if f(x) = 2x/x-5
find f-1(x)
Answer:
5x/x-2
Step-by-step explanation:
rewrite it as x=2y/y-5 to make y the subject
multiply by (y-5) on both sides to get x(y-5)=2y
simplify x(y-5)=2y to get xy - 5x = 2y.
in order to get y as a subject you would need to move all the (y)s to one side.
Which would leave you with xy - 2y = 5x. you can now make y the subject from here through factorisation : y(x-2)=5x.
Then to finish with y as a subject divide (x-2) on both sides to get the answer which is : y = 5x/x-2
Sorry if this is confusing but this is me explaining how my thought process works for this question.
The inverse of the function will be -
f⁻¹(x) = 5/(1 - 2/x)
What is inverse of function? What is a mathematical equation? What do you mean by domain and range of a function?In mathematics, the inverse function of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by [tex]{\displaystyle f^{-1}.}[/tex]A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.
Given is f(x) = 2x/(x - 5)
We have -
y = 2x/(x - 5)
replace [x] with [y] as -
x = 2y/(y - 5)
Solving for y -
y/(y - 5) = x/2
(y - 5)/y = 2/x
(y /y - 5/y) = 2/x
(1 - 2/x) = 5/y
y = 5/(1 - 2/x)
f⁻¹(x) = 5/(1 - 2/x)
Therefore, the inverse of the function will be -
f⁻¹(x) = 5/(1 - 2/x)
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The grocery store is having a deal on two types of
apples. Fuji apples are $6 for 4 apples. Gala apples are
$8 for 5 apples. Find the price per apple for Fuji apples
and Gala apples. Which deal is better?
Answer:
Fugi=$1.50 per apple, Gala=$1.60 per apple. Fugi are cheaper
Answer:
Fuji apples are better because they only cost $1.50
What is the initial value of the sequence?
Hi! If you could please do my assignment, I'd be grateful! I'll also mark brainliest, giving thanks, and hearts for the best. Thank you and have a great day!
Answer:
Smaller Trapezoid: 12
Bigger Paralleogram: 24
Bigger Triangle: 22/40
Smaller Triangle : 2.75/ 5
Step-by-step explanation:
cross multiplication
Bigger Paralleogram: 9 x 16= 144 / 6= 24
Bigger Triangle: 5 x 22= 110 / 2.75 = 40
hope this helps
please help multiple questions using all my points
Answer:
Step-by-step explanation:
Mary has a garden shaped like the figure below. The drawing is not to scale.
What is the area of the garden?
Answer:
the answer is 200 square feet
Step-by-step explanation:
Write an equation of the line that passes through (0, 8) and (6, 8).
y = __
Answer:
y = 8
Step-by-step explanation:
Normally you would use the formula y2 - y1 / x2 - x1 also know as change in y over change in x, but this equation leaves you with a horizontal line.
Matt's den is 10 feet longer than it is wide. If the dents area is 231 square feet, what are the dimensions of the room?
The dimensions of the room are
ft.
(Use a comma to separate answers as needed.)
Answer:
[tex]21\: \mathrm{feet\: by}\: 11 \: \mathrm{feet}[/tex]
Step-by-step explanation:
(Assuming the den is a rectangle)
Let [tex]x[/tex] be the length of the den. Because the length is 10 feet longer than the width, the width of the den can be represented as [tex]x-10[/tex].
The area of a rectangle is given as [tex]l\cdot w[/tex], therefore we can form the following equation:
[tex]x(x-10)=231[/tex]
Expanding this, we have:
[tex]x^2-10x=231, \\\\x^2-10x-231=0[/tex]
This factors into [tex](x-21)(x+11)=0[/tex], therefore [tex]x=21, \: -11[/tex].
Because -11 is extraneous, the length of the den is [tex]21[/tex] feet and the width is [tex]21-10=11[/tex]. Thus, the dimensions of the den are [tex]\fbox{$21\: \mathrm{feet\: by}\: 11 \: \mathrm{feet}$}[/tex].
