Yes, the graphs of a power function and its inverse are symmetric about the line y=x.
What is an inverse function?
A function that "undoes" another function is called an inverse. In other words, if f(x) yields y, then y entered into the inverse of f yields the output x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹.
What is a power function?
Any function where y = xⁿ, where n is any real constant integer, is referred to be a power function. In reality, many of our parent functions, including linear and quadratic functions, are power functions.
Here,
The graphs of self-inverse functions are symmetrical about the line y=x. The domain of a one-to-one function f is the same as the range of its inverse f⁻¹ and the range of f is the same as the domain of f⁻¹.
Hence, the graphs of a power function and its inverse are symmetric about the line y=x.
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Write an equation in slope-intercept form of the line shown.
Let's find the slope of the line containing the points (-4,1) and (2, 3).
Answer:
1/3
Step-by-step explanation:
Compute the slope of the line through the following points:
p_1 = (-4, 1) and p_2 = (2, 3)
The slope of the line through (x_1, y_1) and (x_2, y_2) is:
(y_2 - y_1)/(x_2 - x_1)
Substitute (x_1, y_1) = (-4, 1) and (x_2, y_2) = (2, 3):
= (3 - 1)/(2 - -4)
3 - 1 = 2:
= 2/(2 - -4)
-(-4) = 4:
= 2/(2 + 4)
2 + 4 = 6:
= 2/6
The gcd of 2 and 6 is 2, so 2/6 = (2×1)/(2×3) = 2/2×1/3 = 1/3:
Answer: = 1/3
8 more than triple a number is -8
Answer:
8+3x=-8
x=-5 1/3
Step-by-step explanation:
triple a number means to multiply by 3
More than is to add
8+3x=-8
-8. -8
3x=-16
x=-5 1/3
Hopes this helps please mark brainliest
Paragraph on cyclone
Cyclones are cyclic rotating air masses around a low atmospheric pressure center which when viewed from above looks like a circle. It causes heavy rainfall and thunderstorm. The speed of a cyclone often varies between 30 to 50 km which is enough to destroy anything behind its path. It moves clockwise in the southern hemisphere and anticlockwise in the northern hemisphere.
There are two types of cyclones Tropical cyclones and Extratropical cyclones:
Tropical cyclones: Cyclones that develop in the tropics are known as tropical cyclones.Extratropical cyclones: Cyclones that develop behind the tropics are known as extratropical cyclones.There are different names for cyclones in different countries such as:
Typhoons in the China SeaTropical cyclones in the Indian OceanHurricanes in the Caribbean SeaTornadoes in the USAWilly Willies in Northern AustraliaTo know more about Tropical cyclones:
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The function f={(x,y)|y =mx+c} is a. Quadratic function b. Constant function c. Cubic function d. Linear function
⇒The given function is a linear function as we know the general equation of a straight line is y=mx+c
Option d is the answer.
10 A car depreciates in value at 15% per year If the car is bought for £20,000, how much will it be worth in 5 years.
Answer:
£8884.10625
Step-by-step explanation:
15% of £20,000:
20000x15/100=£3000
20000-3000=£17000
15% of £17000:
17000x15/100=£2550
17000-2550=£14450
15% of £14450:
14450x15/100=£2167.5
14450-2167.5=£12282.5
15% of £12282.5:
12282.5x15/100=£1842.375
12282.5-1842.375=£10440.125
15% of £10440.125:
10440.125x15/100=£1556.01875
10440.125-1556.01875=£8884.10625
Since the car loses 15% of it's value each year, it retains 85% of the value.
Value after 1 year = 85% of original value.
Value after 2 years = 85% of value after year 1
Value after 3 years = 85% of value after year 2
and so on...
We could calculate this year by year or we could do a single calculation to obtain the value. We need to take 85% of the original value a total of 5 times, since we're wondering about the value in 5 years.
value after 5 years = 20000(0.85)(0.85)(0.85)(0.85)(0.85)
value after 5 years = 20000(0.85)^5
value after 5 years ≈ 8874.10625
So the value will be 8874.11 pounds in 5 years.
