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:
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
Related Questions
A train first travels east for 20 kilometers. Then it turns north and travels for 43 kilometers. Next it goes west for 20 kilometers. Finally, it travels south for an unknown number of kilometers. At the end of the journey, the train is back at the original location. How far did it travel southward?
Answers
Answer: the train traveled 43km southwards
Step-by-step explanation:
First, let's define.
North as the positive y-axis.
East as the positive x-axis.
And the initial position of the train is (0, 0).
Now, we know that:
"A train first travels east for 20 kilometers."
The new position will be:
(0, 0) + (20km, 0) = (20km , 0)
"Then it turns north and travels for 43 kilometers."
The new position will be:
(20km, 0) + (0, 43km) = (20km, 43km)
"Next it goes west for 20 kilometers."
If East if the positive x-axis, then West is the negative x-axis.
The new position of the train will be:
(20km, 43km) + (-20km, 0) = (0, 43km)
Then it travels south for an unknown number of kilometers, such that the final position is the same as the initial position, then if the train goes X kilometers to the south (and because North is the positive y-axis, South will be the negative y-axis), we have:
(0, 43km) + (0, -X) = (0, 0)
(0, 43km - X) = (0, 0)
Then we must have that:
43km - X = 0
43km = X
This means that the train traveled 43km southwards.
will mark brainliest for correct answer
Answers
Answer:
Y
Step-by-step explanation:
Look at Y and look at the input and output it shows which one is it and how to find it you welcome :)
Consider this equation.
7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8)
Mia solved the equation and determined that m = 2. Is she correct?
She is incorrect because when substituting 2 for m the result was a true statement.
She is incorrect because when substituting 2 for m the result was a false statement.
She is correct because when substituting 2 for m the result was a true statement.
She is correct because when substituting 2 for m the result was a false statement.
Answers
Answer:
B . She is incorrect because when substituting 2 for m the result was a false statement.
Step-by-step explanation:
Edge. 2020
Answer:
B
Step-by-step explanation:
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9. The model represents an equation.
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1
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-1
1
1
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1
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What value of x makes the modeled equation true?
Answers
Answer:
1
Step-by-step explanation:
aaaaaaaaaaaaaaaaaaaaahhhhhhhhhhhhhhhhh help
Answers
Answer:
x = 27
STEP BY STEP:
3 = x/9
3 = x/3 x 2
9 x 3 = x
27 = x
x = 27
Hope this helped! Have a good day!
What half of 90 percent in the percentages line
Answers
just divide it by 2 :)
Which scenario could be represented by this graph?
Answers
Answer:
its is (b) turns the oven on
Answer:
D
Step-by-step explanation:
I did the test
Find the UNIT RATE:
10 miles: 5 hours
A.2 hours: 1 mile
B.1 hour : 2 miles
C.2 miles: 1 hour
D.1 mile: 2 hours
Answers
Answer:
c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Parallel lines r and s are cut by two transversals, parallel lines t and u.
How many angles are alternate interior angles with angle 9?
Answers
Check the picture below for more information. Hope it helps !
Answer:
2
Step-by-step explanation:
Helllllpppp ASAP!!!!! Figure S is the result of a transformation on Figure R. Which transformation would accomplish this?
Answers
Answer:
d
Step-by-step explanation:
The tennis team has played 28 matches so far this season. They have won 10 matches so far. How many matches will the team need to win for the team to have a 55% success rate?
Answers
Answer: they would have to win 22/40 games
Step-by-step explanation:
22 divided by 40 is 0.55 or 55%
Answer:
x = 12 (I took the FLVS assignment for 04.04, and I'll show you guys how to do this!)
Step-by-step explanation:
The team has completed 28 matches so far and has won 10 of them.
The current success rate is:
[tex]r=\frac{10}{28} *1.00=.35714[/tex]
(1.00 = 100% and .35714 = 35.714%)
We need the success rate to be 55%
Then the team must win a number of "x" matches, so:
[tex]r=\frac{10+x}{28+x} =0.55[/tex]
Now we solve the equation for x:
[tex]\frac{10+x}{28+x} =0.55[/tex]
[tex]10+x=0.55(28+x)[/tex](distributive property here!)
