 0 points => 0 * 2/7  = 0   points

landing on a red sector will give –1 point.  =>  - 1 * 2/7  = -2/7 points

Expected value  =  3/7 + 2/7 + 0 - 2/7

= 3/7

Expected value  =  3/7

3/7   < 1/2

=> game is not fair

If expected value = 3.5/7 = 1/2  then game will be fair

hence if we make 3.5 points for Landing on the blue sector

then game will be fair.

Answer: well i'm too young to answer this lol

1. 7

2. change the value of the colors. each color should have at least 1 or 2 points for each sector.

Step-by-step explanation:

1. two are red (red=1) =2, two are purple (purple=0) =2, two are yellow (yellow=1) =4, one is blue (blue=3) =7

2. dk how to explain this i'm running out of time

factorise x^2-5x-6 please!??!?

Answers

Answer:

(x - 6)(x + 1)

Step-by-step explanation:

Given

x² - 5x - 6

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 5)

The factors are - 6 and + 1 , since

- 6 × 1 = - 6 and - 6 + 1 = - 5, thus

x² - 5x - 6 = (x - 6)(x + 1) ← in factored form

Answer:

(x+1) (x-6)

Step-by-step explanation:

factorice la expresion

x^2 + x - 6x- 6

x(x + 1) -6(x + 1)

la solucion es:

(x + 1) (x - 6)

Please answer correctly !!!!!!!!!! Will mark brainliest !!!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

Zeros:  Set g(r) = (r + 14)^2 - 49 = to 0, obtaining

(r + 14)^2 = 49

Taking the square root of both sides, we get:

r + 14 = ± 7, which results in:

r = -14 + 7 = -7 and r = -14 - 7 = -21

The smaller root is -21 and the larger one is -7.

Vertex:  Compare g(r) = (r + 14)^2 - 49 to y = (x - h)^2 + k, where (h, k) represents the vertex.  We see that h = -21 and k = -49, so that we know the vertex to be (-21, -49).

What is the range of the function g(x) = |x – 12| – 2?

Answers

Answer:

[-2 , +∞[

Step-by-step explanation:

g(12) = |12 - 12| - 2 = -2

if x ≠ 12 then |x - 12| ≥ 0 because the absolute value I should always positive.

then |x – 12| – 2 ≥ -2

then g(x) ≥ -2

then the range is [-2 , +∞[

Answer:

B

Y is greater than or equal to -2

What is the constant of proportionality in the equation y = StartFraction x over 9 EndFraction? 0 StartFraction 1 over 9 EndFraction StartFraction 8 over 9 EndFraction 1

Answers

Answer:

b

Step-by-step explanation:

b

The constant of proportionality in the equation {y = x/9} is equivalent to (1/9).

What is a mathematical function, equation and expression?          

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is the linear equation as follows -

y = x/9

This is the equation of a straight line, which is -

y = mx + c

{m} is slope and is also called the constant of proportionality.

We can write -

y = (1/9)x + 0

So, the constant of proportionality is equivalent to (1/9).

Therefore, the constant of proportionality in the equation {y = x/9} is equivalent to (1/9).

To solve more questions on functions, expressions and polynomials, visit the link below -

brainly.com/question/17421223

#SPJ5

please help for brainliest answer

Answers

Answer:

a) An event with probability 0 is said to be impossible

b) An event with probability 1 is said to be certain

c) The probability of getting a head when flipping an unbiased coin is shown by the letter A

Step-by-step explanation:

a) If something has a 0 on a probability scale, it will never happen. The word used to describe this outcome is impossible.

b) If something has a 1 on a probability scale, it will always happen. The word used to describe this outcome is certain.

c) The probability of getting a head on an unbiased coin is [tex]\frac{1}{2}[/tex] or [tex]0.50[/tex]. This means that we are looking for the letter that is in the exact center of 0 and 1. It can be seen that A is in the dead center of these two numbers, so this is our answer.

How many observations are accounted for in the stem and leaf graph? What did you do to find the answer?