Plz help me!! I dont understand
Answer: D
Step-by-step explanation:
The rest are not
Given the function h(x) = -3x - 6, find h(6).
Answer:
h(6)=-24
Step-by-step explanation:
h(6)=-3(6)-6
h(6)=-18-6
h(6)=-24
The required value of h(6) of the function would be -24.
What is a function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
What are Arithmetic operations?Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.
Given the function h(x) = -3x - 6
We have to determine the value of h(6) of the function
⇒ h(x) = -3x - 6
Substitute the value of x = 6 in the above function, and we get
⇒ h(6) = -3(6) - 6
Apply the multiplication operation
⇒ h(6) = -18 - 6
Apply the addition operation
⇒ h(6) = -24
Therefore, the required value of h(6) of the function would be -24.
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HAAALLLLPPPP plz
The production cost to make 10 shirts is modeled by the expression Syntax error from line 1 column 49 to line 1 column 73. Unexpected 'mathsize'. where y represents the number of meters of fabric needed to make the shirts. Which expression represents the production cost for one shirt?
Answer:
the second one, B
Step-by-step explanation:
This is because in both numbers the decimal was moved back one.
0.18y+55 is the represents the production cost for one shirt.
What is Expression?Expression is a combination of numbers, variables and operators.
Given that production cost to make 10 shirts is modeled by the expression 1.8y+55.
The variable y represents the number of meters of fabric needed to make the shirts.
We need to find the expression represents the production cost for one shirt.
As there are 10 shirts so divide 1.8 with 10
we get 0.18.
And the value remains constant as it is a constant which does not change.
Hence, 0.18y+55 is the expression represents the production cost for one shirt.
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You have performed very well on your new job. Without even requesting it your boss gave you a $2.50 raise. If your previous wage was $6.25, what was the percent increase of your raise?
Answer:
40%
Step-by-step explanation:
$6.25/100=0.0625
$2.50/0.0625=40
so your wage increased by 40%
A researcher compared the heights and shoe sizes for 50 men, selected at random. The equation shown describes a line of best fit for the data, where x is the shoe size and y is the height, in inches. y equals 1.6 x plus 48 Question Based on the equation, what is the approximate shoe size for a man having a height of 60 inches? Answer options with 4 options
Answer:
7.5
Step-by-step explanation:
From the above Question, the equation is given as:
y = 1.6x + 48
Where
x is the shoe size
y is the height, in inches.
What is the approximate shoe size for a man having a height of 60 inches?
This is calculated as:
60 = 1.6x + 48
Collect the like terms
1.6x = 60 - 48
1.6x = 12
We divide both sides by 1.6
x = 12/1.6
x = 7.5
Therefore, the shoe size for a man having the height of 60 inches is 7.5.
Answer:
Fgffg
Step-by-step explanation:
Dogged
3 rays have common vertex. All the angles, which are made by neighbor rays( I think they mean adjacent rays), can be:
a)acute
b)obtuse
c)right
d)none of it.
btw I checked answer, but I still didn't understand, so I need explanation.
