Answer:
Step-by-step explanation:
Given is a function
[tex]f(x) =(x-2)^2[/tex]
This function is a parabola with vertex at (2,0) and axis of symmetry is x=2
Hence for x<2 the curve would be reflection of x>2
To get inverse we must get one to one funciton only.
So restrict the domain of f(x) to [tex][2,∞)[/tex]
Then we have f(x) as one to one with domain x≥2 and range is R+
[tex]f^{-1} (x)=+\sqrt{x} +2[/tex]
For this inverse domain is R+ and range is [tex][2,∞)[/tex]
Answer:
restriction of domain is x>=2
[tex]f^{-1}=\sqrt{x}+2[/tex]
Step-by-step explanation:
Restrict the domain of the function [tex]f(x)=(x-2)^2[/tex] so it has an inverse
To restrict the domain we find the vertex
VErtex form of the equation is
[tex]y=(x-h)^2+k[/tex] vertex is (h,k). restriction of domain is x>=h
[tex]f(x)=(x-2)^2+0[/tex] , vertex is (2,0)
So restriction of domain is x>=2
now we find inverse function
[tex]f(x)=(x-2)^2[/tex]
Replace f(x) with y
[tex]y=(x-2)^2[/tex]
Replace x with y and y with x
[tex]x=(y-2)^2[/tex]
To remove square we take square root on both sides
[tex]\sqrt{x} =y-2[/tex]
Add 2 on both sides
[tex]\sqrt{x}+2 =y[/tex]
[tex]f^{-1}=\sqrt{x}+2[/tex]
how do u do this one?
Answer: 200 messages
========================================================
Check out https://brainly.com/question/11754609 for a similar problem
Plan A's cost equation is y = 0.10x + 30
Plan B's cost equation is y = 50
Equate the two right hand sides, then solve for x
0.10x + 30 = 50
0.10x = 50-30
0.10x = 20
x = 20/0.10
x = 200
If you send/receive 200 messages, then the two plans will both cost the same ($50) per month.
Tossing coins imagine tossing a fair coin 3 times. (a) what is the sample space for this chance process? (b) what is the assignment of probabilities to outcomes in this sample space?
Answer:
We are given that a fair coin is tossed 3 times.
We know that if a fair coin is tossed 3 times, then there are 8 possible outcomes.
(a) what is the sample space for this chance process?
The sample space associated with tossing a fair coin three times are:
Ω = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Where:
H denotes the head and T denotes the tail.
(b) what is the assignment of probabilities to outcomes in this sample space?
We are given that a fair coin is tossed 3 times, which means that all the possible outcomes in the above mentioned sample space has equal chance being selected. Therefore, the assignment of probabilities to outcomes in this sample space is same for all outcomes and is given below:
[tex]p= \frac{1}{8}[/tex]
The price of a smart watch is $109.99 and the sales tax is 6.5%. What is the total cost of the smart watch? Enter your answer in the box.
if you know any other answer on quiz plz give them itll be appreciated greatly :)
A solution to an equation is a number when substituted back into the original equation produces a what statement
Answer:
true statement
Step-by-step explanation:
Substituting a solution back into the original equation will make the equation true.
Write a linear function for the line represented by the point-slope equation
y −4 = 3 (x − 4)
Must show your work to receive full credit.
Answer:
f(x) = 3x-8
Step-by-step explanation:
y −4 = 3 (x − 4)
We want to write the equation in y = mx+ b form
Distribute the 3
y-4 = 3x -3*4
y-4 = 3x -12
Add 4 to each side
y -4+4 = 3x-12+4
y = 3x-8
Since the want it in function form, f(x)
f(x) = 3x-8
PLEASE ANSWER THIS QUESTION !! 30 POINTS AND BRAINLIEST TO THE FIRST PERSON!
Answer:
x<=11
Step-by-step explanation:
2(x-3 ) <= 16
Distribute the 2
2x -6 <= 16
Add 6 to each side
2x -6+6<= 16+6
2x <= 22
Divide by 2
2x/2 <= 22/2
x<=11
Officer Brimberry wrote 24 tickets for traffic violations last week, but only 21 tickets this week. What is the percent decrease? Give your answer to the nearest tenth of a percent.
Answer:3 percent because
Answer:
Percent = 62.5%
Step-by-step explanation:
Which number is written in scientific notation?
A) 7.8 x 10^-5
B) 3.4 x 100^2
C) 0.84 x 10^6
D) -5 x 10^-12
Answer:
I would say A. 7.8 x 10^-5
Step-by-step explanation:
7.8 x 10^-5 can also be written as 7.8 times 10 to the negative fifth power or the exponent of negative five. But, if you solve it you would get 0.000078 as the real number.