[tex]10+x=15.4+0.55x[/tex]
Now, move the 0.55x to the other side by subtracting it from both sides:
[tex]10+x-0.55x=15.4[/tex]
And move the 10 by doing the same thing (subtracting from both sides):
[tex]x-0.55x=15.4-10[/tex]
[tex]0.45x=5.4[/tex]
(You might ask: 15.4 - 10 = 5.4, but how do you get 0.45x out of x - 0.55x? Use Quick Math, and you should get the answer!)
[tex]x=\frac{5.4}{0.45}[/tex]
[tex]x = 12[/tex]
So, by following these steps, x = 12 is your answer!
The team must win 12 matches to have a success rate of 55%.
Hope this helps! Have a wonderful day!
HELP PLS!!!! SOLVE ALGEBRA
Answers
Answer:
#11) D) x<0 or x≥7
Step-by-step explanation:
Hope this helps
helppppppppppppppppp
Answers
Answer:
I think its measure of variation
Step-by-step explanation:
Answer:
Yall i got banned so this is my second account
Step-by-step explanation:
need help asap this is due in 20 min!!! i will gove brainliest too! questions 8-11
Answers
8. x= 7
9. x= 9
10. x= -10
11. x= -18
Please help me answer this
Answers
Answer: y = x - 5
Step-by-step explanation: hope this helps! :)
A function is shown on the graph what is the domain of the function?
Answers
Answer:
you need to add the graph
Answer:
no graf
Step-by-step explanation:
-7(x-4)
.......................
Answers
Answer:
28−7x
i think :]
PLZ HELP IM BEING TIMEDDD!!!!!
Answers
Answer:
its b.
Step-by-step explanation:
also youre gonna get banned lol
3(x + 2) = -5 - 2(x - 3) *
Answers
Answer:
x = -1
Step-by-step explanation:
3(x + 2) = -5 -2(x-3)
open parenthesis
3 * x + 3 * 2 = -5 + -2 * x + -2 * -3
3x + 6 = - 5 - 2x + 6
subtract 6 from both sides
3x + 6 - 6 = -5 - 2x + 6
3x = -5 -2x
add 2x from both sides
3x + 2x = -5 - 2x + 2x
5x = -5
divide both sides of the equation by 5
5x/5 = -5/5
x = -5/5
x = -1
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:
81_
Evaluate 3!
6
336
6720
40,320
Answers
Answer:
6
Step-by-step explanation:
3!= 3(2)*1 = 6
ABCD is a kite with AB≈BC.
Answers
Answer:
Line BD⊥ Line AC
ΔDMC ≅ ΔDMA
using y=mx+b find the slope for
7) 8x + 3y = −9
Answers
Answer:
-8/3
Step-by-step explanation:
8x + 3y = - 9
Let's make y the subject of the formula.
y = - 9/3 - 8x/3
Rearrange
y = - 8x/3 - 3
The slope is the coefficient of x which is - 8/3
If you don't understand, please leave a comment
Please gimme brainliest
Jody bought some scarves that cost $8
each. She spent a total of $40. How
many scarves did she buy?
Answers
Answer:
5 scarves
Step-by-step explanation:
8x5=40
what is 621 divided by 9
Answers
Answer:
621/9=69
Step-by-step explanation:
Answer:
69
Step-by-step explanation:
69x 9= 621
What is -2-(-7)
Plssssss explain
Answers
Answer:
5
Step-by-step explanation:
Showing the work:
= -2-(-7)
= -2--7
= -2+7
= 5
Answer:
5
Step-by-step explanation:
the answer is up at the top
Click on photo if neccessary
Answers
PLEASE ANSWER ASAP!!! 45 POINTS!
Answers
Answer:
x =2 [tex]\\\sqrt{24[/tex]
Step-by-step explanation:
a2+b2=c2
(10*10)+(8*8)=x
Please help!! And show work please! I'll give brainlist..!
Answers
You roll a six-sided die and spin the spinner below. What is the
probability of rolling a 3 and spinning blue?
Answers
Answer:
Its a 1 in 6 chance of rolling a 3
Step-by-step explanation:
Let me know how many color and i can tell you the probability if spinning blue, enjoy.