Answers
The inverse of the function f(x) = 8√x for x > 0 is g(x) = x^2/64.
To find the inverse of the function f(x) = 8√x for x > 0, we need to interchange the roles of x and y and solve for y.
Let's start by rewriting the function using y instead of f(x):
y = 8√x
Next, we'll swap x and y:
x = 8√y
To isolate y, we can square both sides:
[tex]x^2 = (8\sqrt y)^2\\\\x^2 = 64y[/tex]
Now, divide both sides by 64:
[tex]x^2/64 = y[/tex]
Simplifying further:
[tex]y = x^2/64[/tex]
Therefore, the inverse of the function f(x) = 8√x for x > 0 is given by [tex]g(x) = x^2/64.[/tex]
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Related Questions
Cora arrived at school at 7:55 am She left for 1 hour for a doctors appointment. She was dismissed from school at 3:15 pm. How long was Cora at school?
Answers
A principal of $400 is invested in an account at 6% per year compounded annually. What is the total amount of money in the account after 5 years? A. $526.00 B. $531.37 C. $535.29 D. $520.00
Answers
[tex]e = b \times (1 + \frac{i}{100} ) {}^{n} [/tex]
In this formula:
e represents the outcome
b represents the money at the beginning
i represents the interest rate
n represents the number of years.
Filling in this formula, we get:
[tex]e = 400 \times (1 + \frac{6}{100}) {}^{5} [/tex]
[tex]e = 400 \times 1.06 {}^{5} [/tex]
[tex]e = 535.29[/tex]
Therefore the answer is C. $535.29
The total amount of money in the account after 5 years is $535.29.
To calculate the total amount of money in the account after 5 years, we can use the compound interest formula: [tex]A = P{(1 + r/n)}^{(nt)[/tex], where A is the total amount, P is the principal, r is the annual interest rate, n is the number of times compounded per year, and t is the number of years.
Given that the principal is $400, the annual interest rate is 6%, and the compounding is done annually, we have:
A = 400(1 + 0.06/1)^(1*5) = 400(1.06)^5 = 400 * 1.338225 = $535.29
Therefore, the total amount of money in the account after 5 years is $535.29.
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A recipe calls for 1/4 cup of flour.Carter only a measurement cup that holds 1/8 cup. How can carter measure the flour he needs for his recipe
Answers
⅛ + ⅛ = ¼
Answer:
Carter can measure the flour he needs for his recipe by filling his measurement cup twice.
Step-by-step explanation:
Since Carter has a smaller cup, he would have to fill his cup a number of times until the sum of the number of cups he has fill repeatedly adds up to the recipe requirement.
The number of times Carter would have to measure his cup with flour to get the recipe call may be computed by dividing the recipe call amount with the size of Carter's measurement cup
= 1/4 ÷ 1/8
= 1/4 × 8/1
= 2
7. Given the vertices of ∆ABC are A (2,-5), B (-4,6) and C (3,1), find the vertices following each of the transformations FROM THE ORIGINAL vertices: a. Rx = 3 b. T<3,-6> c. r(90◦, o)
Answers
Rx = 3
in this reflection, the image has been reflected along the x = 3 line. then all the points on the image are reflected along this vertical line. the distance between each point and the vertical line is noted and by that same distance its moved to the opposite side of the vertical line, while the y coordinates stay the same.
A(2,-5)- x coordinate is 2, its 1 unit away from x=3, it should move by 1 unit to the other side of x = 3, then x = 4. y stays as it is.
A' - (4,-5)
B(-4,6) - distance from x = 3, is (-4-+3) is seven units, moves by 7 units to the other side
B' (10,6)
C(3,1) = distance from 3 = 0, therefore the point stays at is,
C' (3,1)
Q2)
next is a translation, in translation the size nor shape changes, each point in the original image moves the same distance in the same direction.
T (3,-6) (x,y) = this means that the x coordinates move by +3 points to the right and y coordinates move downwards by 6 units
A (2,-5) ---> (2+3,-5-6)
A' (5,-11)
B (-4,6) ---> (-4+3,6-6)
B' (-1,0)
C (3,1) ---> (3 + 3, 1-6)
C' (6,-5)
Q3)
r(90°,0)
this is a rotation done in the clockwise direction. then the image takes a rotation to the right direction around the origin.
then the x, y coordinates of the preimage become ;
(x,y) = (y,-x)
A(2,-5) --> A' = (-5,-2)
B(-4,6) ---> B' = (6,4)
C(3,1) ---> C' = (1,-3)
What is the measure of AC ? (First Picture)
Enter your answer in the box.