A salesperson at a clothing store earns a commission of 2.5% on all the sales he makes. Which inequalities represent the sales, s, in dollars, he needs to make to earn a commission of more than $100
Answer:
Option A is correct.
Inequality represents the sale s in dollars:
[tex]0.025s\geq 100[/tex]
[tex]s> 4000[/tex]
Step-by-step explanation:
Let s represents the sales in dollars.
Given :A salesperson at a clothing store earns a commission of 2.5% on all the sales he makes.
Earns a Commission = 2.5% of s = [tex]\frac{2.5}{100} \times s = \frac{25s}{1000} = 0.025s[/tex]
It is also given that he needs to make to earn a commission of more than $100
then, we have an inequality:
[tex]0.025s\geq 100[/tex]
divide both sides by 0.025 we get;
[tex]s> 4000[/tex]
Therefore, an inequality represents the sales in dollar ; [tex]0.025s\geq 100[/tex] or [tex]s> 4000[/tex]
Answer:
s > 4,000, s > 4,000
Step-by-step explanation:
Since he needs to make $100 the choices that give him $100 or more are correct.
Identify the value of p. Give your answers in simplest radical form. HELP PLEASE!!
Answer:
C
Step-by-step explanation:
using the cosine ratio to find p
cos 45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{p}[/tex]
cross- multiplying gives
p × cos45° = 6 → [ cos 45° = [tex]\frac{1}{\sqrt{2} }[/tex]]
p × [tex]\frac{1}{\sqrt{2} }[/tex] = 6
multiply both sides by [tex]\sqrt{2}[/tex]
⇒ p = 6[tex]\sqrt{2}[/tex] ( third option on list )
To determine the value of p in simplest radical form, solve the equation by simplifying the denominator and taking the square root of both sides. The value of p is 2.
Explanation:To identify the value of p, we need to solve the equation and simplify it to the simplest radical form. Let's start by simplifying the denominator and expressing it as a perfect square.
Next, we can take the square root of both sides of the equation to eliminate the square. This will help us isolate p. Once we do that, we can solve for p by getting rid of the square root on the left side of the equation. After simplifying, we find that p = 2.
So, the value of p is 2.
How much pizza will each person get if 4 people share 3 4 of a pizza equally? A) 1 3 B) 1 4 C) 1 6 D) 3 16
If the length of one base of a trapezoid is 5, the length of the other base is 2x + 7, and the length of the midsegment is 6x – 24, what is the value of x? Show equations and all work that leads to your answer.
Answer:
x = 6
Step-by-step explanation:
The midsegment of a trapezoid is the line parallel to the parallel sides of the trapezoid, which connects the midpoints of the non-parallel sides.
The length of the midsegment of the trapezoid is half the sum of the length of the parallel sides.
i.e,
Length of the midsegment = (1/2) *(Length of base1 + Length of base2)
6x - 24 = (1/2) * (5 + 2x + 7)
12x - 48 = 2x + 12
10x = 60
x=6
∴ x = 6
Combine and simplify these radicals. square root of 3 times the square root of 16
Answer:
[tex]\sqrt{3} * /sqrt{16} = 4\sqrt{3}[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:
square root of 3 times the square root of 16 looks like this
[tex]\sqrt{3} .\sqrt{16}[/tex]
we try to break the numbers inside the radical to there prime factors
so
[tex]\sqrt{3} .\sqrt{2.2.2.2}[/tex]
the prime factors which are in pair , comes out of the radical so
[tex]\sqrt{3} .2.2[/tex]
which simplifies to
[tex]4\sqrt{3}[/tex]
can someone PLEASE HELP ME ASAP
Answer: The correct answer for number 1. is 11
help please 15 points
Answer:
its called line FGH
Step-by-step explanation:
its because the line is FGH
Hope this helps :)
A line is named by two of the points on the line, with a line drawn above the letters.
For the line in the attached image, the answer would be the first choice.
PLEASE HELP! 100 POINTS! WILL GIVE BRAINLIESTT!
Your local shoe store anticipated giving away 2,500 pairs of shoes in one month, but they only sold 2,215 pairs of shoes. What was the approximate percent error? Show your work to find the percent error.
Answer:
= 11.4%
Step-by-step explanation:
Percent error = (target - actual)/target * 100
target = 2500
actual = 2215
Lets substitute in
Percent error = (2500-2215)/2500 * 100
= 285/2500*100
=.114 * 100
= 11.4%
Answer:
11.4%
Step-by-step explanation:
Translate the graph according to the rule (x, y) → (x – 2, y). The first graph goes with the question.