Answer:
[tex]b)\ Obtuse[/tex]
Step-by-step explanation:
[tex]We\ are\ given\ that:\\There\ are\ three\ rays.\\Lets\ mark\ them\ Ray\ OP, OQ,\ and\ OR\ with\ their\ common\ Vertex\ O.\\\\Now,\\We\ know\ that\ the\ sum\ of\ all\ angles\ around\ a\ point[or\ here\ Vertex\ O]\\ should\ be\ equal\ to\ 360.\\Here,\\\\Lets\ consider\ each\ case\ sepearately.\\If\ all\ the\ angles\ formed: \angle POR, \angle ROQ, \angle POQ,\ are\ acute\ then:\\\angle POR, \angle ROQ, \angle POQ<90\\If\ we\ add\ them\ together,[/tex]
[tex]\angle POR+ \angle ROQ+ \angle POQ<90+90+90<270[/tex]
[tex]But\ here\ the\ sum\ of\ the\ angles\ are\ less\ than\ 270,\ but\ the\ sum\ should\\ instead\ be\ 360.\\Hence,\ the\ angles\ formed\ by\ the\ rays\ are\ NOT\ acute.[/tex]
[tex]Similarly,\\If\ all\ the\ angles\ formed: \angle POR, \angle ROQ, \angle POQ,\ are\ right\ then:\\\angle POR, \angle ROQ, \angle POQ =90\\When\ we\ add\ them\ again:\\\angle POR+ \angle ROQ+ \angle POQ=90+90+90=270\\But\ again\ the\ sum\ here\ is\ equal\ to\ 270,\ but\ instead\ the\ sum\ had\ to\\ be\ equal\ to\ 360.\\Hence,\\The\ angles\ formed\ are\ NOT\ right.[/tex]
[tex]Lets\ consider\ the\ Last\ Case,\\If\ the\ angles\ formed: \angle POR, \angle ROQ, \angle POQ\ are\ obtuse,\\\angle POR, \angle ROQ, \angle POQ>90\\When\ we\ add\ them:\\\angle POR+ \angle ROQ+ \angle POQ>(90+90+90)>270\\Here,\\The\ angles\ formed\ are\ greater\ than\ 270.\ As\ 360>270,\ the\ angles\ ARE\\ obtuse.[/tex]
Need help asap please
Answer:
The answer is row C
Step-by-step explanation:
6 - 3 = 3
Which skateboarder is faster:
Jada, who travels 2 miles in 12 minutes at a constant speed, or
Clare, who travels 2 miles in 10 minutes at a constant speed?
Explain how you know.
Answer:
Clare is faster
Step-by-step explanation:
They are both traveling the same distance but Clare travelled it in less time which means she is going faster.
Answer: Clare
Step-by-step explanation: If it the same mile, just look whoever’s time is the least is the fastest.
Simplify the expression. . 1 V 3.0 2
Answer:
81x^4/16 (81x to the fourth over 16)
Step-by-step explanation:
First you apply the exponent rule: (a/b)^c -> a^c/b^c
So it looks like this: 3x^2/4^2
Then you apply the exponent to the whole thing, and 3^4 is 81, x^4 stays like that, and 2^4 is 16
You can't simplify any more after that so that's your answer
Hope this helps!
PLEASE HELP MEEEEE !!!!!! Like rn
Answer:
Your screen is black hun
Step-by-step explanation:
An airplane prepares for landing. When it begins its descent towards the airport, the plane's
altitude is 27,000 feet. After descending at a steady rate for 6 minutes, its altitude is 19,000
feet. Write an equation for the altitude of the plane. What will the altitude of the plane be after
descending for 12 minutes?
The required equation represents the descent motion of the airplane is y = 27000 - 1333.333x and 11000 feet.
Given that,
An airplane prepares for landing. When it begins its descent towards the airport, the plane's altitude is 27,000 feet. After descending at a steady rate for 6 minutes, its altitude is 19,000 feet. Write an equation for the altitude of the plane.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The slope of the motion of the airplane,
m = 27000 - 19000 / 6 = 1333.33
The equation of the plane is given as,
y - y₁ = m (x - x₁)
Substitute the value in the above equation,
y - 27000 = -1333.33[x - 0]
y = 27000 - 1333.33x
Now put x = 12 in above equation,
y = 27000 - 1333.33[12]
y = 11000
Thus, the required equation represents the descent motion of the airplane as y = 27000 - 1333.333x and 11000 feet.
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can anyone help with this?
Answer:
zuzhztxrctwhdvdhsuwjd
Money changer A offers an exchange rate of 1 CAD = 0.635 EUR, with no transfer fee. Which money changer gives the most money in euros for a transfer 800 CAD?