What is the measure of BC ? (Second Picture)
Enter your answer in the box.
Answers
Answer:
Part 1) [tex]arc\ AC=33\°[/tex]
Part 2) [tex]arc\ BC=130\°[/tex]
Step-by-step explanation:
Part 1) What is the measure of AC ?
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m<ABC=\frac{1}{2}(arc\ AC)[/tex]
substitute the values and solve for x
[tex]2.5x+4=\frac{1}{2}(7x-2)[/tex]
[tex]5x+8=(7x-2)[/tex]
[tex]7x-5x=8+2[/tex]
[tex]2x=10[/tex]
[tex]x=5\°[/tex]
Find the measure of arc AC
[tex]arc\ AC=7x-2=7(5)-2=33\°[/tex]
Part 2) What is the measure of BC ?
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m<BDC=\frac{1}{2}(arc\ BC)[/tex]
substitute the values
[tex]65\°=\frac{1}{2}(arc\ BC)[/tex]
[tex]2*65\°=(arc\ BC)[/tex]
[tex]arc\ BC=130\°[/tex]
A rectangular deck
is 12 ft by 14 ft. When the length and width are increased by the same amount very becomes 280 squares ft. By how much were the dimensions increased ?
Answers
The other response seems more complex so probably ignore mine. I probably misinterpreted the question.
Original width: 12 ft. New width x + 12.
New area:
[tex] A = LW [/tex] or [tex] LW = A [/tex]
[tex] (x + 14)(x + 12) = 280 [/tex]
[tex] x^2 + 14x + 12x + 168 = 280 [/tex]
[tex] x^2 + 26x - 112 = 0 [/tex]
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-26 \pm \sqrt{26^2 - 4(1)(-112)}}{2(1)} [/tex]
[tex] x = \dfrac{-26 \pm \sqrt{676 + 448}}{2} [/tex]
[tex] x = \dfrac{-26 \pm \sqrt{1124}}{2} [/tex]
[tex] x = \dfrac{-26 \pm 2\sqrt{281}}{2} [/tex]
[tex] x = -13 \pm \sqrt{281} [/tex]
[tex] x \approx -29.76 [/tex] or [tex] x \approx 3.76 [/tex]
We discard the negative answer.
Answer:
Exact:
[tex] (-13 + \sqrt{281})~ ft [/tex]
Approximate:
[tex] 3.76 ~ft [/tex]
Use the quadratic formula to solve 9x2 + 6x – 17 = 0.
Answers
Answer:
The person that answered “C” is completely wrong. The answer is D. Mark me brainliest after you get the answer right :)
Step-by-step explanation:
What is the sum of 2 numbers is 100 and their difference is 6?
Answers
x -y = 6
Adding these equations gives
2x = 106
x = 53
y = 53 -6 = 47
The numbers are 47 and 53.
What is the solution of the equation (x – 5)2 + 3(x – 5) + 9 = 0? Use u substitution and the quadratic formula to solve.
Answers
x² - 10x + 25 + 3x - 15 + 9 = 0
x² - 7x - 16 = 0
[tex]x = \frac{7 + \sqrt{(-7)^2-4(1)(-16)} }{2} [/tex] or [tex]x = \frac{7 - \sqrt{(-7)^2-4(1)(-16)} }{2} [/tex]
[tex] x = \frac{7 + 3i \sqrt{3} }{2} [/tex] or [tex] x = \frac{7 - 3i \sqrt{3} }{2} [/tex]
(Answer B)
Answer: [tex]x=\frac{7\pm 3i\sqrt{3}}{2}[/tex]
Explanation:
Since, given quadratic function, [tex](x-5)^2 + 3(x-5) + 9 = 0[/tex] -----(1)
let us consider,[tex]x-5=p[/tex] -----(2)
Put this value in equation (1),
We get, [tex]p^2+3 p+9=0[/tex], which is also a quadratic equation.