Look at the picture.
(x, y) → (x + 2, y)
Translate the graph of f(x) 2 units right.
-------------------------------------------------------------
(x, y) → (x, y + n) - translate the graph n units up
(x, y) → (x, y - n) - translate the graph n units down
(x, y) → (x - n, y) - translate the graph n units left
(x, y) → (x + n, y) - translate the graph n units right
Which ordered pair COULD represent point P on the graph?
A) (2, 6)
B) (-3, 6)
C) (-2, -5)
D) (3, -5)
Answer:
the answer is d
Step-by-step explanation:
you can tell because it's past 2 and close to 3. it's -5 because it's past -4. so their is your answer to why it's d
The ordered pair that represents point P on the graph is **D) (3, -5)**. Point P lies in the fourth quadrant, where both the x-coordinate (3) and the y-coordinate (-5) are positive.
The ordered pair that could represent point P on the graph is **D) (3, -5)**. Point P is located in the fourth quadrant where both x and y coordinates are positive. The graph shows a Cartesian plane with axes labelled and scaled. Point P appears to be close to coordinates (3, -5), indicating it's located at a positive distance along the x-axis and a negative distance along the y-axis.The directions on a sewing pattern say to cut an extra 15% of fabric to account for error. Chloe needs 0.75 yard of frantic to make a skirt, and she cuts 0.1125 yard. Did Chloe cut the right amount of fabric?
Answer:
Yes she did
Step-by-step explanation:
There is .75 yards and she cut .1125 of it, it make it 15% as .75 x .15 = .1125
The coldest surface temperature on the moon is 57 degrees colder than twice the coldest surface on Earth. What is the coldest surface temperature on Earth if the coldest temperature on the moon is -116 degrees?
Answer:
Step-by-step explanation:
Answer:
The problem can not be solved since information is missing.
The coldest surface temperature of the moon needs to be given in the text.
THIS IS THE ACTUAL ANSWER
NO JOKE
A contaminant is found in a solution at a level of 3/500%. What fraction of the solution is this
Answer:3/5
Step-by-step explanation:
First we change 500% to fractions
Changing percentage to fraction is dividing the number by 100
500% = 500/100
Putting this we get 3/(500/100)
Then when a number is being divided by a fraction, to get the answer, we multiply the number by the inverse of the fraction
3/(500/100) = 3 x 100/500 = 300/500 = 3/5
If contaminant is found in a solution at a level of 3/500%. Then 3/5 is fraction of the solution
What is Fraction?A fraction represents a part of a whole.
Given,
A contaminant is found in a solution at a level of 3/500%
Let us convert five hundred percentage to a fraction.
500% is converted to fraction by dividing 500/100
So let us divide three by 500/100
3/ (500/100)
When a fraction is divided with another fraction, then the denominator is multiplied inversely with numerator
3×100/500
=300/500
3/5
Hence if contaminant is found in a solution at a level of 3/500%. Then 3/5 is fraction of the solution
To learn more on Fractions click:
https://brainly.com/question/10354322
#SPJ2
Kasia wants to create a triangle with angles measuring 37 degrees, 62 degrees, and 81 degrees. She says that only one unique triangle is possible given these angle measures. Which statement about Kasia’s claim is true?
Kasia is incorrect. Since the angles sum to 180 degrees and no side lengths are given, multiple triangles can be drawn with these angle measures.
Kasia is incorrect. No triangle can be made with these angle measures because they do not sum to 180 degrees.
Kasia is correct. Since the angles sum to 180 degrees and no measurements are given, only one unique triangle is possible.
Kasia is correct. Since the angles do not sum to 180 degrees, only one unique triangle is possible.
Answer:
option: A is correct
Step-by-step explanation:
kaisa's claim is incorrect. clearly the sum of the three angles is 180 degrees therefore we could easily create a triangle with the help of this information but we can't say that this traingle will be unique so we need to know some more information regarding its side.hence multiple triangles could be drawn with these angle measures.
hence option A is correct.
Answer:
A
Step-by-step explanation:
Which of this fraction are greater then1/2 but less then 3/4 .7/8 .2/5 .1/3 .5/8 .3/6
Answer: 7/8
Step-by-step explanation:
think of each faction as a pie or pizza.
each one will have the number of slices as the bottom number of the fraction.
now shade in the top numbers and see if it more than your 1/2
you will see 7/8 is the answer since it will be one piece left from being complete or "gone"
hope this helped angel!!
A certain type of bacteria increases continuously at a rate proportional to the number present. if there are 500 present at a given time and 1,000 present 2 hours later, how many hours (from the initial given time) will it take for the numbers to be 2,500
The number of hours from the initial given time that will take for the bacteria to grow to 2500 number is 4.64 hours approx.
