Inverse of the given function F(x) = ( x + 3 )² + 1 is F⁻¹(x) = [√( x - 1 ) ] - 3
Given is a function of x, F(x) = ( x + 3 )² + 1
These question can be solved by following 4 easy steps
Step 1 : Switch the F(x) with the variable y
This implies, F(x) = ( x + 3 )² + 1 becomes y = ( x + 3 )² + 1
Step 2 : Interchange the variable x and y in the above obtained equation
This implies, from the equation y = 3 x³- 4, we get
x = ( y + 3 )² + 1
Step 3 : Solve the new obtained equation for y
This implies, we have to simplify the equation by rearranging the terms to get the equation in terms of the variable x.
x = ( y + 3 )² + 1
=> x + 1 = (y + 3 )²
=> (y + 3 )² = x + 1
=> y = √( x - 1 ) - 3
Hence we obtain the required equation.
Step 4 : Switch the variable y with F⁻¹(x)
This implies, y =√( x - 1 ) - 3 becomes F⁻¹(x) = √( x - 1 ) - 3
Therefore, we get the inverse of the given function F(x) = ( x + 3 )² + 1 as F⁻¹(x) = √( x - 1 ) - 3
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Which action is an example of someone taking action to accept personal responsibility for eating right? continuing to eat while watching television consuming high-fat foods every day writing down foods consumed at each meal in a day going to the store on an empty stomachWhich action is an example of someone taking action to accept personal responsibility for eating right? continuing to eat while watching television consuming high-fat foods every day writing down foods consumed at each meal in a day going to the store on an empty stomachWhich action is an example of someone taking action to accept personal responsibility for eating right? continuing to eat while watching television consuming high-fat foods every day writing down foods consumed at each meal in a day going to the store on an empty stomach
The action that is an example of someone taking action to accept personal responsibility for eating right is writing down foods consumed at each meal in a day.
How to take responsibility for eating?There are several ways to take responsibility for our eating habits and one of them is to write down the foods that we consume during each meal that we take in a day.
This would enable us to keep track of the calories we consume and therefore give us a better idea of which foods to eat and which to avoid to maintain our recommended dietary intake.
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Answer:
Which action is an example of someone taking action to accept personal responsibility for eating right?
(A.) continuing to eat while watching television
(B.) consuming high-fat foods every day
(C.) writing down foods consumed at each meal in a day
(D.) going to the store on an empty stomach
Step-by-step explanation:
2022-2023 :)
36
8. Kendall is making a shelf for her room.
The length of the shelf is 3.5 times the
width of the shelf. If the width of the
shelf is 1.6 feet, what is the length of
the shelf?
Find the inverse of each function.
y=log₀.₅x
The inverse of the function y = log₀.₅ x is f⁻¹ (x) = (0.5) ˣ.
We are given the function:
y = log₀.₅ x
We need to find the inverse of the function.
First we will find the value of x in terms of y.
The logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.
We can write it as:
(0.5)^ y = x
x = (0.5) ^ y
now, the inverse of the function will be:
f⁻¹ (x) = (0.5) ˣ
Therefore, the inverse of the function y = log₀.₅ x is f⁻¹ (x) = (0.5) ˣ.
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360000/180 in standard form
Answer:
2000
Step-by-step explanation:
Write each fraction as a percent 17/20
Answer:
85%
Step-by-step explanation:
[tex]\frac{17}{20} * 100 = 85[/tex]
Answer:
85%
Step-by-step explanation:
See attachment for answers.
The ratio of eds toy cars to petes toy cars was 5:2 after ed gave pete 30 cars te owned a equall amount of cars how many cars did they have all together
Answer:
87
Step-by-step explanation:
5/2 ×30 = 75
2/5× 30=12
75 +12 = 87
Therefore , the total number of cars they altogether is 87
What is an equation of the line that is perpendicular to y = 3x - 9and that
passes through the point (3, 1)?
y =
Answer:
y = -1/3x + 2
Step-by-step explanation:
The slope of a line that is perpendicular has an opposite inverse of the slope of the line given.
