Mathematics High School

Write a rational function with an x-intercept at (-9,0), a vertical asymptote at x=3, and a hole located at (1,-5). Then, identify the horizontal asymptote.

Answers

Answer 1

Answer:

The rational function is [tex]f(x) = \dfrac{x^2 + 8\cdot x - 9}{x^2 - 4 \cdot x + 3}[/tex]

The horizontal asymptote occur at y = 1

Step-by-step explanation:

Given that the function has an x-intercept at (-9, 0), we have;

(x + 9) is a factor of the function

Also, given that the function has a vertical asymptote at x = 3, we have that a factor of the denominator of the function is (x - 3)

With a hole at (1, -5), we have, (x - 1) in both the numerator and the denominator and when x = 1, f(x) = -5

The general form of the function can be presented as follows;

f(x) = ((x + 9)·(x - 1))/((x - 3)(x - 1)) = (x² + 8·x - 9)/(x² - 4·x + 3)

Given that the power of the numerator and the denominator are equal, the horizontal asymptote occur at ratio of the leading coefficient of the numerator and the denominator which from the above equation is 1/1 = 1

The horizontal asymptote occur at y = 1

Please find attached the graph of the function created with Microsoft Excel

Write A Rational Function With An X-intercept At (-9,0), A Vertical Asymptote At X=3, And A Hole Located

Related Questions

People at the state fair were surveyed about which type of lemonade they preferred. The results are shown below:

Pink Lemonade: 156 males, 72 females
Yellow Lemonade: 104 males, 48 females

Answers

Answer

Step-by-step explanation:

You would require the table with the number of males and females who prefer either pink or yellow lemonade at the state fair.

Pink Lemonade Yellow Lemonade TOTAL

Male 156 104 260

Female 72 48 120

TOTAL 228 152 380

P(pink lemonade | female) = 72 / (48 + 72) = 72 / 120 = 0.6

P(pink lemonade) = (156 + 72) / (156 + 72 + 104 + 48) = 228 / 380 = 0.6

Therefore, The event "prefers pink lemonade" and "female" are independent because P(pink lemonade | female) = P(pink lemonade) = 0.6

Independents events are events that can happen independently on their own. Events A and B are independent if P(A|B) = P(A).

The "prefer pink" event and "female" event are independent because [tex]P(P|F) = P(P) = 0.6[/tex]

To do this, we make the following representations:

[tex]P \to[/tex] Pink Lemonade

[tex]Y \to[/tex] Yellow Lemonade

[tex]M \to[/tex] Male

[tex]F \to[/tex] Female

The "prefer pink" event and "female" event are independent if:

[tex]P(P|F) = P(P)[/tex]

[tex]P(P|F) \to[/tex] the probability that a selected person prefers pink provided that the person is female

[tex]P(P) \to[/tex] the probability that a selected person is female

P(P| F) is calculated as:

[tex]P(P| F) = \frac{n(P\ n\ F)}{n(F)}[/tex]

i.e. the number of females who prefers pink divided by the number of females

From the table, we have:

[tex]n(P\ n\ F) = 72[/tex]

[tex]n(F) = 72 + 48 =120[/tex]

So, the probability is:

[tex]P(P| F) = \frac{72}{120}[/tex]

[tex]P(P| F) = 0.6[/tex]

[tex]P(P)[/tex] is calculated as:

[tex]P(P) = \frac{n(P)}{Total}[/tex]

i.e. the all people who prefer pink divided by total number of people

From the table, we have:

[tex]n(P) = 156 + 72 = 228[/tex]

[tex]Total = 156 + 72 + 104 + 48 = 380[/tex]

So, the probability is:

[tex]P(P) = \frac{228}{380}[/tex]

[tex]P(P) = 0.6[/tex]

Recall that:

The "prefer pink" event and "female" event are independent if:

[tex]P(P|F) = P(P)[/tex]

And we have:

[tex]P(P| F) = 0.6[/tex]

[tex]P(P) = 0.6[/tex]

Hence, the events are independent because:

[tex]P(P|F) = P(P) = 0.6[/tex]

Option (a) is correct

Answers

Answer:

Use the SOH CAH TOA

Step-by-step explanation:

Angle = 60°

x = opposite o

y = adjacent a

10√ 3 = hypotenuse h

To find x we use SOH {sineø = o/h}

Sin 60° = x/10√ 3

x=10√ 3 * sin 60

X=15

You can use Pythagoras theorem or CAH{cosø = a/h}

Cos 60°= y/10√ 3

y=Cos 60° * 10√ 3

y=5√ 3

7.
After determining the number of T-shirts and caps to purchase, the senior
class officers forgot to include shipping costs. The fabric textile company
charges shipping and handling fees according to the number of T-shirts and
caps purchased
One of the class officers writes the function f(n) = 20n + 275, where n is the
number of T-shirts purchased, and f(n) is the amount of money available to
spend on caps.
Which description does 20 represent in the class officer's function? Select all
that apply.
A. the shipping cost
B. the cost per T-shirt
C. the rate of change in the graph
D. x-intercept
Ey-intercept

Answers

Answer:

Step-by-step explanation:

can someone help me with this one ?