Answers

Answer:

i put 2

Step-by-step explanation:

help!!! an experiment consists of randomly choosing a colored card from a box. use the results in the table to find the experimental probability of each event. simplify all answers. red : 7, yellow: 12, orange: 8, white: 13

Answers

Answer:

chance of:

red 7/40 = 17.5%

yellow 3/10 = 30%

orange 1/5 = 20%

white = 13/40 = 32.5%

Step-by-step explanation:

7+12+8+13 = 40 total cards

7 red/ 40 possible

12 yellow/40 possible = 3/10

8 orange/40 possible = 1/5

13 white/40possible

Using it's concept, it is found that the experimental probability of each outcome is given by:

Red: 0.175 = 17.5%.Yellow: 0.3 = 30%.Orange: 0.2 = 20%.White: 0.325 = 32.5%.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In an experimental probability, these numbers are taken from previous outcomes.

In this problem, there are 40 cards.

7 are red, hence P(red) = 7/40 = 0.175 = 17.5%.12 are yellow, hence P(yellow) = 12/40 = 0.3 = 30%.8 are orange, hence P(orange) = 8/40 = 0.2 = 20%.13 are white, hence P(white) = 13/40 = 0.325 = 32.5%.

More can be learned about probabilities at https://brainly.com/question/14398287

Please answer correctly !!!!!!!!!! Will mark brainliest !!!!!!!!!!!

Answers

Answer:

No, x = -12/23 , y = -14/23

Step-by-step explanation:

Solve the following system:

{-3 x - 4 y = 4 | (equation 1)

y - 5 x = 2 | (equation 2)

Swap equation 1 with equation 2:

{-(5 x) + y = 2 | (equation 1)

-(3 x) - 4 y = 4 | (equation 2)

Subtract 3/5 × (equation 1) from equation 2:

{-(5 x) + y = 2 | (equation 1)

0 x - (23 y)/5 = 14/5 | (equation 2)

Multiply equation 2 by 5:

{-(5 x) + y = 2 | (equation 1)

0 x - 23 y = 14 | (equation 2)

Divide equation 2 by -23:

{-(5 x) + y = 2 | (equation 1)

0 x+y = (-14)/23 | (equation 2)

Subtract equation 2 from equation 1:

{-(5 x)+0 y = 60/23 | (equation 1)

0 x+y = -14/23 | (equation 2)

Divide equation 1 by -5:

{x+0 y = (-12)/23 | (equation 1)

0 x+y = -14/23 | (equation 2)

Collect results:

Answer: {x = -12/23 , y = -14/23

The sum of two numbers is 10. The larger number is 4
times the smaller number. What are the two numbers?
Original system: x + y = 10,
y = 4x
Slope-intercept form:
y = -x + 10
y = 4x

Answers

Answer:

x=8 and y=2

Step-by-step explanation:

x+y=10

x=4y

x+y=10

4y+y=10

5y=10(divide both sides by 5)

y=2

x=4y=4*2=8

Answer:

2 and 8.

Step-by-step explanation:

y = -x + 10

y = 4x

If we subtract we eliminate y:

0 = -x + 10 - 4x

0 = -5x + 10

5x = 10

x = 2.

and y = 4 * 2 = 8.

Angles A and B are supplementary. Angle A has a measure of 80°. What is the measure of angle B?
The measure of angle B is

Answers

Answer:

The measure of angle B would be 100°

Step-by-step explanation:

Supplementary means two angles add up to 180 degrees. Let's say A+B=180. Since we know what A is, we can substitute that in, B+80=180. Now solve. B=100

Answer is 100. Supplementary basically means 2 angles ,when added form 180. If angle 1 is mentioned as 80. Angle 2 will be whole - angle 1
=180 - 80
=90 degrees

Just In case you are wondering what complementary means it’s the same thing but instead of the angles forming 180 it will form 90.

Hope you have understood

What is the exponential regression equation for the data set?
WILL GIVE BRAINLIEST!
THIS IS URGENT EMERGENCY \

Answers

Answer:

Exponential Regression. An exponential regression is the process of finding the equation of the exponential function that fits best for a set of data. As a result, we get an equation of the form y=abx where a≠0 .

Step-by-step explanation:

what is the y-intercept of y=-3x-2

Answers

Answer:

the answer is 2.