The slope of the line given is 3. The opposite inverse is -1/3.
Use the slope (-1/3), the x(3) and the y(1) to find the y-intercept (b) and to write the equation of the line.
y =mx + b
1 = -1/3(3) + b
1 = -1 + b Add 1 to both sides
2 = b
y = -1/3x + 2
Round 6.1687 to the nearest hundredth
Answer:
6._ _ is the hundreth.
Since the diget after 6 is infact greater than or equal to 5.. (8>5).
We can round up to 6.17
Necesito ayuda urgenteee
Un cine tiene 800 butacas: durante la semana la asistencia fue: el lunes
2/5, martes 4/5, miércoles 4/5, jueves 1/5, viernes 3/5, sábado y domingo
completo. El precio de la entrada 8’7 €. ¿Cuál fue la recaudación de toda
la semana?
The total collection is 33408
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Total = 800 seats
On Monday 2/5
So, seats= 800*2/5 = 1600/5
=320 seats
On Tuesday
seats = 800 * 4/5
=3200/5
= 640
On Wednesday
seats = 800 * 4/5
=3200/5
= 640
On Thursday
seats = 800 * 1/5
=800/5
= 160
On Friday
seats = 800 * 3/5
=2400/5
= 480
As, the ticket price is €8.7
On Monday price of ticket = 320*8.7=2784On Tuesday price of ticket = 640*8.7=5568On Wednesday price of ticket = 640*8.7= 5568On Thursday price of ticket = 160*8.7=1392On Friday price of ticket = 480*8.7=4176On Saturday price of ticket = 800*8.7=6960On Sunday price of ticket = 800*8.7=6960Hence, the total collection = 33408
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The translation of the complete question is
I need urgent help
A cinema has 800 seats: during the week the attendance was: on Monday
2/5, Tuesday 4/5, Wednesday 4/5, Thursday 1/5, Friday 3/5, Saturday and Sunday complete. The ticket price is €8.7. What was the collection of all
week?
16.) CONSTRUCT ARGUMENTS Mariah is training for a sprint-
distance triathlon. She plans on cycling from her house to
the library, shown on the grid with a scale in miles. If the
cycling portion of the triathlon is 12 miles, will Mariah
2
have cycled at least of that distance during her bike ride?
Justify your argument.
Using the distance between two points, it is found that she cycles a distance of 8.6 miles, which is more than 8 miles, hence more than 2/3 of the cycling portion of the triathlon.
What is the missing information?The coordinates are given as follows:
Library (4,9).Mariah's House: (9, 2).It asks if the distance that he cycles from her house to the library is at least 2/3 of 12 miles = 8 miles.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence the distance between her house and the library is:
[tex]D = \sqrt{(9 - 4)^2 + (2 - 9)^2}[/tex]
D = 8.6 miles.
She cycles a distance of 8.6 miles, which is more than 8 miles, hence more than 2/3 of the cycling portion of the triathlon.
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f(x)=2x+5/3x find f-1(x)
please answer quickly!
Answer:I think its 2x-5/3
Step-by-step explanation:
please let me know if I'm wrong.
Write each expression in simplest form. (x⁻¹⁰ / x⁵)²/₅
The radical expression of the term (x⁻¹⁰ / x⁵)²/⁵ is ⁵√(1/x¹⁰)
What is a radical?A radical is a number that is denoted by a root and can be easily identified because before the number is the symbol √, which lets us know that it is a root.
In this case we have an exponential number since it is raised to a number, radicals can be expressed as powers raised to fractions as follows:
√a = a¹/²
We reduce the fraction value
(x⁻¹⁰ / x⁵) = x⁻⁵ = 1/x⁵
If our term is raised to 2/5, it can be expressed as:
(1/x⁵)²/⁵ = ⁵√(1/x⁵)² = ⁵√(1/x¹⁰)
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The function y=20(0.975)ˣmodels the intensity of sunlight beneath the surface of the ocean. The output y represents the percent of surface sunlight intensity that reaches a depth of x feet. The model is accurate from about 20 feet to about 600 feet beneath the surface.
b. Find the percent of sunlight at a depth of 370 feet.