An athlete run at a rate of 309 yd. /min. If one lap i 315 yard how many lap doe he run in 19 minute?
If an athlete runs at a rate of 309 yd. /min. If one lap is 315 yard athlete then athlete covers 18.63 laps in 19 minutes
What is a conversion factor?
A fraction that is equal to "1" is a conversion factor. The numerator and denominator are the same amount, but they are expressed in different units. It is used to change a number's unit of measurement. In order to do that, multiply the initial number by the fraction equal to "1"; this maintains the original number's value but modifies the units.
An athlete run at a rate of 309 yds. /min.
If one lap is 315 yard
Then total number of yards covered by the athlete is 5871.
I.e. 309 x 19 = 5871.
So total laps covered by the athlete in 19 minutes is
[tex]\frac{5871}{315}=18.63[/tex]
Hence, athlete covers 18.63 laps in 19 minutes
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according to a report published by the federal interagency forum on child and family statistics (2015), identify the group of families in which the proportion of children has contracted sharply from 1980 to 2013.
The group of families in which the proportion of children has contracted sharply from 1980 to 2013 is Middle-Income group.
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Its very annoying and I feel like its impossible
Five poitive whole number add up to 47
One of the number i a multiple of 9
The other four number are equal. Work out the reult when the five number are multiplied. Optional working
The multiplication of 5 whole numbers is 16875
Given that
5 positive whole numbers add up to 47
we solve these by using system of equation
let 5 whole numbers be p, q, r, s and t
equation is: p + q + r + s + t = 47
one of the number is a multiple of 9 the other four numbers are equal
let p be the multiple of 9
equation is: p + q + q + q = 47
p + 4q = 47
let's try trial and error method q and p are whole numbers, they cannot be decimal
let p = 9
9 + 4q = 47
4q = 47-9
4q = 38
q = 9.5 it is not whole number, so this is not the number
let p= 18
18 + 4q = 47
4q = 47-18
4q = 29
q = 7.25 it is not whole number, so this is not the number
let p = 27
27 + 4q = 47
4q = 47 -27
4q = 20
q = 5
then multiplication of these 5 whole numbers is
27 * 5*5*5*5 = 27*625=16875
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Johnny has some nickels and dimes in his pocket, and the change is worth $0.75. He has twice as many dimes as nickels. How many of each type of coin does Johnny have?
| BTW this is a system of equations question
The number of each of the coin in Johnny's possession are
Nickel = $0.75Dimes = $1.5How to determine the number of each of the coin Johnny hasInformation from the question
Johnny has some nickels and dimes in his pocket, and the change is worth $0.75
He has twice as many dimes as nickels
The change worth $0.75
Nickels, N - Dimes, D = 0.75
D - N = 0.75
twice as many dimes as nickels
2N = D
N = D / 2
therefore
D - D/2 = 0.75
D/2 = 0.75 = N
D = 1.5
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Select the point that is solution to the system of inequalities.
y x^2-6
A. (0,-2) B. (0,6) C.(1,6) D. (-4,-2)
Please help!
The common shaded zone, as illustrated in the graph attached, will represent the answer to the set of equations. There isn't a common location where the two equations intersect.
Given that,
The system of inequality
y < x² + 2
y > x² - 6
We have to find the common point of the system of inequality.
We know that,
The graph is shown in the image.
Using the graphing technology,
A will be the first equation's vertex (0,2)
The parabola's outer region will be shaded and its boundary will be a dotted line because y is less than the value required by the quadratic equation.
In a similar way, the second equation's vertex, (0,-6), will be a dotted parabola with shaded inner portions.
The common shaded zone, as illustrated in the graph attached, will represent the answer to the set of equations. There isn't a common location where the two equations intersect.
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The function f(x) = 4x + 10 models the amount of money francis makes when babysitting for x hours. How much money will he make for 2 hours of babysitting work?.