Step-by-step explanation:

the basic form of this equation is y=mx+c where c is the y intercept and m is the gradient. c=2 so 2 is the y intercept

The answer is 2. The y intercept follows the slope of the equation

What is the difference of the two polynomials (9x^2+8)-(2x^2+3x)

Answers

Answer:

7x^2 -3x +8

Step-by-step explanation:

(9x^2+8)-(2x^2+3x)

Distribute the minus sign

(9x^2+8)-2x^2-3x)

Combine like terms

9x^2 -2x^2 -3x+8

7x^2 -3x +8

Answer:

[tex]5x {?}^{2} + 8 - 3x [/tex]

[tex]9x {?}^{2} + 8 - (4x {?}^{2} + 3x) \\ 9x {?}^{2} + 8 - 4x - 3x \\ 5x {?}^{2} + 8 - 3x[/tex]

Solve the exponential equation using logarithmic properties y=3^2x-4

The 2x is an exponent

Answers

Answer:

[tex]\frac{log(y+4)}{2log3}[/tex]

Step-by-step explanation:

Given the exponential equation [tex]y = 3^{2x}+4[/tex], to get 2x, we will make 2x the subject of the formula as shown;

[tex]y = 3^{2x}-4\\y+4 = 3^{2x}\\taking\ log\ of\ both\ sides\\log(y+4) = log3^{2x}\\ log(y+4) = 2xlog3\\dividing\ both\ sides\ by\ 2log 3\\\ x = \frac{log(y-4)}{2log3} \\[/tex]

The last expression gives the required value of x

What is the distance between the pool in the main office in miles? Round to the nearest 10th period (8,1)(6,-6)

Answers

Answer & Step-by-step explanation:

For this problem, we are going too have to use the distance formula.

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

We can plug in the coordinate points that we are given to their respectful places.

[tex]Distance=\sqrt{(6-8)^2+(-6-1)^2}[/tex]

[tex]Distance=\sqrt{(-2)^2+(-7)^2}[/tex]

[tex]Distance=\sqrt{4+49}[/tex]

[tex]Distance=\sqrt{53}[/tex]

[tex]Distance=7.3[/tex]

So, the distance between the pool and the main office is 7.3 miles.

Each week Danny eats 540 grams of cereal over 8 weeks. He finishes a total of 12 boxes of cereal. Each box contains the same amount of cereal. How many grams of cereal are in each box?

Answers

Answer:

360 grams of cereal

Step-by-step explanation:

First you have to do 540 times 8 to find out how many grams of cereal he ate over the eight weeks.

Then you have to divide the answer by 12 to get 360 grams of cereal.

I hope this helped ;)

how do you factor 5x^2b^2 + 14xb^2 -3b^2

Answers

Answer:

[tex]5b^2(x-0.2)(x+3)[/tex]

Step-by-step explanation:

The first thing that I noticed was that all of the terms had a common factor of [tex]b^2[/tex]. You can therefore factor that out first:

[tex]5x^2b^2 + 14xb^2 -3b^2= \\\\b^2(5x^2+14x-3)[/tex]

Now, you have a quadratic equation inside the parentheses. Factoring, you find that the roots are -0.2 and 3, meaning that you can further factor this expression to be:

[tex]5b^2(x-0.2)(x+3)[/tex]

Hope this helps!

The first term of an arithmetic sequence is -5, and the tenth term is 13. Find the common difference.

2

1.8

8/9

Answers

Answer:

2

Step-by-step explanation:

If the common difference is d we can write:

-5 + 9d = 13

9d = 18

d = 2

Answer:

d = 2.

Step-by-step explanation:

First term = -5

10th term = -5 + 9d    where d is the common difference, so

-5 + 9d = 13

9d = 18

d = 2.

Order the cones described below from least to greatest volume. Cone​ 1: radius 4 cm and height 12 cm Cone​ 2: radius 8 cm and height 6 cm Cone​ 3: radius 6 cm and height 7 cm

Answers

Answer:

Cone 1 ⇒ Cone 3 ⇒ Cone 2

Step-by-step explanation:

V=πr²h /3

V cone1 = 3.14*4²*12/3= 200.96 cm³V cone2 = 3.14*8²*6/3 = 401.92  cm³V cone3  = 3.14*6²*7/3= 263.76 cm³

Order the cones from least to greatest volume

Cone 1 ⇒ Cone 3 ⇒ Cone 2

Suppose a car rental company charges $22.50 plus 10 cents per mile write an equation you could solve to find how many miles you drove if the rental charge was 40.00

Answers

Answer:

Equation= 40=22.50+.10(how many miles)

175 miles= How many miles you drove.