How to calculate the instantaneous rate of growth of a function?Suppose that a function is defined as;
[tex]y = f(x)[/tex]
Then, suppose that we want to know the instantaneous rate of the growth of the function with respect to the change in x, then its instantaneous rate is given as:
[tex]\dfrac{dy}{dx} = \dfrac{d(f(x))}{dx}[/tex]
Assuming that the bacterial growth can be approximated by a continous and differentiable function y = f(x), where x represents the number of hours spent from the initial time, we're given that:
[tex]\dfrac{dy}{dx} \propto y[/tex]Supposing the proportionality constant be k, then we get:
[tex]\dfrac{dy}{dx} = ky[/tex]
Solving this differential equation, we get:
[tex]\dfrac{dy}{y} = kdx\\\\\text{Integrating both the sides without limits}\\\\\int \dfrac{dy}{y} = \int x dx\\\\\ln(y) + \ln(c) = kx\\\\\ln(yc) =kx\\ yc = e^{kx}\\y = \dfrac{e^{kx}}{c}[/tex]
where ln(c) represents the integration constant. (we took ln(c) because, firstly, ln's range is whole real number (which gives us the access to use it as integration constant), and secondly that it can merge with ln(y) to simplify the work)
Since we're given that:
At x = t (for some value of t in hours), we're given that y = 500,
and for x = t+2, y = 1000,
so we get two equations as:
[tex]\\500 = \dfrac{e^{kt}}{c}\\\\1000 = \dfrac{e^{k(t+2)}}{c}\\[/tex]
Thus, we get:
[tex]\dfrac{e^{kt}}{500} = \dfrac{e^{k(t+2)}}{1000} \\\\kt = \ln(0.5) + k(t+2)\\\\k = \dfrac{-\ln(0.5)}{2}} \approx 0.3465[/tex]
Thus, we get:
[tex]\\500 = \dfrac{e^{kt}}{c} \\\\c = \dfrac{e^{0.3465t}}{500}[/tex]
Thus, we get:
[tex]y = \dfrac{e^{0.3465x}}{\dfrac{e^{0.3465t}}{500}} = 500e^{0.3465(x-t)[/tex]
Let from the initial given time t, it takes h hours more for bacterias to be 2500, then we get:
[tex]2500 = 500 \times e^{0.3465 (t+h - t)}\\0.3465(h) = \ln(5)\\\\h = \dfrac{\ln(5)}{0.3465} = 4.644 \: \rm hours \: approx.[/tex]
Thus, the number of hours from the initial given time that will take for the bacteria to grow to 2500 number is 4.64 hours approx.
Learn more about differential equations here:
https://brainly.com/question/14658115
Determine which of the given numbers are roots of the polynomial f(x)=6x^2+x-1.
A. 1/2, 1
B. -1/2, 2
C. -1/2
D. 1
Answer:
Step-by-step explanation:
factor the trinomial: (3x-1)(2x+1)=0
x = 1/3 or -1/2
In △ABC, AD and BE are the angle bisectors of ∠A and ∠B and DE ║ AB . Find the length of DE if perimeter of ABDE is 30 cm and AB = 12 cm
Answer:
DE = 6 cm
Step-by-step explanation:
Let DE = x cm.
Since DE is parallel to AB therefore by the alternate interior angles theorem, m∠BAD = m∠ADE and m∠ABE = m∠DEB ............(1)
As AD is an angle bisector of ∠A, therefore m∠EAD = m∠DAB ; Since BE is an angle bisector of ∠B ⇒ m∠ABE = m∠EBD.
Therefore, from (1) We get , m∠EAD = m∠ADE and m∠EBD = m∠BED.
So, the triangles ADE and EDB are then isosceles with AE = ED and ED = DB.
So AE = DE = DB = x, and since the perimeter of ABDE is 30 cm, then
12 + x + x + x = 30
⇒ 12 + 3x = 30
⇒ x = 6
Hence, the length of DE is 6 cm.
Answer:
DE=6cm
Step-by-step explanation:
Let x=DE, since AB║DE, therefore ∠BAD=∠ADE and ∠ABE=∠BED. (1)
Also, we are given that AD is the angle bisector of ∠A and BE is the angle bisector of ∠B,
Therefore, ∠EAD=∠DAB and ∠ABE=∠EBD (2)
From (1) and (2), ∠EAD=∠ADE and ∠EBD=∠BED
⇒The ΔADE and ΔEDB then becomes the isosceles triangle with AE=Ed and ED=DB (Sides opposite to equal angles are always equal)
Therefore, AE=DE=DB=x
We are given that the perimeter of ABDE is 30 cm, therefore,
Perimeter of ABDE= sum of all the sides of ABDE
⇒30=AB+BD+DE+AE
⇒30=12+3x
⇒30-12=3x
⇒x=6cm
Therefore, the length of DE= 6cm
A bond purchased at $500.00 now has a value of $650.00 what is the percent increase of its value?
