How do I find the range of this rational function, how do I do the steps in order to find it, please help!!!
Answers
Answer:
Range= (0,∞) and (-∞,0)
Step-by-step explanation:
Theres no real process to finding this out you just look at what type of function you have, your graph and your asymptote. We can see that the parts above the asymptote go up and towards ∞ and the part below goes down to -∞ but they can not cross 0
Answer:
(-infinity, -32/81] U (0, positive infintiy).
( use the sideways 8 symbol for infinity).
Step-by-step explanation:
The range is all possible y values in a function.
We can find the inverse of the function to find the range.
[tex]y = \frac{8}{ {x}^{2} - 7x - 8 } [/tex]
Replace x with y
[tex]x = \frac{8}{ {y}^{2} - 7y - 8 } [/tex]
Write the LCD as two binomial,
[tex]x = \frac{8}{(y + 1)(y - 8)} [/tex]
Multiply both sides by both binomial
[tex]x(y + 1)(y - 8) = 8[/tex]
[tex](xy + x)(y - 8) = 8[/tex]
[tex]x {y}^{2} - 8yx + xy - 8x = 8[/tex]
[tex]xy {}^{2} - 8yx + xy = 8 + 8x[/tex]
[tex]y( {x}^{2} - 8x + x) = 8 + 8x[/tex]
[tex] \frac{8 + 8x}{ {x}^{2} - 7x } [/tex]
[tex] {x}^{2} - 7x = 0[/tex]
[tex] {x}^{2} - 7x + 12.25 = 12.25[/tex]
[tex](x - 3.5) {}^{2} = 12.25[/tex]
[tex](x - 3.5) = 3.5[/tex]
[tex]x = 3.5[/tex]
Plug that in to the function to find it range.
We get approximately
[tex] - \frac{35}{81} [/tex]
So this means a point on our function must include -35/81.
The vertical asymptote is 0 so our y cannot be zero but it goes infinitely up so our range is
(-infinity, -32/81]U (0, positive infintiy).
( use the sideways 8 symbol for infinity).
Related Questions
Simplify: (-5x + 7) - (x2 – 3x +2)
Answers
Answer:
-x^2-2x+5
Step-by-step explanation:
-x2 - 2x + 5 = -1 • (x2 + 2x - 5)
Factoring x2 + 2x - 5
The first term is, x2 its coefficient is 1 .
The middle term is, +2x its coefficient is 2 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 1 • -5 = -5
Step-2 : Find two factors of -5 whose sum equals the coefficient of the middle term, which is 2 .
-5 + 1 = -4
-1 + 5 = 4
Observation : No two such factors can be found !!
-x2 - 2x + 5
Anyone knows the answer???
Answers
Answer:
351.9 m²
Step-by-step explanation:
[tex]SA=2\pi r^2+2\pi rh[/tex] where r is the radius of the base and h is the height of the cylinder
We're given the diameter of the base, which is 8 m. Therefore, the radius is 4 m (after dividing by 2).
Plug in 4 as r and 10 as h
[tex]SA=2\pi (4)^2+2\pi (4)(10)\\SA=2\pi (16)+2\pi (40)\\SA=32\pi +80\pi \\SA=112\pi[/tex]
Therefore, the surface area of the cylinder is approximately 351.9 m² after rounding to the nearest tenth.
I hope this helps!
The water diet requires one to drink two cups of water every half hour from when one gets up until one goes to bed, but otherwise allows one to eat whatever one likes. Four adult volunteers agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The weights (in pounds) are
Person 1 2 3 4
Weight before the diet 180 125 240 150
Weight after six weeks 170 130 215 152
For the population of all adults, assume that the weight loss after six weeks on the diet (weight before beginning the diet minus weight after six weeks on the diet) is normally distributed with mean (µ). When testing the claim that the diet leads to weight loss after six weeks for all adults given that α=0.05, do you reject or fail to reject the Null Hypothesis, why or why not?
Answers
Answer:
hope this help you
have a nice day/night
Tomas drew a rectangle with an area of 6 square centimeters.what is the greatest possible perimeter of this rectangle?Explain please. i want 20 answers please
Answers
3 mugs have the same capacity as 2 bottles. The capacity of 10 mugs and
8 bottles is 15.4 l. Find the capacity of a mug.
Answers
Answer:
0.70L
Step-by-step explanation:
3m=2b
convert 8 b to mugs
therefore 8b=12m
12m+10m=22m
15.4/22=0.700l
Solve 3≥y−2. Graph the solution. The solution is
Answers
Answer:
y ≤ 5
Step-by-step explanation:
too lazy to explain :/
PLS HELP 20 PTS
how many solutions are there to this nonlinear system?
a. two solutions
b. no solutions
c. one solution
Answers
Hope this helps
Plz help me this very important
Answers
Jack borrowed $ 4,000.00 and paid $ 585.00
in simple interest after 4 year 6 months. What
was the annual rate of interest?