The percent of surface sunlight intensity that reaches a depth of 370 feet is 0.0017%
We have been given the function which models the intensity of sunlight beneath the surface of the ocean which is
y = [tex]20 * (0.975)^{x}[/tex] (1)
where, y = the percent of surface sunlight intensity that reaches a depth of x feet.
x = depth in feet
b) We need to find the percent of sunlight at a depth of 370 feet that is we have been given, x = 370feet.
putting the required values in equation (1) we get
[tex]y = 20*(0.975)^{370}[/tex]
y = 20* 0.000085
y = 0.0017%
Hence 0.0017% of sunlight intensity reaches a depth of 370 feet
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Solve each equation.
x²+7 x-8=0
After solving, the factors of the equation x²+7x-8=0 are:
(x + 8) and (x - 1)What is an equation?A mathematical statement made up of two representations joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value for the variable x as x = 7 after solving this equation.So,
Given equation: x²+7x-8=0Then,
x²+7x-8 = 0x²+x( - )-8 = 0x²+x( 8 - 1 )-8 = 0x²+8x -x -8x(x + 8) -1( x+8)Factors are: (x + 8) and (x - 1)
Therefore, after solving, the factors of the equation x²+7x-8=0 are:
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Simplify this expression. Assume that x is nonzero. x^10 x x^3
Answer:
[tex]\sf x^{13}[/tex]
Step-by-step explanation:
Exponent law:If bases are same, add the exponents.
[tex]\sf \boxed{a^m*a^n =a^{m+n}}[/tex]
[tex]\sf x^{10}*x^3} = x^{10+3}\\[/tex]
[tex]\sf = x^{13}\\[/tex]
Hey there!
x^10 * x^3
x^10
= x * x * x * x * x * x * x * x * x * x
x^3
= x * x * x
x * x * x * x * x * x * x * x * x * x + x * x * x
= x^13
Or
10 + 3 = 13
Therefore, your answer should be:
x^13
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Find all the zeros of each function. f(x)=x⁴-16
The required zeros of the polynomial f(x) are 2, -2, and ±√-4.
What are zeros of the polynomial?
All the possible values of x that will make the polynomial zero are called the zeros of the polynomial, p(x). Zeros of a polynomial can either be negative or positive.
Solving for the zeros of a polynomial
f(x)=x⁴ - 16
Let, f(x) = 0
x⁴-- 16 = 0
(x²)² - 4² = 0
(x² + 4) (x² - 4) = 0
(x² + 4)(x - 2)(x + 2) = 0
i.e. x² + 4 = 0, x - 2 = 0, x + 2 = 0
x = 2, -2, ±√-4
Hence, the required zeros of the polynomial f(x) are 2, -2, and ±√-4.
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0.96 x 0.12 step by step pls
Answer:
0.1152
Step-by-step explanation:
multiply 0.96 by 0.12 to get 0.1152.
Simplify each rational expression. State any restrictions on the variables.
12-x-x² / x²-8 x+15
The required simplication of rational expression is -(4 + x) / (x - 5).
What is a rational number?
Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.
Simplifying the rational expression, 12 - x - x² / x² - 8x + 15
Given a rational expression,
12 - x - x² / x² - 8x + 15
On simplifying, we get,
For numerator, 12 - x - x²: (3 - x)(4 + x)
For denominator, x² - 8x + 15: (x - 5)(x - 3)
Now, 12 - x - x² / x² - 8x + 15 = (3 - x)(4 + x) / (x - 5)(x - 3)
= -(4 + x) / (x - 5)
Restriction is that the denominator, x - 5 should not be 0.
Hence, the required simplication of rational expression is -(4 + x) / (x - 5)
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Brainliest! Please answer quickly! Thank you
How many 5 ounce glasses of milk can you pour from a gallon of milk.? How many ounces of milk will you have left over? A gallon of milk contains 128 ounces.
Show your work.