The amount of money that he will make for 2 hours of baby sitting work is $18
The function is
f(x) = 4x + 10
The function f(x) is the amount of money Francis makes when babysitting for x hours
The function is the mathematical statement that shows the relationship between one variable and another variable. If one variable is dependent variable then the other variable will independent variable
The function
f(x) = 4x + 10
The number of hours x = 2 hours
Substitute the values of x in the function
f(2) = 4(2) + 10
f(2) = 8 +10
f(2) = $18
Hence, the amount of money that he will make for 2 hours of baby sitting work is $18
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1/4 plus (-1/2) equivalent or non
Solution of 1/4 plus (-1/2) giving the answer in equivalent form of fraction
-1/4 least form of the fraction-2/8 equivalent form of the fractionHow to determine the addition problemThe problem involves addition of fractions
The fractions with different numerators and denominators when compared with another fraction but the same value with the fraction are said to be equivalent fractions.
The fraction required are:
= 1/4 plus (-1/2)
= 1/4 + -1/2
= 1/4 - 1/2
= 1/4 - 2/4
= -1/4
-1/4 is in the least form of the fraction.
The equivalent form is written as
-2/8
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What’s the newer to this??
Answer:point c
Step-by-step explanation:
because point c is three lines down from -1. making -1 and 3/8
Answer:
Point C
Step-by-step explanation:
Because -1 3/8 is negative, it is less than 0.
Point A is eliminated.
Because | -1 3/8 | > | 1 |,
Point B is eliminated.
There are 8 tick marks in between (and including) the integers. Each small unbolded tick mark represents 1/8.
Because 3/8 is 3 times 1/8, count 3 down from -1.
You are left with C.
Simplify the expression to a polynomial in standard form: (x + 1) (2x^2 - 3x - 7)
Answer:
2x^3-x^2-10x-7
Step-by-step explanation:
Distribute x to 2x^2, 3x, and -7
Then, distribute 1 to 2x^2, 3x, and -7
Hope this helps.
:)
Determine the value for k in the equation k-173.54 = 294.57
Answer:
468.11
Step-by-step explanation:
k = 294.57 + 173.54 = 468.11
Answer:
k = 468.11
Step-by-step explanation:
Given equation,
→ k - 173.54 = 294.57
Now the value of k will be,
→ k - 173.54 = 294.57
→ k = 294.57 + 173.54
→ [ k = 468.11 ]
Hence, value of k is 468.11.
y= mx + b
Molly is helping her younger sister run a lemonade stand. They earn $2 for each cup of lemonade they sell.
Write an equation that shows how their total earnings, y, depend on the number of cups sold, x.
Do not include dollar signs in the equation. what does y equal?
The correct equation that shows their total earnings, y, depend on the number of cups sold, x will be;
⇒ y = 2x
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
They earn $2 for each cup of lemonade they sell.
Now,
Let number of cups = x
And, Total earnings = y
Since, They earn $2 for each cup of lemonade they sell.
So, We get;
⇒ y = 2x
Where, x is number of cups and y is total earnings.
Thus, The correct equation that shows their total earnings, y, depend on the number of cups sold, x will be;
⇒ y = 2x
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Balance each of the following equations
Answer:
[tex]2Sb+3I_2=2SbI_3[/tex]
[tex]P_4+3O_2=2P_2O_3[/tex]
[tex]2SO_3=2S+3O_2[/tex]
[tex]2Fe_2O_3+3C=4Fe+3CO_2[/tex]
[tex]CH_4+2O_2=CO_2+2H_2O[/tex]
Step-by-step explanation:
Each side of the equations need to have the same number of each element.
Equation 1
Since there are 2 I on one side of equation 1, and 3 on the other side, I will do the following:
[tex]Sb+3I_2=2SbI_3[/tex]
Now the number of Sb is unbalanced, so I balance it like so:
[tex]2Sb+3I_2=2SbI_3[/tex]
Equation 2
Using the same strategy, I focus on one element at a time. I can balance the P like this:
[tex]P_4+O_2=2P_2O_3[/tex]
Now, I can balance the O. There are 6 on the right, so if I put 3 on the left, there will be 6 there as well!
[tex]P_4+3O_2=2P_2O_3[/tex]
Equation 3
Starting with O this time, I put 2 on the left and 3 on the right to bring them both to 6.