Answers

Answer:

For the question 7 its congruent for 8 it's not congruent

Step-by-step explanation:

1/5 ( 15 + 10k ) = please help and make sure your answer is accurate.

Answers

The answer is 3 + 2k

This is because multiplying by 1/5 is like dividing each term by 5

10k + 15 = 5 • (2k + 3)

A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 3100 seats. The students left 1395 seats vacant. What percentage of the seats in the theater were filled by the 6th graders on the trip?

Answers

Answer: 55% of the seats in the theater were filled by the 6th graders on the trip.

Step-by-step explanation:

Given: Total seats = 3100

Seats vacant= 1395

Seats occupied by 6th graders = 3100-1395 = 1705

The percentage of the seats in the theater were filled by the 6th graders on the trip = [tex]\dfrac{\text{Seats occupied by 6th graders}}{\text{Total seats}}\times100[/tex]

[tex]=\dfrac{1705}{3100}\times100\\\\= 55\%[/tex]

Hence, 55% of the seats in the theater were filled by the 6th graders on the trip.

WHOEVER ANSWERS IT WILL GET BRAINIST ASAP DUE IN 5 MINUTES

Answers

Answer:

Step-by-step explanation:

What's the pattern 7,19,31,43

Answers

Answer:

It’s 7, 19, 31, 43

Explanation:

You already have it.

+12 each time
7+12=19
19+12=31
31+12=43

Say the fraction in decimal form. 1/10

Answers

The fraction is decimal form is 0.1

Answer:

0.1

Step-by-step explanation:

Please mark me brainleist

2 3 4 5 6 7 8 9 10
TIME REMAINING
41:13
The Bears have won 7 and tied 2 of their last 13 games. They have not forfeited any games. Which ratio correctly compares their wins to losses?
7:13
13:7
4:7
7:4

Answers

The Answer Will Be 7:4

what is "The temperature outside at 6 a.m. is 4 degrees celsius. The temperature rising by 1.5 degrees celsius every hour." in a mathematical equation!! please help

Answers

Answer:

7 a.m is 5.5

Step-by-step explanation:

(6=4)+1.5=(_+1.5)

make a T chart

thats how it should work for you

60% of 89 is what number?

Answers

It’s 53.4 hope this helps

Answer:

53.4

Step-by-step explanation:

Leon is using an area model to multiply 38×14. First, he makes a rectangle that is 38 units long and 14 units tall. Then, he breaks it into smaller parts using place value to make it easier to multiply. Use the drop-down menus to show the area of each part.

Answers

Answer:

300, 120, 80 and 32 respectively.

Step-by-step explanation:

To break it down for easy multiplication, write

38 as 30 + 8

14 as 10 + 4

Now let's multiply

(30 + 8)(10 + 4) = 300 + 120 + 80 + 32

So the areas of each part would be

300, 120, 80 and 32 respectively.

PLEASE HELP IT IS EASY!!!!!!!!!!!!!! I HAVE AN EXAM!!!!!!!!!!!!!!! A student took 75 minutes to answer a combination of 30 multiple-choice and extended-response questions. She took 2 minutes to answer each multiple-choice question and 5 minutes to answer each extended-response question.

Determine which two equations best represent the situation given that R represents the number of extended-response questions and M represents the number of multiple-choice questions.
Determine the number for each type of question on the test.

Answers

Answer:

M+R=30

2M+5R=75

R=5

M=25

Step-by-step explanation:

-2(M+R=30)

2M+5R=75

-2M-2R=-60

2M+5R=75

__________

3R=15

R=5

2M+5(5)=75

2M+25=75

2M=50

M=25

3. a) The dimensions of your game cover are 20 cm x 15 cm. However, you need to have a strip of
constant width around the border for labeling purposes (game console type, etc). This width will
take up 32% of your game cover's total space. What is the width of the border? Make sure to
state any values that don't make sense.

Answers

20cm×15 cm =300

/100 = 0.32

9514 1404 393

Answer:

1.5 cm

Step-by-step explanation:

All areas are in cm^2. For a width w, the border will have an area equal to the product of its centerline length and its width:

border area = 2((20-w) +(15-w))·w = w(70 -4w)

This area is 32% of the total cover area, so is ...

0.32(20)(15) = 96

Equating these expressions for the area gives ...