Answer: A bond purchased at $500.00 now has a value of $650.00 what is the percent increase of its value?
To make it simple for you, the final ANSWER is a 30% increase, due to the fact that taking $500.00 and multiplying that by 0.3 gives you 150, which you add on to 500, giving you 650. Hope that helps!
Answer: The required percent increase in the bond's value is 30%.
Step-by-step explanation: Given that a bond purchased at $500.00 now has a value of $650.00.
We are to find the percent increase of the value of bond.
According to the given information, we have
Purchasing value of the bond = $500.00
and
present value of the bond = $650.00.
So, increase in the value of the bond = $(650.00 - 500.00) = $150.00.
Therefore, the percent increase of the bond's value is given by
[tex]\dfrac{150.00}{500.00}\times 100\%=\dfrac{3}{10}\times 100\%=30\%.[/tex]
Thus, the required percent increase in the bond's value is 30%.
Fill in the value of the function, when the input is 2: y = −4 + 2
Answer:
y=-6
Step-by-step explanation:
y=-4(2)+2
y=-8+2
y=-6
(2,-6)
Answer:
y = - 6
Step-by-step explanation: You have to substitute 2 for x in order for you to get your solution.
y = - 4x + 2
y = - 4(2) + 2
y = - 8 + 2
y = - 6
Remember, a negative times a positive, becomes a negativeHope this helps you!!! :)
What is the length of the midsegment of the trapezoid made by the vertices A(0, 5), B(3, 3), C(5, -2) and D(-1, 2). Show equations and all work that leads to your answer.
Answer:
[tex]\frac{3\sqrt{13} }{2}[/tex]
Step-by-step explanation:
First we have to identify the parallel sides of the trapezium.
We know that the slopes are equal for parallel lines.
Slope of (x₁,y₁) and (x₂,y₂) is given by
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Slope of AB:
[tex]m_{AB} = \frac{3-5}{3-0}=-\frac{2}{3}[/tex]
Slope of BC:
[tex]m_{BC} = \frac{-2-3}{5-3}=-\frac{5}{2}[/tex]
Slope of CD:
[tex]m_{CD} = \frac{2+2}{-1-5}=-\frac{4}{6}=-\frac{2}{3}[/tex]
Slope of DA:
[tex]m_{DA} = \frac{2-5}{-1-0}=3[/tex]
We see that the slopes of AB and CD are equal, so, AB and CD are the parallel sides.
The length of the midsegment = (1/2)*(length of base1 + length of base2 )
Length of the bases can be calculated using distance formula,
[tex]d= \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
AB = [tex]\sqrt{(3-0)^{2}+(3-5)^{2}}= \sqrt{9+4} =\sqrt{13}[/tex]
CD = [tex]\sqrt{(-1-5)^{2}+(2+2)^{2}}= \sqrt{36+16} =\sqrt{52}=2 \sqrt{13}[/tex]
Length of the midsegment = (1/2) (√13 + 2√13) =3√13/2
Use the domain and range of each of the following relations to determine which is a function.
A. {3,7,-7,9}
B. { (3,9), (7,-4), (-7,7) }
C. { (3,9), (7,-4), (-7,7) }
D. { (3,9), (7,-4), (7,6), (-7,7) }
Answer:
B
Step-by-step explanation:
i took a test with this question
We want to see which one of the given relations is a function.
The correct options are:
B and C.
To see this, we first need to define what a function is.
A function is a relationship that maps elements from one set, the domain, into another set, the range.
Such that each element in the domain can be mapped into only one element on the range.
The standard notation to these relations is (x, y).
This means that x, from the domain, is being mapped into y, from the range.
Now let's analyze the given options:
A) {3,7,-7,9}
This is just a set of values, no relation there, so this is not a function.
B) { (3,9), (7,-4), (-7,7) }
Here we have a relation, and we can see that each element on the domain is being mapped into only one element from the range, so this is a function.
C) { (3,9), (7,-4), (-7,7) }
This is the exact same set as the one on B.
D) { (3,9), (7,-4), (7,6), (-7,7) }
Here we can see that the element x = 7 is mapped into two different values, so this is not a function.
Then the options that represent functions are B and C.
If you want to learn more, you can read:
https://brainly.com/question/21426493