[tex]2SO_3=S+3O_2[/tex]
Now there are 2S on the left and only 1 on the right, so I balance it:
[tex]2SO_3=2S+3O_2[/tex]
Equation 4
Starting with O again, there are 3 on the left and 2 on the right.
[tex]2Fe_2O_3+C=Fe+3CO_2[/tex]
Now, the Fe are unbalanced as well. There are 4 on the left and 1 on the right:
[tex]2Fe_2O_3+C=4Fe+3CO_2[/tex]
Finally, balance the C, there is 1 on the left and 3 on the right.
[tex]2Fe_2O_3+3C=4Fe+3CO_2[/tex]
Equation 5
This one is pretty hard to read, so I will assume that the equation looks like this (please comment if this is incorrect)
[tex]CH_4+O_2=CO_2+H_2O[/tex]
Let's balance the H first:
[tex]CH_4+O_2=CO_2+2H_2O[/tex]
Now the O. There are 2 on the left and 4 on the right.
[tex]CH_4+2O_2=CO_2+2H_2O[/tex]
In a ale, the cot of a coat i reduced from $85 to $67. 50. Calculate the percentage reduction in the cot of the coat
The percentage reduction in the cost of the coat is 20.58 %
As given,
Cost of coat = $ 85
Price in sale= $ 67.50
Reduced price =$ 85 - $ 67.50= $ 17.5
Therefore to find the percentage reduction in the cost of the coat
% Reduction = (Reduced price / original price) x 100
= ( 17.5 / 85 ) x 100
= 20.58 %
Hence, the percentage reduction in the cost of the coat is 20.58 %
The percentage reduction formula is a mathematical tool that helps determine how much of a substance can be removed from a sample. This formula can be used to calculate the percentage of a substance that can be removed from a sample if the starting concentration and the ending concentration are known.
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Si tuviera 4 huevos y un ladrón me lleva 3 y el gallo que tengo pone 5 cuántos huevos tengo.
Tengo un total de 3 huevos en la última.
Los rompecabezas también son una excelente manera de pensar fuera de la caja. Resolver acertijos fortalece las conexiones entre las células cerebrales y forma nuevas células cerebrales, mejorando así la memoria. Resolver acertijos es una excelente manera de mejorar tu memoria a corto plazo.
Este acertijo viral debe leerse con atención. Su primer pensamiento podría ser que este es un problema matemático simple.
Si tuviera cuatro huevos
Un ladrón me da 3 huevos,
Mi gallo de granja pone 5 huevos,
¿Cuántos huevos tengo?
La explicación lógica de este acertijo es "Para empezar, el acertijo dice 'Si tuviera 4 huevos', pero este es solo un escenario y no tenías ningún huevo en primer lugar. Así que eso es 0 huevos.
Entonces el ladrón te dio 3 huevos.
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A contractor purchases 6 dozen pairs of padded work gloves for $89.28. incorrectly calculates the unit price as $14.88 per pair for the expense report. What is the correct unit price?
Answer:
It is about $0.07 per pair for the expense report.
Step-by-step explanation:
You have to divide 89.28 by 6 to get the unit price. 89.28/6=0.06720430107 or about $0.07. Hope this helps! I am up doing math too -_-. Please don't mark me brainliest, I just love to help.
If CP=590 and profit=75, find SP
Answer:
Sp=cp+p
sp=590+75
sp=625
A bag contains 30 red marbles and 15 purple marbles. Mr. Clark wants to add 270 marbles to the bag. He wants the ratio of red to purple marbles to remain the same. How many of each should he add? A. 70 red marbles 200 purple marbles B. 200 red marbles and 70 purple marbles C. 180 purple marbles and 90 red marbles D. 180 red marbles and 90 purple marbles
Answer: 20 PURPLE marbels
Step-by-step explanation:
no explanation
Answer:
the is 200 purple marbles 70 red marbles
the diameter of a circle is 10 yards. find the approximate circumference for the circle, using 3.14 for pie.
Answer:
31.4 yards
Step-by-step explanation:
Formula for circumference is C = π*d
10*3.14
31.4 yards
Hope this helps!