96 = 70w -4w^2

w^2 -17.5w = -24 . . . . . divide by -4

w^2 -17.5w +8.75^2 = -24 +8.75^2 . . . . . complete the square

(w -8.75)^2 = 52.5625 . . . . simplify

w -8.75 = ±√52.5625 = ±7.25

A border width only makes sense if it is between 0 and 7.5 cm, so the appropriate value for w is ...

w = 8.75 ± 7.25 . . . . . . . . . add 8.75

w = 8.75 -7.25 = 1.50 . . . . . the solution w=16 makes no sense

The border width is 1.5 cm.

A blue print for a house has a scale of 1 in: 5feet The living room has a length of 25 inches and a width of 3 inches what is the actual area of the living room

Answers

Answer: 1875 square ft

Step-by-step explanation:

Ratio: 1 in: 5ft

Living room length: 25in=125ft

Living room width: 3in=15ft

125x15= [tex]1875^{2} ft\\[/tex]

1.25 × 109 + 3.50 × 109 + 3.25 × 109 =

Answers

Answer:

872 is the final answer

Step-by-step explanation:

Answer: The answer is 872

Step-by-step explanation:

solve for c: 2(c - 6) = 9c + 2

Answers

It equals -2
Hope this picture helps

A salesperson at a jewelry store earns 8% commission each week. Last week, Heidi sold $530 worth of jewelry. How much did she make in commission? How much did the jewelry store make from her sales?

Answers

Answer:

she made $42.40

the store made $487.60

Step-by-step explanation:

530 x .08

Evaluate the following numerical expression.

6 + 2^3 • 3 =

Answers

Answer:

Step-by-step explanation:

2^3=8

8x3=24

24+6=30

Please help me with this i can't think Please and thank you

Answers

Answer:

hot ❤

Step-by-step explanation:

Answer and ill mark brainlist!!

Answers

Answer:

the slope is 1

Step-by-step explanation:

X is the slope . Ye :)
Full equation is y=x+4

PLEASE HELP ILL GIVE THE BRAINLEST FOR THE RIGHT ANSWER

graph y= -1/2-6

Answers

Just use the -6 as y-axis and go one down, two to the right if u mean the equation to be -1/2x-6

-5x + 4y = 3
x = 2y - 15
solve for x and y
I'm failing please send help

Answers

Answer:

Let's solve for x.

−5x + 4y = 3

Step 1: Add -4y to both sides.

−5x + 4y+ −4y =3+ −4y

−5x = −4y +3

Step 2: Divide both sides by -5.

-5x divided by 5 = -4y+3 divided by -5

x=4/5y + −3/5

Step-by-step explanation:

are you smarter than a 7th grader get your answers by answering this question please please please please please

Answers

Answer:

Step-by-step explanation:

8 - (2-3) -1 = 8

6 - (-2) = 8

8-(2-3)-1=6-(-2)

Please help as soon as possible! Thank you

Answers

Answer:

line PQ is congruent to like SR. reason: given

angle PQR is congruent to angle SRQ. reason: given

Line QR is congruent to line QR. reason: reflexive property of equality.

Triangles PQR and SQR are congruent by the SAS postulate

Step-by-step explanation:

ASAP ASAP ASAP ASAP. PLS PLSPLS

Answers

First you wanna add the y plus 3 equals 4 minus 5

What's the value of x? 4 (x - 6) + 6 = 6x - 6

Answers

Answer:

x=-6

Step-by-step explanation:

Answer:

I got X = -6 hope I'm right

PLS HELPPPPP

This is due today....

Answers

Answer:

its B becuase the exspresion of it is the hours of the 16 like 8 16 like that

Step-by-step explanation:

Question
Solve the equation. Enter the answer in radical form, and then use a calculator to approximate the
solution to two decimal places, if necessary. Use a graphing calculator to graph the related function to
check your answer.
5x2 - 16 = 29
The solutions are x =
and x-

Answers

Answer:

solving the equation [tex]5x^2 - 16 = 29[/tex] we get the solution: [tex]\mathbf{x=3,x=-3}[/tex]

Step-by-step explanation:

We need to solve the equation [tex]5x^2 - 16 = 29[/tex]

We need to solve the equation to find the value of x.

We can solve this equation using simple DMAS rule.

We are given:

[tex]5x^2 - 16 = 29[/tex]

Add 16 on both sides

[tex]5x^2 - 16+16 = 29+16\\5x^2=45[/tex]

Now, divide both sides by 5

[tex]\frac{5x^2}{5}=\frac{45}{5} \\x^2=9[/tex]

Now, we know that [tex]\sqrt{x^2}=\pm x[/tex]

Taking square root on both sides.

[tex]\sqrt{x^2}=\sqrt{9}\\x=\pm3[/tex]

So, we get values of x:

[tex]x=3, x=-3[/tex]

Therefore, solving the equation [tex]5x^2 - 16 = 29[/tex] we get the solution: [tex]\mathbf{x=3,x=-3}[/tex]

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