25 5-ounce-glasses of milk can be poured out from a gallon of milk and 3/5 ounces of milk will be left over
How to find the how many 5 ounce glasses of milk can you pour from a gallon of milkAssuming
1 gallon 4 quarts
1 quart 2 pints
1 pint 2 cups
1 cup = 8 fluid ounces
if 1 quart 2 pints, then 4 quarts will be
= 4 * 2 = 8 pints
if 1 pint 2 cups, then 8 pints will be
= 8 * 2 = 16 cups
if 1 cup is 8 fluid ounces, then 16 pints will be
= 8 * 16 = 128 fluid ounces
solving the amount of 5 ounce glasses of milk in a ballon
= 128 / 5
= 25.6
= 25 3/5
Hence we can say that a gallon of milk will give 25 5-ounce-glasses of milk and 3/5 ounces of milk left over
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Answer:1 gallon 4 quarts
1 quart 2 pints
1 pint 2 cups
1 cup = 8 fluid ounces
if 1 quart 2 pints, then 4 quarts will be
= 4 * 2 = 8 pints
if 1 pint 2 cups, then 8 pints will be
= 8 * 2 = 16 cups
if 1 cup is 8 fluid ounces, then 16 pints will be
= 8 * 16 = 128 fluid ounces
solving the amount of 5 ounce glasses of milk in a ballon
= 128 / 5
= 25.6
= 25 3/5
Hence we can say that a gallon of milk will give 25 5-ounce-glasses of milk and 3/5 ounces of milk left over
Step-by-step explanation:
A rectangular room has an area of 575 square feet. The length of the room is 2 feet less than the width of the room. Find the length and width of the room, in feet, and separate them with a comma.
Answer:
w=17.613
l=15.613
Step-by-step explanation:
w×l=area
l=w-2
therefore w×(w-2)=575
rearrange the equation to make a quadratic
(w^2)-2w-575=0
w=-(b+ or - sqrt (b^2-4ac))/2a
a=1
b=-2
c=-575
using quadraric formula to solve
w=17.613 or -15.613
cant be -15.613
l=w-2
=15.613
Work out (9 × 10¹) – (2 × 10³) Give your answer in standard form.
Answer:
Standard notation/form
-1.91 × 10³
Hope this helps.
Karina drinks 42 oz of water in 1 day. In 1 week, Karina drinks 294 oz.
Step-by-step explanation:
???????????????????????
Answer: Your answer is 6.
Step-by-step explanation:
You need to divide 42 from 294.
Fill in the blanks
A(n) ? with a base e is a __________.
When e>1, the base - e exponential function is an increasing function.
What accurately is an exponential function?When the input variable x appears as an exponent in the formula f(x) = ax, it indicates an exponential function.The exponential curve is affected by both the exponential function and the value of x.The exponential function is a fundamental mathematical function whose formula is as follows:f(x) = aˣ
Where a>0 is not equal to 1.x can be any genuine number.If the value of the variable is negative, the function for (-1<x<1) is undefined.Here,
"x" is the variable.The function's base, "a," is a constant.Depending on the exponential function, an exponential curve can increase or decrease.If a quantity increases or decreases by a predetermined percentage on a regular basis, it should exhibit either exponential growth or exponential decay.So,
If b>1:Then the exponential function.So, f(x) = b^x is an increasing function.Therefore, when e>1, the base - e exponential function is an increasing function.
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Ryan works as a tutor for $15 an hour and as a waiter for $10 an hour. This month, he worked a combined total of 81 hours at his two jobs.
Let be the number of hours Ryan worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.
An expression for the combined total dollar amount he earned this month:
Total Earning = 15b + P(N - b)
where, b is the total hours worked as a tutor
P is the amount earned by Ryan per hour as a waiter
N is the total number of possible hours Ryan can work in a month
In this question,
Ryan works as a tutor for $15 an hour and as a waiter for $10 an hour. This month, he worked a combined total of 81 hours at his two jobs.
Let the number of hours Ryan works daily as a waiter be x
and the number of hours worked daily as a tutor be y
Ryan earns $15 per hour as tutor.