Answer:
[tex] \sf C = 31.4 \: yards[/tex]
Step-by-step explanation:
The formula to find the circumference of a circle is :
[tex] \sf \: C = \pi \: d[/tex]
Here,
d --> Diameter ---> 10 yards
Let us find it now.
[tex]\sf \: C = \pi \: d \\ \sf \: C = 3.14 \: \times 10 \\ \sf \: C = 31.4 \: yards[/tex]
I have no idea how to do this. Please help.
Answer:
None
Step-by-step explanation:
In order to solve an inequality you must isolate x on one side, so begin bringing the numbers from one side to another to make x the subject.
(numbers change their sign when brought to the other side)
5 > - 6 - 2x
5 + 6 > - 2x
11 ÷ - 2 > x
-5.5 < x (the sign switches when you divide or multiply by a negative number)
The solution is -5.5, which means none of the values provided are the solution.
PLEASE HELP ME WITH THIS!!!
The composite figure has an area of 205 square feet
How to determine the area of a composite figure
In this question we find the composite figure formed by two right triangles and two rectangles, whose total area is the sum of the areas of the two right right triangles and two rectangles. Then, the area formula is shown below:
A = Σ A' + Σ A''
Where:
A - Total area, in square feet.A' - Total area of the two rectangles, in square feet.A'' - Total area of the two right triangles, in square feet.The area formulas for right triangles and rectangles:
Right triangles
A = 0.5 · b · h
Where:
b - Base, in feet.h - Height, in feet.Rectangles
A = b · h
Now we proceed to calculate the area of the composite figure:
A = 0.5 · (13 ft) · (20 ft) + 0.5 · (11 ft) · (4 ft) + (4 ft) · (8 ft) + (7 ft) · (3 ft)
A = 130 ft² + 22 ft² + 32 ft² + 21 ft²
A = 130 ft² + 75 ft²
A = 205 ft²
The area of the composite figure is equal to 205 square feet.
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f(x) = x^2. What is g(x)?
If the function f(x) = [tex]x^2[/tex], then the function g(x) = [tex]-x^2-2[/tex]
From the given graph
The function is
f(x) = [tex]x^2[/tex]
The function is the rule the shows the relationship between one variable and another variable. If one variable is independent variable and another variable will be dependent variable. We can also says that the it show the relationship between input and output of the function
We can see that the function g(x) is the reflection of the function f(x) at y = -2
The reflection of f(x) = - f(x)
= - [tex]x^2[/tex]
The reflection of f(x) at y = -2 is
f(x) = [tex]-x^2-2[/tex]
Then the function g(x) = [tex]-x^2-2[/tex]
Hence, If the function f(x) = [tex]x^2[/tex], then the function g(x) = [tex]-x^2-2[/tex]
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pls guys i need help whats 1 + 1
Answer:
2
Step-by-step explanation:
Answer: 1 + 1 is two!
Step-by-step explanation:
We know this because, we can count our fingers. Your pointer finger and your index finger put together is a total of two fingers!
There are other ways to do simple addition, but I find counting fingers the easiest!
Hope this helped you! Have a great day :)
please answer fast and a explanation would be nice but doesn’t have to be there
The inequality in the slope-intercept form is y≥(3x/7)+3 when the graph is in of a linear inequality.
What is meant by slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent slope; the reason for this usage is unclear, but it can be found in O'Brien's (1844)[2] and Todhunter's formulations of the equation for a straight line as y = mx + b and y = mx + c, respectively.
Let the linear equation be
y=m x +c
From the graph the lines are passing through the points (-7,0), (0,3)
Slope m =(3-0)/(0+7)
m=3/7
c=y-intercept
Therefore, c=3
Substitute the values in the above equation.
y=(-3/7)x+3
7y=3x+21
But, here we need to use the inequality which satisfies the shaded region.
Let us consider the point (1,2)
7(2)=3(1)+21
14=24 (But 14≠24)
Therefore, 14≥24
So, we have to use ≥ sign
7y≥3x+21
y≥(3x/7)+3
The inequality in the slope-intercept form is,
y≥(3x/7)+3
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