Since, quadratic formula for finding the root of quadratic equation of type [tex]ax^2+bx+c=0[/tex] is, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}} {2a}[/tex]
Here, a=1, b=3 and c=9, so, [tex]p=\frac{-3\pm\sqrt{3^2-4\times1 \times9}} {2\times1}[/tex]
Thus, [tex]p=\frac{-3\pm3\sqrt{-3}} {2}[/tex] ⇒ [tex]p=\frac{-3\pm3i\sqrt{3}} {2}[/tex] (because √-1=i)
Now, from equation(2) [tex]x-5=\frac{-3\pm3i\sqrt{3}} {2}[/tex]
⇒[tex]x=\frac{-3\pm3i\sqrt{3}} {2}+5=\frac{7\pm 3i\sqrt{3}}{2}[/tex]
⇒[tex]x=\frac{7\pm 3i\sqrt{3}}{2}[/tex]
Jennifer recorded the temperature of water samples and the time it took 50g of salt to dissolve in the samples. Jennifer's data models a direct variation. Which table contains Jennifer's data?
Answers
80°32
83°33.2
84°33.6
90°36
Answer:
The answer is C.
Step-by-step explanation:
I know that its c because i literatly just tried it and it said corect it was on USA. test prep
If p is a true statement and q is false then p V q is true
Answers
Answer:
Step-by-step explanation:
True
Which ordered pair (a, b) is a solution to the given system?
Answers
(3,1) means that a = 3 and b = 1
Plug in a = 3 and b = 1 into the first equation
2a - 5b = 1
2*3 - 5*1 = 1.... replace 'a' with 3, replace b with 1
6 - 5 = 1
1 = 1
we get a true equation, so we have confirmed the first equation
Do the same for the second equation
3a+5b = 14
3*3+5*1 = 14 .... replace 'a' with 3, replace b with 1
9+5 = 14
14 = 14
we get a true equation, so the second equation has been confirmed
Both equations are true when (a,b) = (3,1). So the answer (3,1) has been confirmed fully
In 1992, only 275 people owned cellphones in Metropolis. Each year, cell phone use has continuously grown by 82%. How many cellphone users were there in 2000?
Answers
y = A (b) ^ t
Where,
y: number of people with cell phones
A: initial number of people with cell phones
b: growth rate
t: time
Substituting values:
y = 275 * (1.82) ^ t
For the year 2000 we have t = 8.
Substituting:
y = 275 * (1.82) ^ 8
y = 33105.77794
nearest whole integer:
y = 33105
Answer:
there were 33105 cellphone users in 2000
what should you do first to simplify the expression (43 + 9) ÷ 76 + 5
Answers
You should always find the value inside the parenthesis first when simplifying an equation.
Tell me if you need help solving the equation!
Hope this helps!
expression (43 + 9) ÷ 76 + 5
43+9 =52 52 ÷ 76 + 5
The price of a 250 dollar coat increased 7% last year. The coat is now on sale for one half off. What is the sale price?
Answers
Tamara says that raising the number i to any integer power results in either -1 or 1 as the result, since i^2 = -1. Do you agreed or disagree with Tamera? Explain
Answers
Tamara's claim that raising the complex number i to any integer power results in either -1 or 1 is incorrect. The powers of i follow a cyclic pattern which includes i, -1, -i, and 1.
Explanation:I must disagree with Tamara's statement that raising the complex number i to any integer power results in either -1 or 1. The powers of i actually follow a recurring pattern: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1, and then the pattern repeats.
For i to the power of 1, the result is just i itself.For i to the power of 2 (i^2), the result is indeed -1.For i to the power of 3 (i^3), the result is -i.For i to the power of 4 (i^4), the result is back to positive 1.So, while -1 and 1 are indeed in the sequence of results, they're not the only possibilities. Specifically, -i and i are also possible results of raising i to an integer power.
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A rectangular note card has a perimeter of 18 inches and an area of 20 square inches. What are the dimensions of the note card?
Answers
4 x 5 = 20
5 + 5 + 4 + 4 = 18
hope I helped (:
find all the zeros for each function.
p(x)=2x^3-3x^2+3x-2
*show work*
Answers
A graph of p(x) shows it has one real zero, at x=1. Dividing that out (and dividing out the scale factor of 2) reveals the remaining factor to be
.. (x -1/4)^2 +15/16
When we set this to zero, we have
.. (x -1/4)^2 +15/16 = 0
.. (x -1/4)^2 = -15/16
.. x -1/4 = i√(15/16)
and the remaining roots are
.. x = 1/4 ±i√(15/16)
.. x = (1 ±i√15)/4
The zeros are x = 1, x = (1 ±i√15)/4.