Answers
Answer:
3.25%
Step-by-step explanation:
The formula for simple interest is I = PRT, where I = interest earned/paid, P = principal amount deposited or borrowed, R = rate of interest as a decimal, and T = time in years.
I = PRT
585 = (4000)(r)(4.5)
585 = 18,000r
r = 0.0325
Multiply by 100 to get the percentage
0.0325 = 3.25%
D = L ( m/k + v^2/25)
Make v the subject of the formula.
Answers
Answer:
Answer and steps in picture.
-m/k -m/k
25(D/L - m/k) = v^2/25(25)
Sqrt 25(D/L - m/k) = sqrt v^2
Sqrt 25(D/L - m/k) = v
what does noncollinear
Answers
9514 1404 393
Answer:
not on the same line
Step-by-step explanation:
Any two distinct points define a line. Additional points may or may not be on that line. If they are on the line, they are collinear with other points on the same line.
Any point not on the line is noncollinear with the points that are on the line.
hi guys what is and can u please do the method 4050 divided by 100
Answers
Answer:
40.5
Step-by-step explanation:
what i do is I divided first by 10. because 100 is 10x10.
so 4050 divided by 10 is 405.
405 divided by 10 is 40.5
4050 divided by 100 = 40.5
A 20 in wagon wheel has 6 spokes. What is the outside distance between the end of the spokes if they are spaced evenly(arc length)?
Answers
Answer:
10.47 inches
Step-by-step explanation:
circumference = πD = 3.14(20) = 62.8 inches
62.8 inches/6 spaces = 10.47 inches per space
Solve these equations.
Answers
Answer:
no solution
Step-by-step explanation:
|x-33| = -33
An absolute value must be greater than or equal to zero
The right hand side is a negative number.
There is no solution
Answer:
No solution
Step-by-step explanation:
When you do the absolute value, it is equal to a negative number. Which does not make sense so no solution
Given f z please help
Answers
Answer:
z = -11, z = -2
Step-by-step explanation:
Given that, ([tex]f(z)=\sqrt{z+27} -z[/tex]) and ([tex]f(z)=7[/tex]), set up an equation that puts the first value of ([tex]f(z)[/tex]) equal to the other given value of the function.
[tex]f(z)=\sqrt{z+27}-z=7[/tex]
Use inverse operations to solve,
[tex]\sqrt{z+27}-z=7\\\\\sqrt{z-27}=7+z\\\\z+27 = (7+z)^2\\\\z + 27 = 49+14z+z^2\\ -(27+z)\\\\0 = z^2+13z+22[/tex]
Factor,
[tex]0=(z+11)(z+2)[/tex]
Solve using the zero product property, the zero product property states that any number times zero equals zero;
[tex]z=-11,z=-2[/tex]
Answer:
Then solve the rest using the quadratic formula
please help me i can't figure this out
A 6 meters per second
B 5 meters per second
C 4 meters per second
D 7 meters per second
Answers
Answer:
B 5 meters per second
Step-by-step explanation:
Pick two points on the graph, and find the slope.
For example, you can use the points
(0, 8500) and (1700, 0)
slope = (difference in y)/(difference in x)
slope = (0 - 8500)/(1700 - 0) = -8500/1700 = -5
The slope is negative because the plane was losing altitude as it descended.
It descended at a rate of 5 meters per second.
Answer: B 5 meters per second
Answer:
B. 5 meters per second
Step-by-step explanation:
slope=8500÷1700=5
Plane descended at the rate of 5 meters per second.
hope it helps
have a great day!!
The ratio of dogs to cats at the local
shelter is 2 to 5. There are 20 dogs at
the shelter. What is the total number
of cats and dogs at the shelter?
A. 28
B. 50
C.
70
D. 8
Need
Answers
Answer:
B 50
Step-by-step explanation:
Option 1) 2/5 = 20/x | 20/2 = 10 so x = 10 | 5 times x 10 =50
Option 2) dogs 2 to cats 5 | 2/5 = 20/x | .40 = 20/x | .40x = 20 | x = 50
Option 3) you can look and see that 20 is 10 times more than 2 and therefore infer that x is 10 times more than 5 which is 50
RM 74.97 is reduced for an item priced at RM 249.90. Find the percentage of a discount.
Answers
Answer:
249.90/74.97=.3
.30*100=30%
Martin spent $2.60 on his lunch. Sandwiches cost $1.25. Milkshakes cost $0.65. How much MORE does a sandwich cost than a milkshake?
Answers
Answer:
0.60 more
Step-by-step explanation:
Sandwich: 1.25
Milkshake: 0.65
We need to find the difference between the 2
1.25 - 0.65 = 0.6
A sandwich costs 60 cents MORE than a milkshake
Determine the intercepts of the line I need help quick!!!!!
