The inverse of the function for [tex]g^{}(x) = \frac{x^{3} }{8}+16[/tex] is [tex]g^{-1}(x)=2\sqrt[3]{x-6}[/tex]
What is inverse of the function?"The inverse function of a function f (also called the inverse of 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]f^{-1}[/tex]."
We have
[tex]g^{}(x) = \frac{x^{3} }{8}+16[/tex]
Replace g(x) with y
[tex]y =[/tex] [tex]\frac{x^{3} }{8}+16[/tex]
Interchange the variables
[tex]x= \frac{y^{3} }{8}+16[/tex]
Rewrite the equation as
[tex]\frac{y^{3} }{8}+16= x[/tex]
⇒[tex]\frac{y^{3} }{8}= x-16[/tex]
Multiply both sides of the equation by 8
[tex]8.\frac{y^{3} }{8}=8(x-16)[/tex]
⇒[tex]{y^{3} }=8(x-16)[/tex]
⇒[tex]{y^{3} }=8x-128[/tex]
⇒[tex]{y} }=\sqrt[3]{8x-128}[/tex]
⇒[tex]{y} }=2\sqrt[3]{x-6}[/tex]
Replace y with [tex]g^{-1}(x)[/tex]
⇒[tex]g^{-1}(x)=2\sqrt[3]{x-6}[/tex]
Hence, The inverse of the function for [tex]g^{}(x) = \frac{x^{3} }{8}+16[/tex] is [tex]g^{-1}(x)=2\sqrt[3]{x-6}[/tex]
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What percentage would my grade be if I got a 50% on a project that is worth 20% of my grade and my grade is 87%/B+.
How much would my grade go down?
PLEASE HELP ME
Answer:
you got 21.5/50 on final grade
and aslo follow me for more information
Dinner at olive garden cost $52.37. You Leave a 20% tip, What is the total cost
Answer:
62.84
Step-by-step explanation:
52.37 times 1.20(how you calculate tip) =62.84
Answer:
$62.84
Step-by-step explanation:
Tip is $10.47 add that with 52.37
If you want to leave a 20% tip, multiply the cost by 0.20 to get the tip amount or multiply the cost by 1.20 to get the total including tip.
8 x 9/3= x 1/3
What number makes the equation true?
Answer:
72
Step-by-step explanation:
3×(8×9/3=X1/3) then 8×9=X, then X=72
Please help me and show working. I have a test very soon.
Answer:
c = 3
Step-by-step explanation:
Given
[tex]\frac{2}{c-2}[/tex] - [tex]\frac{3}{c+2}[/tex] = [tex]\frac{7}{c^2-4}[/tex] ← factor the difference of squares
[tex]\frac{2}{c-2}[/tex] - [tex]\frac{3}{c+2}[/tex] = [tex]\frac{7}{(c-2)(c+2)}[/tex]
Multiply through by (c - 2)(c + 2) to clear the fractions
2(c + 2) - 3(c - 2) = 7 ← distribute and simplify left side
2c + 4 - 3c + 6 = 7
- c + 10 = 7 ( subtract 10 from both sides )
- c = - 3 ( multiply both sides by - 1 )
c = 3
Please help:)
this worth 100 POINTS!!
Answer:
I think the second answer
Step-by-step explanation:
I'm late but it's the second answer!
Henry's Pizza sells pizza by the slice for lunch. An employee recorded how many slices of each type of pizza were sold today.
onion 4
pepperoni 36
cheese 20
supreme 6
veggie 16
What is the experimental probability that the first slice sold during lunch tomorrow will be a slice of cheese pizza?
24% (24/100)
Got answer by adding all of them together and dividing by 20
Answer:
10/41
Step-by-step explanation:
what is the unit rate of 2250 pencils in 18 boxes
Answer:
184
Step-by-step explanation:
i did it this on a test a while back
Answer: 125 Pencils per Box
Step-by-step explanation:
This is a fraction equal to
2250 Pencils ÷ 18 Boxes
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 18
2250 Pencils ÷ 18
18 Boxes ÷ 18
=
125 Pencils
1 Box
=
125 Pencils
Box
= 125 Pencils per Box
HELLP PLZ ZZZZZZ FOR MY HOMEWORK......