_____
You could use synthetic or long division to find
.. p(x)/(x -1) = 2x^2 -x +2
and then use any of several methods to determine the zeros of this are
.. x = (1 ±i√15)/4
The firing of a Revolutionary War cannon is used to open the local Fourth of July festivities. The muzzle of the cannon barrel is 6 feet above ground level. The height of the cannon ball being fired from the Revolutionary War cannon as a function of elapsed time is modeled by the function h(t) = –16t2 + 75t + 6, where h(t) is the height of the cannon ball in feet, and t is the elapsed time since firing in seconds. Determine at approximately what elapsed time(s) the cannon ball will be at a height of 55 feet.
Answers
[tex]-16t^2 + 75t + 6=55\\-16t^2+75t-49=0. \text{ Computing the discriminant:}\\75^2-4(-16)(-49)=2489.\text{ So by quadratic formula we get the sol:}\\\dfrac{-75-\sqrt{2489}}{-32}=3.9\text{ seconds.}[/tex]
Can someone check my answers?
1. Simplify the sum or difference.
sqrt 5 + 6 sqrt 5
A) 6 sqrt 5
B) 30
C) 6 sqrt 10
D) 7 sqrt 5
2. Simplify the sum or difference.
4 sqrt 2 - 7 sqrt 2
A) negative sqrt 6
B) -3 sqrt 2
C) -11 sqrt 2
D) 11 sqrt 2
3. Simplify the sum or difference.
3 sqrt 7 - sqrt 63
A) -2 sqrt 7
B) -6 sqrt 7
C) -4 sqrt 3
D) 0
4. Simplify the sum or difference.
-6 sqrt 10 + 5 sqrt 90
A) 9 sqrt 10
B) -9 sqrt 10
C) -39 sqrt 10
D) -10
5. Simplify the product.
sqrt 6 (sqrt 2 + sqrt 3)
A) sqrt 8 + 3
B) sqrt 30
C) 2 sqrt 3 + 3 sqrt 2
D) 4 sqrt 2 + 3
Answers
2. 4sqrt2 - 7sqrt2 = (4-7)sqrt5 = -3sqrt2 (answer is B)
3. 3sqrt7 - sqrt63 = 3sqrt7 - sqrt7 * sqrt9 = 3sqrt7 - 3sqrt7 = 0 (answer is D)
4. -6sqrt10 + 5sqrt90 = -6sqrt10 + 5*(sqrt10 * sqrt9) = -6sqrt10 + 5*(3sqrt10)
= -6sqrt10 + 15sqrt10 = 9sqrt10 (answer is A)
5. sqrt6*(sqrt 2 + sqrt 3) = sqrt12 + sqrt18 = 2sqrt3 + 3sqrt2 (answer is D)
1 - D
2 - B
3 - D
4 - A
5 - C
6 - A
7 - D
8 - B
9 - B
10 - C
i just took the "Operations with Radical Expressions practice" for WA connexus, these answers are 100 percent correct
Is 11p-7q polynomial
Answers
Specifically, it is a "polynomial EXPRESSION" ; but not a "polynomial equation" ; because it is not an "equation.
There are more than one variables/variable expressions, so it is a polynomial.
Find the area of the triangle that has a base of 4.2 mm and a height of 1.5 mm.
Answers
I hope this helps
Brian deposited $4000 into an account with 5.4% interest, compounded monthly. Assuming that no withdrawals are made, how much will he have in the account after 6 years?
Answers
FV=p(1+r/100n)^nt
where:
FV=future value
p=principle
r=rate
n=terms
t=time
thus substituting our values in the formula we get:
FV=4000(1+5.4/1200)^(6×12)
FV=$5,526.57
Answer: $5,526.57
Bc¯¯¯¯¯ is parallel to de¯¯¯¯¯. what is ab? enter your answer in the box.
Answers
What is the sum of the first eight terms of the series?
(−600)+(−300)+(−150)+(−75)+(−37.5)+...
Round the answer to two decimal places.
