What Is the value of -6?
Answer:
the value of -6 is -6
Step-by-step explanation:
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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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].
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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What is the initial value of the sequence?
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
please help me with this
Answer:
its A :)
Step-by-step explanation:
PLEASE FAST DUE IN 10 MINUTES I WILL MAKE YOU BRAINLIEST
What can you say about the measurements of a ramp with a slope of 1/4?
Answer:
all answers on the graph will be 4 times that amount
Step-by-step explanation:
rise over run
basically if y is 1 and its of a slope of 1/4 then youd multiply it by 4. 2/8 3/12
as well as it will always be a positive slope :)
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!
-7y-8=6y+18 i need help with this urgent!
Answer:
Y= -2
Step-by-step explanation:
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
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:
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]
Only number 14 and pls explain txs
Step-by-step explanation:
since right angle triangle,then:
180-(90+35)=B=55
use cosB=opposite/hypotenuse
cos55=x/12
x=cos55x12
x=6.88
9514 1404 393
Answer:
9.8
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship involving the adjacent side and the hypotenuse:
Cos = Adjacent/Hypotenuse
cos(35°) = x/12
Multiplying by 12 gives x:
x = 12·cos(35°) = 12×0.81215
x = 9.8
can anyone help with this?
Answer:
zuzhztxrctwhdvdhsuwjd
The sum of two numbers is -6. The difference is 16. Find the two numbers.
Answer:
[tex]-5\:\mathrm{and}\: 11[/tex]
Step-by-step explanation:
We can write the following system of equations:
[tex]\begin{cases}x+y=6\\x-y=16\\\end{cases}[/tex]
Adding both equations together, we isolate [tex]x[/tex] and get:
[tex]2x=22,\: x=11[/tex]
Plugging [tex]x=11[/tex] in any of the equations, we can solve for [tex]y[/tex]:
[tex]11+y=6,\: y=-5[/tex]
Verify that the solution pair [tex](11, -5)[/tex] works [tex]\checkmark[/tex]
Therefore, the two numbers are [tex]\fbox{$-5\:\mathrm{and}\: 11$}[/tex].
m = 5.71 + 0.25n
j = 4.66 + 0.60n
In the equations above, m and j represent
the price per gallon of milk and orange juice,
respectively, n months after December 31, 2018.
What was the price per gallon of milk when it was
equal to the price per gallon of orange juice?
A) $5.96
B) $6.21
C) $6.46
D) $6.71
Answer:
C) $6.46
Step-by-step explanation:
Equations
The price per gallon of milk (m) and the price per gallon of orange juice (j) are given below:
m = 5.71 + 0.25n
j = 4.66 + 0.60n
Where n is the number of months after December 31, 2018.
It's required to find the value of n when both prices are equal:
4.66 + 0.60n = 5.71 + 0.25n
Subtracting 0.25n:
4.66 + 0.60n - 0.25n = 5.71
Subtracting 4.66:
0.60n - 0.25n = 5.71 - 4.66
Operating:
0.35n = 1.05
n = 1.05/0.35
n = 3
The price per gallon of milk for n=3:
m = 5.71 + 0.25*3
m = 5.71 + 0.75
m = $6.46
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..)
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:
please help multiple questions using all my points
Answer:
Step-by-step explanation:
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.
Plz help me!! I dont understand
Answer: D
Step-by-step explanation:
The rest are not
Anyone know the answer to this?
Answer:
124.80 ft
Step-by-step explanation:
Height of Daniel = 6 ft
The angle of elevation from his eyes to the top of the statue is = 68°
Daniel is 48 ft away from the base of the statue
To find the height of the statue apply the tangent of an angle formula then add height of Daniel as;
Tan 68° = h/48
h= {48 tan 68°} + 6 ft
h= 124.804168964
h= 124.80 ft
A 100 feet driveway climbs 5 feet in height to reach the garage. What is the angle of the driveway in degrees. Report answer to nearest 0.1\displaystyle ^{\circ} ∘ (one decimal place).
Answer:
Slope and Width
If it's too flat, drainage may become an issue, and if it's too steep, the surface becomes slippery and dangerous. As a general rule, a driveway should be less than a 15% grade, which means that it should not rise more than 15 feet over a distance of 100 feet.
Step-by-step explanation:
mark as BRAINLY
What is the perimeter of rhombus STAR
Answer:
160 cm
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
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%
Need help asap please
Answer:
The answer is row C
Step-by-step explanation:
6 - 3 = 3
a 100oz bottle costs $2.97 and a 200oz bottle costs $5.78 what is the unit price of each one?
Answer: BOTTLE 1 =0.0297 BOTTLE 2 =0.0289
Step-by-step explanation:
In a unit rate, the denominator is always 1. So, to find unit rate, divide the denominator with the numerator in a way that the denominator becomes 1. For example, if 50 km is covered in 5.5 hours, the unit rate will be 50 km/5.5 hours = 9.09 km/hour
bottle 1: $2.97/100 oz = unit rate
bottle 2: $5.78/200 oz=unit rate
BOTTLE 1 =0.0297
BOTTLE 2 =0.0289
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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