Answer:
4 books
Step-by-step explanation:
$3.80 divided by 95cents = 4
You have 30 minutes to exercise at the gym. The Stairmaster burns 7 calories per minute, while the stationary bike burns 12 calories per minute. You want to burn 290 calories total using both machines. How much time should you spend on each machine?
Answer:
14 min on Stairmaster
16 min on Bike
Step-by-step explanation:
s = time on Stairmaster
b = time on bike
System of Equations:
s + b = 30
7s + 12b = 290
let 's' = 30-b
Substitution Method:
7(30-b) + 12b = 290
210 - 7b + 12b = 290
5b + 210 = 290
5b = 80
b = 16
s + 16 = 30
s = 14
SOMEONE PLEASE HELP !!
Answer:
you would have to add them together
Step-by-step explanation:
you add 9pi cm^2 to 1/4
hop this helps kid
Answer:
The radius is 199.85 cm^3
Consider the equation:
X^2-6 = 2 – 18x
1) Rewrite the equation by completing the square
2) What are the solutions to the equation?
The equation should be rewritten by completing the square as x² + 18x + (18/2)² = 8 + (18/2)².
The solutions to the equation is x = -9 + √89 or x = -9 - √89.
What is a quadratic equation?In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Next, we would solve the given quadratic equation by using the completing the square method;
x² - 6 = 2 - 18x
x² + 18x = 8
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
x² + 18x + (18/2)² = 8 + (18/2)²
x² + 18x + 81 = 8 + 81
Part 2.
x² + 18x + 81 = 89
x² + 9x + 9x + 81 = 89
x(x + 9) + 9(x + 9) = 89
(x + 9)(x + 9) = 89
x = -9 + √89 or x = -9 - √89.
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Use the distance formula to find the distance to the nearest tenth, from R17, -2) to W(-2, 3).
Answer:
17.7
Step-by-step explanation:
I'm assuming you meant R(17, -2) to W(-2, 3). Here the x-coordinate changes by 17 - (-2), or 19, and the y-coordinate by 5. Think of these as the legs of a right triangle. The distance between these points is the length of the hypotenuse of this triangle: d = √(5^2 + 17^2)
or √314, which, to the nearest tenth is 17.7.
Find the rate of change from the table.
==================================================
We're asked to find the slope:
m = slope
m = (y2-y1)/(x2-x1)
m = (50-20)/(4-2)
m = 30/2
m = 15
The rate of change is 15. Each time x goes up by 1, y increases by 15.
slope = rise/run = 15/1
rise = 15, run = 1
I used the middle two columns of the table, but you could use any two columns you want. I subtracted the y values together to get the change in y, which is the rise. The change in x, aka run, is the difference in x values. You must subtract the values in the same order. If done in the wrong order, you might get -15 as the incorrect answer.
Look at the two right rectangular prisms.
1 ft
Ift
1 ft
2 ft
2.5 ft
What is the volume of solid in cube feet
Answer:
I cannot tell you the answer because there isn't adequate information.
But to calculate the volume of a rectangular prism, simply multiple the length width, and height (LWH)
EASY MATH PLEASE HELP! NO LINKS! NEED COMPLETE EXPLAINATION WITH ANSWER!!
Answer: a.) 18 x 8
Step-by-step explanation: if you break down the equation 6^3= 18 and 4^2=8 then take 18x8 simple as that
Someone please help I’ll give brainliest!!!!
Answer:
move the line up one
Step-by-step explanation:
What is the equation, in standard form, of a circle with center (−5, 8) and radius 5?
Enter your answer by filling in the boxes.
Answer:
( x + 5 )² + ( y - 8 )² = 25
Step-by-step explanation:
Standard form for the equation of a circle - ( x - h )² + ( y - k )² = r²
Where r = radius and Center is located at ( h , k )
We are given that the center is at ( -5 , 8 )
Thus, h = -5 and k = 8
We are also given that the radius = 5
Thus, r = 5
Now we just plug all of the given values into the standard form equation
( x - (-5))² + ( y - 8 )² = 5²
*simplify*
in - ( - 5 ) the two negative sign cancel out and it turns into + 5
5² = 25
Thus, the equation is ( x + 5 )² + ( y - 8 )² = 25
please help me please
Many schools have a regular outdoor school one day a week.