−1200.50
−1195.31
−1190.63
−1181.25
Answers
7 cakes cost £5.60 , what would be the cost of:
10 cakes
5 cakes
12 cakes
Answers
so 10 cake costs 10×0.8=£8
5cake costs 5×0.8=£4
12 cake costs 12×0.8=£9.6
10 cakes: £0.8×10=£8
5 cakes: £0.8×5=£4
12 cakes: £0.8 ×12=£9.6
Ramon spends 2/5 of his monthly income on rent ,1/5 of his income on utilities and 3/4 of the amount remaining on food and recreation.He saves 193.50 a month,What is Ramon’s monthly income?
Answers
Then:
Rent: [tex] \frac{2}{5} x[/tex]
Utilities: [tex] \frac{1}{5} x[/tex]
Food and Recreation: [tex] \frac{3}{4}(x-( \frac{2}{5} x+\frac{1}{5} x))= \frac{3}{10} x[/tex]
Now adding all the expenses: [tex] \frac{2}{5} x+ \frac{1}{5} x+ \frac{3}{10} x= \frac{9}{10} x[/tex]
We see that the expenses are 90% of the income, so the savings must be 10% of the income.
[tex] \frac{1}{10} x=193.5[/tex]
x=1935.0 this is your income
Hope this helps...
helpppppppppppppppppppppppppp
Answers
perimeter = 6 + 3√2 ft
Explanation:
The triangle given is an isosceles right-angled triangle.
This means that two of its legs are equal = 3 ft
Now, we will get the length of the third leg which is the hypotenuse using the Pythagorean theorem as follows:
(third leg)^2 = (3)^2 + (3)^2
(third leg)^2 = 18
third leg = sqrt(18) = 3√2 ft
Finally, we will get the perimeter as follows:
perimeter = 3 + 3 + 3√2
perimeter = 6 + 3√2 ft
Hope this helps :)
The probability that a bakery has demand for 2 3 4 or 5 birthday cakes on any given day are 0.32, 0.24, 0.25 and 0.19 respectively. construct a probability distribution for this data
Answers
On the horizontal axis, put your 4 different categories of 2, 3, 4, or 5.
On the vertical axis, label it by the percents: 0.10, 0.20, 0.30, 0.40
Then, make a bar at the correct height for each category.
There are many penguins on a hill. 53 penguins waddled off the hill. Now 21 penguins remain on the hill. How many penguins were on the hill to start?
74 penguins
72 penguins
32 penguins
34 penguins
Answers
Answer:
74 Penguins
Step-by-step explanation:
1. 53+21
2. =74
Penguins are my favorite animal. What's yours?
Answer:
There were originally 74 penguins on the hill.
Step 1: Determine the Values we NeedFor starters, we need to define the variable that we will use to solve this equation. I will use x.
We know that our original amount is x, and we need to find it to solve the problem.
The Factsx stands for the original amount of penguins on the hill.53 penguins waddle off of the hill.21 penguins remain after the 53 penguins waddle off of the hill.To find x, we will set up an algebraic equation that allows us to find the value easily.
Step 2: Set up the Algebraic EquationNow, we will need to set up the equation with the facts we have determined.
We know that we need to set our equation equal to x to find our total. To do this, we know that our initial amount is x, and we remove 53 penguins from this total since they waddle off of the hill.
Since we "remove" from the total, this means that we will subtract 53 penguins from x, our initial amount. We are left with the 21 penguins that do not leave the hill, or otherwise, remain on the hill.
[tex]x - 53 = 21[/tex]
Step 3: Rearrange and Solve the EquationFinally, we are ready to solve the equation to find our initial amount of penguins.
To solve this equation, we must combine our like terms.
Because our numbers (constants) do not have any letters (variables) attached to them, we will combine them.
The main goal of an algebraic equation is to get the variable (in this case, x) by itself. To do this, we can perform reverse operations to get the constants together.
You'll notice that 21 does not have a sign associated with it, but 53 does, and it is a subtraction symbol.
The reverse operation of subtraction is addition. Therefore, to combine the two values, we can add both 53 and 21 to each other to find x.
[tex]x = 53 + 21[/tex]
Using any method of choice, add the two values together.
[tex]x = 53 + 21 = 74[/tex]
Then, to simplify, remove the operation and only leave the sum of the operation.
[tex]\boxed{x = 74}[/tex]
Therefore, the initial number of penguins—the number of penguins on the hill to start—is equivalent to 74 penguins.
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