Answer:
800 CAD = 508 EUR
Step-by-step explanation:
From the above question:
1 CAD = 0.635 EUR
800 CAD = x
Crososs Multiply
x = 800 CAD × 0.635 EUR
x = 508 EUR
Therefore,
800 CAD = 508 EUR
please help i will mark branliest
Answer:
A. S=3w
Step-by-step explanation:
Hope it helps
-7y-8=6y+18 i need help with this urgent!
Answer:
Y= -2
Step-by-step explanation:
(Who ever answers the question for this lil bear> ʕ •ᴥ•ʔ, gets Brainliest!!)
Sam and Joe are working to solve 6 ÷ 1/4___. Sam thinks the answer is 24. Joe thinks the answer is 1/24. Explain who is correct. Use a model to help explain your thinking
ʕ •ᴥ•ʔ : "You don't have to use a model to help explain your thinking, but I do recommend using one!"
Answer:
Sam is right.
Step-by-step explanation:
Key skills needed: Fraction Modelling, Fraction Division
1) We are given this problem --> [tex]6[/tex] ÷ [tex]\frac{1}{4}[/tex]
2) This means we need to find how many [tex]\frac{1}{4}[/tex]'s are in 6.
3) There are 2 ways to approach this problem
1. The first way is via using the fractional division properties:
Let's say we are given a problem --> [tex]a[/tex] ÷ [tex]\frac{b}{c}[/tex]
This can be made into --> [tex]a[/tex] × [tex]\frac{c}{b}[/tex]
It is a simple property that should be remembered.
This means that [tex]6[/tex] ÷ [tex]\frac{1}{4}[/tex] is the same as [tex]6[/tex] × [tex]\frac{4}{1}[/tex] which is 24.
2. The second way is with using a model (which I am not very good with). The model way is the image I will post.
Hope you understand both ways and have a nice day!! :D
please help me with this
Answer:
its A :)
Step-by-step explanation:
Division number story with the answer 5/2
Answer:
I have one below (It's kind of simple though..)
Step-by-step explanation:
Harry Had 5 Potions he made in Potions Class. He would like to share the 5 potions with his 2 friends, Ron and Hermione. How many potions do they each get? Write the equation for how many each person gets in fractional form
(This is a simple one I don't have a complicated one..)
Multiply binomials by polynomials
Expand.
Your answer should be a polynomial in standard form.
(n2 – 3n+ 1)(2n + 3) =
Answer:
2n³ - 3n² - 7n + 3
Step-by-step explanation:
Given
(n² - 3n + 1)(2n + 3)
Each term in the second factor is multiplied by each term in the first factor, that is
n²(2n + 3) - 3n(2n + 3) + 1(2n + 3) ← distribute the parenthesis
= 2n³ + 3n² - 6n² - 9n + 2n + 3 ← collect like terms
= 2n³ - 3n² - 7n + 3
Simplify (2/3)^3 (1/5 *2/3)^-3 (1/5)^4
Answer:
1/5
Step-by-step explanation:
im pretty sure thats it! and have a great day!
Answer:1/5 or 0.2
by-step explanation:
1. Find the slope of a line passing though the points. Write the formula and indicate
the type of slope (2, 9 ) and (-3, 6).
Answer:
The answer is 3/5
Step-by-step explanation:
try math caculators to help you with these questions thats where i go the solution from.
-Best of luck
PLEASE HELP I WILL GIVE BRAINLIEST:)
Answer:
x= 107.3-51
56.3
Step-by-step explanation:
Equation: First define your variables. We'll say x= the second number.
So we can make our equation x= 107.3-51
107.3-51 is 56.3.
So the solution is 56.3
Answer:
56.3 i the second angle
Step-by-step explanation:
107.3=x+51
subtract 51
56.3 is the second angle