At Mosby, they often walk 125 meters from the school to the mountain top Jonsberget (140 masl) which is located directly behind the school.
How high is the school above sea level?
Answer:
The final outcome impact of the Civil War was that the North had won the war and slavery was abolished. The impact of the Civil War was the evolution of new war weapons and changes in the economy and the way people lived.The final outcome impact of the Civil War was that the North had won the war and slavery was abolished. The impact of the Civil War was the evolution of new war weapons and changes in the economy and the way people lived.
Step-by-step explanation:
If the mass of a metal bar which is 3.25 m long is 15 kg. Find its mass per meter
Step-by-step explanation:
If 3.25m is equal to 15kg then what about 1m?
3.25m = 15kg
1m =?
Then by cross multiplication we get 4.615 kg
A type of fish for your aquarium costs $8 each. You can spend at most $48. How many of these fish can you buy? Write an inequality to model the problem. Then solve the inequality to find the number of fish.
Answer:
x ≤ 6
Step-by-step explanation:
Cost of fish = $8
You can spend at most $48
How many of these fish can you buy?
Let
x = number of fishes you can buy
The inequality is
8x ≤ 48
Divide both sides by 8
x ≤ 48/8
x ≤ 6
1
What is the solution to the equation 4
1 7 1
8 8*3*?
X=-5
X=-4
X=4
x=5
Answer:
im sorry
Step-by-step explanation:
i need points or else i fail
simply 3x to the power of 2 of over 9x to the power of 5
Answer:
1/6561x³ or 6561x⁻³
Step-by-step explanation:
(3x)²/(9x)⁵
(3²)(x²)/(9⁵)(x⁵)
9x²/59049x⁵
9/59049x³
1/6561x³ or 6561x⁻³
If there are 4 outcomes, what is the
probability that I get tails then tails?
Answer:
50%
Step-by-step explanation:
because it is a two side coin
A polynomial has zeros x = 2, x = 0, X = 1, X = 2
What is the polynomial in factored form?
A) f(x) = x(x - 2)(x + 1)(x + 2)
B) f(x) = x(x + 2)(x-1)(x + 2)
C) f(x) = x2(x + 2)(x - 1)(x - 2)
D) f(x) = x(x + 2)(x - 1)(x - 2)
Answer:
f(x)= x(x+2)(x-1)(x-2)
Step-by-step explanation:
before taking the zeros each zeros were in the forrm
x+a=0 where 'a' is any number
then after taking the zeros, the zeros were in the form x=0 x=2 x=1
so we are gonna take then back to the form before taking the zeros
PLEASE HELP DUE TODAYY
Answer:
y <= 0
Step-by-step explanation:
it's shaded when the value of y is 0 or below 0 (the vertical axis)
What is the slope of the line that passes through the points (-1, 2) and (-4, 3)?
Answer:
-0.5
Step-by-step explanation:
(3-2)=1
(-4-1)=-5
1÷(-5)= -0.5
9.
Find the slope of the line.
A. -1/4
B. 4
C. 1/4
D. -4
Answer:
9. A. -1/4
Step-by-step explanation:
Plug the points into the equation y2-y1/x2-x1. In this case, I chose the points (0,-2) and (4,-3). This would make the equation -3--2/4-0. This would be equal to -3+2/4 or -1/4. Therefore, the slope is -1/4.
If this has helped you please mark as brainliest
Answer:
A. -1/4
Step-by-step explanation:
PLEASE ANSWER PLEASE! I
Answer:
4.45454545455
=4.45
Step-by-step explanation:
so yeah your right just put a bar under 45 like this,,,,
4.45
a 420$ dressed is 20% off, how much is the sales price?
Answer:
$336
Step-by-step explanation:
420 x 0.2 = 84
420 - 84 = 336
Answer:
the answer is going to be $336