Step-by-step explanation:

Equation= 40=22.50+.10(how many miles)

40-22.50=.10(how many miles)

17.5=.10(how many miles)

175 miles= How many miles you drove.

solve for x
please help !!

Answers

Answer:

34

Step-by-step explanation:

j

Answer:

it would be 31

Step-by-step explanation:

write down in terms of n 4 ,1 -2, -5 ,-8

Answers

Answer:

aₙ= 3n+1

Step-by-step explanation:

4 ,1 -2, -5 ,-8

AP with a₁=4 and d= -3

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

aₙ= 4+3*(n-1)= 4+3n-3= 3n+1

aₙ= 3n+1

If x2=y3, what is the value of z does x3z=y9?

Answers

If x² = y³ , for what value of z does [tex]x^{3z}[/tex] =  [tex]Y^{9}[/tex]  ?

Answer:

z= 2

Step-by-step explanation:

To solve the question given, we will follow the steps below;

[tex]X^{3z}[/tex] =  [tex]Y^{9}[/tex]   -----------------------------------------------------------------(1)

but   applying the law of indices mᵃᵇ = (mᵃ)ᵇ

then

[tex]Y^{9}[/tex]  = [tex](Y^{3})^{3}[/tex]

replace  [tex]Y^{9}[/tex]  by  [tex](Y^{3})^{3}[/tex]  in equation (1)

[tex]X^{3z}[/tex] =  [tex]Y^{9}[/tex]

[tex]X^{3z}[/tex] =   [tex](Y^{3})^{3}[/tex]   --------------------------------------------------------------------(2)

but  from the question x² = y³

replace y³ by x²  in equation (2)

[tex]X^{3z}[/tex] =   [tex](Y^{3})^{3}[/tex]

[tex]X^{3z}[/tex] =   [tex](X^{2})^{3}[/tex]

[tex]X^{3z}[/tex] =   [tex]X^{6}[/tex]

3z = 6

divide both-side of the equation by 3

3z/3 = 6/3

On the left-hand side of the equation, 3 at the numerator will cancel-out 3  at the denominator leaving us with just z while on the right-hand side of the equation 6 will be divided by 3

z= 2

Q5) (2.00 marks)
The sum of two numbers is 16 and their product is 48. What are the two numbers?

Answers

12 and 4
12 + 4 = 16
12 x 4 = 48

The time it takes to set up a circus tent varies inversely with the number E of elephants used. If 4 elephants can set up a tent in 30 hrs how long will it take 2 elephants?

Answers

Answer:

It will take 60 hours for 2 elephants to set up the tent.

Step-by-step explanation:

Represent set-up time by T and the number of elephants by E.  T varies inversely with E:

T  = k/E, or TE = k

If 4 elephants can set up a tent in 30 hours, then 30(4) = k, and

T = 120/E

Now let E = 2.  We get T = 120/2, or 60

It will take 60 hours for 2 elephants to set up the tent.

Carmen has a sign with dimensions 5 ft × 7.5 ft. She wants to reduce it to make a postcard. Postcard sizes are 3.5 in. × 5 in., 4 in. × 6 in., and 4.25 in. × 6 in. Which size postcard should she use? Explain.

Answers

Answer:

The size of the post card she should use is 4 in. × 6 in.

Step-by-step explanation:

The parameters given are;

Dimensions of sign = 5 ft. × 7.5 ft

Hence, the ratio of the side sizes are;

5:7.5 which is the same as 2:3, therefore, to obtain the most accurate design of the sign on the post card, the size of the post card must be in direct proportion to the size of the sign which gives;

Side length ratio of post card = 2:3 = 4:6 = 4 in. × 6 in.

The size of the post card she should use is therefore = 4 in. × 6 in.

PLEASE HELP, I WILL MARK BRAINLIEST!

Answers

Answer:

hope this helps you

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