So, we get an expression for the daily earnings on tutoring = 15y
Let Ryan earns $P per hour as waiter.
so, we get an expression for the daily earning as a waiter = Px
The total possible hours Ryan can work in a month is dependent on conditions not specified.
Assuming 24 working days (6 days weekly for 4 weeks) in a month with maximum approved work hours of 12 hours daily, the total hours Ryan can work will equal 24 x 12 = 288 hours
This 288hrs is an estimate and can change based on applicable hours of work daily and number of working days in a month; it can also be represented as N
If b is the total hours Ryan worked as a tutor this month, the hours Ryan can work as a waiter in a month is equal to 288 - b
So, in a month, Ryan will earn 15b as a tutor and P(288-b) as a waiter or optionally P(N - b)
So, the combined dollar amount earned in a month is:
Total Earning = 15b + P(N - b)
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Gary, the local traffic guy is in his helicopter. He takes off from his base location and notices two car accidents south of him. He measures the angle of depression from the helicopter to the first accident at 63° and the angle of depression from the helicopter to the second accident at 49°. The helicopter is hovering 5000 feet above his base location. He needs to tell emergency services the locations of the accidents based on where he is. What are the distances from his base location to the accidents?
The distances from base location to first and second accident site is 2551 feet and 4347.8 feet.
The angle of depression is 63° and 49°. Also, joining the base location, accident site and position of helicopter, we will get a right angled triangle. Using tangent of given angle we will find the distance between base location and accident site.
Distance of first accident site
tan theta = perpendicular ÷ base
tan 63° = 5000 ÷ base
Base = 5000 ÷ 1.96
Base = 2551 feet
Distance of second accident site
tan 49° = 5000 ÷ base
Base = 5000 ÷ 1.15
Base = 4347.8 feet
Therefore, the distance of base location to first accident site is 2551 feet and distance to second accident site is 4347.8 feet.
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Determine the slope of the blue and green line
Answer:
2/-9
Step-by-step explanation:
Which properties can be changed by a transformation? (Check ALL that apply.)
Shape
Size
Position
Color
Eve write (1.2x10^5)divided by (3x10^2)
Answer:
1.2 x. 100000
3. x. 100
=120000
300
=400
Psychologists use an exponential model of the learning process, f(t)= c(1-e -kt) , where c is the total number of tasks to be learned, k is the rate of learning, t is time, and f(t) is the number of tasks learned.
a. Suppose you move to a new school, and you want to learn the names of 25 classmates in your homeroom. If your learning rate for new tasks is 20 % per day, how many complete names will you know after 2 days? After 8 days?
We will know 8 complete names after 2 days and 20 complete names after 8 days.
Here, we are given an exponential function: f(t)= c{1- [tex]e^{-kt}[/tex]}
where f(t) = number of tasks learned.
c = total number of tasks to be learned
k = rate of learning
t = time
Now, when we move to a new school, number of names we need to learn ⇒ c = 25
learning rate for new tasks = 20%
⇒ k = 0.2
and time = 2 days
⇒ t = 2
Substituting these values in the given function we get-
f(2) = 25{1- [tex]e^{-0.2 *2}[/tex]}
= 25{1- [tex]e^{-0.4}[/tex]} [tex]e^{-0.4}[/tex]
= 0.67
Thus, f(2) = 25( 1-0.67 )
f(2) = 25(0.33)
f(2) = 8.25
Thus, we will be able to learn 8 complete names in 2 days.
If t = 8f(8) = 25{1- [tex]e^{-0.2 * 8}[/tex]}
= 25{1- [tex]e^{-1.6}[/tex]}
= 25(1- 0.20)= 25(0.80)
= 20
Thus, we will be able to learn 20 complete names in 8 days.
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Solve 5x-12-6x=-10x+7-1 (please fill out each step)
Step 1. Collect like terms
Step 2.Move variables to one side of the equation (addition/subtraction property of equalities)
Step 3. Move constant to the other side of equation (Addition/subtraction property of equalities)
Step 4.(multiplication/division property of equalities)
5x-12-6x=-10x+7-1
=5x-6x+10x=7-1+12
= 9x=18
=9x/9=18/9
=x=2