Answers
Answer:
x-inter = (-40,0), y-inter= (0,15)
Step-by-step explanation:
the fitnessgram pacer test is an automated aerobic capacity test that progressively gets more difficult as it continues.
The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the rate of three jobs per 8-hour day. The company's repair facility is a single-server system operated by a repair technician. The service time varies, with a mean repair time of 2 hours and a standard deviation of 1.5 hours. The company's cost of the repair operation is $28 per hour. In the economic analysis of the waiting line system, Robotics uses $35 per hour cost for customers waiting during the repair process. What are the arrival rate and service rate in jobs per hour
Answers
Answer:
The correct answer is:
[tex]\lambda=0.375 \ jobs \ per \ hour[/tex][tex]\mu=0.5 \ jobs \ per \ hour[/tex]Step-by-step explanation:
The given values are:
Service time varies,
Repair time = 2 hours
Standard deviation = 1.5 hours
Robotics uses per hour cost,
= $35
Company's cost per hour,
= $28
(a)
⇒ Arrival rate = Jobs per hours
then,
= [tex]\frac{8 \ hours}{3 \ jobs}[/tex]
= [tex]2.666 \ hours \ per \ job[/tex]
The jobs per hour will be:
⇒ [tex]\lambda=\frac{1}{2.666}[/tex]
[tex]=0.375[/tex]
(b)
⇒ Service rate = jobs per hour
then,
μ = [tex]\frac{1 \ repair \ job}{2 \ hours}[/tex]
= [tex]0.5 \ jobs[/tex]
u(3u+4)-u(u+2)
HELP PLEASE I NEED IT RN
Answers
Please help me! NO sites or links please!
xoxo
Answers
first you change all the denominator to the same 1/8x2 = 2/16 and 5/16 no need to change and 3/8x2 = 6/16 . And then you add them all together and it will be the answer of D ( you don’t need to add the denominator)
A researcher posts a radio advertisement offering $35 in exchange for participation in a short study. The researcher accepts the first eight people who respond to the advertisement. Which of the following statements is true about the sample? (5 points)
A. It is a valid sample because the first eight people were selected to participate.
B. It is not a valid sample because it is not a random sample of the population.
C. It is a valid sample because money was offered to participants.
D. It is not a valid sample because it is only a short study.
Answers
Answer:
B.
Step-by-step explanation:
Its meh best guess
Answer:
B.
Step-by-step explanation:
I think it is B
Lucy drank 6 liters of water after 2 days. How many liters of water did she drink after 6 days?
Answers
Answer:
18 Liters of water
please help me. right answer will get brainliest
Answers
Answer:
I attached the answers :)
Step-by-step explanation:
hope this helps :)
(Its a bit messy becuz i used a mouse to write, sry about that)
please help this is so hardddd
Answers
Answer:
x < 9 ; x > 15
Step-by-step explanation:
| x - 12 | > 3
x - 12 > 3
x > 12 + 3
x > 15
-x + 12 > 3
-x > 3 - 12
-x > -9
x < 9
Combined:
x < 9 ; x > 15
what is the value for θ: sin (θ+20) = cos θ
Answers
Answer:
Step-by-step explanation:
What is the area of the triangle?
Answers
Answer:
11 ½ * 4* 5.52 *5.5=11.....….Question 4
The results of the Woodlands Middle School poll show that 20% of
the students prefer the aquarium and 50% of the teachers the
aquarium.
Which of the following statements is true?
There is evidence that teachers at Woodlands Middle may prefer the aquarium
more than students.
There is not enough evidence to support a relationship between destination
preference (aquarium or amusement park) and school role (student or teacher).
Woodlands Middle may prefer the aquarium
There is evidence that students
more than teachers.
Answers
Answer:
There is evidence that teacher at Woodlands Middle May prefer the aquarium more than students
Step-by-step explanation:
There is evidence that teachers at Woodlands Middle may prefer the aquarium (Option A) is the true statement from all the available options.
Why do we do sampling?We do sampling so that we don't have to work on entire population of items but only on that sample in a way that we can predict information about population.
Most of the times, it isn't possible in real world to work on entire populations. Samples come out for rescue by assumptions that they will have some properties of the population pertained in them.
Thus, the sample should be taken out such that it includes data of the population as much as it can in unbiased way so as to imitate population.
Poll oftenly uses sampling.
The data obtained from the poll shows that:
20% of the students prefer the aquarium and 50% of the teachers the
aquarium.
That means, from the poll, we found that out of total students, 20% prefer aquarium whereas 50% of total teacher prefer aquarium.
Since we conclude from sampling only as this is the usual way we do conclusion about population, and since percentage shows that less students' proportion prefer aquarium than the proportion of teachers prefering aquarium, thus,
There is evidence that teachers at Woodlands Middle may prefer the aquarium (Option A) is the true statement from all the available options.
Learn more about sampling here:
https://brainly.com/question/24842573