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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]

"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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Answer:

13c + 1

Step-by-step explanation:

4c + 2 + 4c + 1 + 2c + 3c - 2

8c + 5c + 3 - 2

13c + 1

Answer:

1. y < -12

2. x > -12

Step-by-step explanation:

Just create a number line with the arrow going towards the direction that the greater/less than symbol is pointing

Answer:

A statistical question

Step-by-step explanation:

A statistical question is a question that can be answered by collecting data that vary. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question.

Answer:

11.4 metres

Step-by-step explanation:

Use Pythagoras theorem for a right-angled triangle

a^2 + b^2 = c^2

if you cut the rectangle in half, it will become a right angled triangle.

a and b are two sides of the rectangle, while c is the diagonal or hypothenuse

so 9^2 + 7^2 = c^2

81 + 49  = c^2

c^ 2 = 130

square root 130 = c

you should get approximately 11.4 metres

Answer:

√(8×32)

√(256)

[tex]16[/tex]

[tex]is \: your \: answer[/tex]

I hope it helps

have a nice day

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Answer:

9√3

Step-by-step explanation:

Answer:

[tex]9\sqrt{3}[/tex]

Step-by-step explanation:

we know that 3*81 = 243, so we can say

[tex]\sqrt[]{3} * \sqrt{81}[/tex]

And we know that square root of 81 = 9

so we can simplify this to:

[tex]9\sqrt{3}[/tex]

Hope this helps!

Answer:

X = 3

Step-by-step explanation:

To solve for x, you can first divide both sides of the equation by 3. The reason you do this is because the left side is being multiplied by 3, so dividing would cancel it out

(3(3 + x) = 15 + x)/3   =  3 + x = 5 + 1/3x

Now, subtract 3 from both sides to isolate x on the left side

x = 2 + 1/3x

Lastly, subtract 1/3x from both sides

2/3x = 2

Now, divide both sides by 2/3 to get x = 3.

Answer:

3x+4

Step-by-step explanation:

3 ft every second is the rate of change or the slope. 4 ft above the ground is the y-intercept.

Answer:

y=3x+4

Step-by-step explanation:

3x is 3 feet multiplied by however many seconds

4 is the additional 4 feet that the balloon had started at

The simplified form of the given algebraic expression is; 96x⁶y⁵

We are given the algebraic problem;

(4x²y)(3xy)(2xy)³

Expanding the above gives us;

4x²y * 3xy * 2³x³y³

⇒ 4x²y * 3xy * 8x³y³

⇒ 96x⁶y⁵

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Answer:

Its 96x6y5 or B)

Step-by-step explanation:

The guy above or below me explained it correctly.

Answer:

-15x - 12 + 9x^2

Step-by-step explanation:

(-7x - 5) - (-9x^2 + 8x + 7)

-7x - 5 + 9x^2 - 8x -7

-15x - 12 +9x^2

what is that 2 by the 9x

We will simplify the given expression to get:

9x^2 - 15x - 12

Here we have the expression:

(-7x - 5) - (-9x^2 + 8x + 7)

To simplify it, we just perform the difference between the polynomials:

-7x - 5 + 9x^2 - 8x - 7

Now we group terms with correspondent powers of x:

9x^2 + (-7x - 8x) + (-5 - 7)

Now we simplify this:

9x^2 - 15x - 12

This is the quadratic equation simplified.

If you want to know more about simplification, you can read:

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Answer:

The correct answers are O The frequency is 5. and O The period is 2π/5

Step-by-step explanation:

I took the quiz and got it right

Answer:

1= 112°

3= 68°

4= 22°

5= 90°

Step-by-step explanation:

comment if u need explanation :)

[tex]tan( \theta) = \frac{opposite}{adjacent} [/tex]

The opposite in this diagram is the side directly opposite to the ange theta.

So,

[tex]tan( \theta) = \frac{17}{17} = 1[/tex]

So the answer is 1.

Answer:

4 1/20

Step-by-step explanation:

1 4/5 - (-2 1/4) You need the closing bracket.

1 4/5 + 2 1/4

Change to improper fractions.

[tex]\frac{5*1 + 4}{5} + \frac{4*2+1}{4}[/tex]

9/5 + 9/4               Change so that both have the same denominator.

[tex]\frac{9*4}{5*4} + \frac{9*5}{4*5}[/tex]

36/20 + 45/20

81/20 which believe it or not is an acceptable answer.

4 1/20  is another acceptable answer

Answer:

Option (1)

Step-by-step explanation:

Sequence has been given as,

[tex]a_n=\frac{n^3+3n}{n^2-6n}[/tex]

[tex]\lim_{n \to \infty}\frac{n^3+3n}{n^2-6n}[/tex]

[tex]=\lim_{n \to \infty}\frac{\frac{n^3+3n}{n^3} }{\frac{n^2-6n}{n^3} }[/tex]

[tex]=\lim_{n \to \infty}\frac{1+\frac{3}{n^2}}{\frac{1}{n}-\frac{6}{n^2} }[/tex]

= ∞

That means with the increase in the value of 'n' sequence gets larger and larger.

Therefore, sequence will diverge.

Option 1 will be the correct option.

Answer:

a-the sequence diverges

Step-by-step explanation:

edg 2023

Using translation concepts, the function whose graph is plotted is given by:

y = 0.5cos(x).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the y-intercept is different of zero, hence it is a cosine function. The amplitude is of 0.5, hence the function is multiplied by 0.5, that is, y = 0.5cos(x), which means that option C is correct.

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Answer:

$ 160

Step-by-step explanation:

3/8 × n = $ 60

so, n = $ 60 ÷ 3/8

= $ 60 × 8/3

= $ 160

so, Mikayla's savings = $ 160

Any number ending with a even number is even

B. 41680

C. 55822

D. 87318

E. 93256

Answers are B, C, D, E

Answer:

y=X+7

Step-by-step explanation:

(-1, 6)

1x up 1 over 1

y=mx+b

--------------------------

Plug 6 for y, and 1 for x.

Like this [tex]6=x (+-)#[/tex]#

We know x is -1. 6=(-1*1)+#

6=-1+#

y=X+7

-------------------

-1*1+7=6

Answer:

a)  0

b) -5

Step-by-step explanation:

We want to find f(x) = -4

This means find the value of x  where y=-4

The value of x  where y=-4 is x=0

Then find f(2)

This means find the value of y when x =2

The value of y when x=2 is -5

Answer:

Step-by-step explanation:

9y+7=2y+98(being vertically opposite angles)

9y-2y=98-7

7y=91

y=91/7

y=13

Answer:

r ≈ 7.18%

Step-by-step explanation:

a = p(1 + r)^n

-----------------------

a = 10000 * 2 = 20000

p = 10000

n = 2035 - 2025 = 10

Plug in the knowns

20000 = 10000(1 + r)^(10)

Divide both sides by 10000

2 = (1 + r)^(10)

Take the log of both sides

log2 = 10 * log(1 + r)

Divide bot sides by 10

(log2)/10 = log(1 + r)

use calculator

0.030102999566398 = log(1 + r)

antilog both sides

10^0.030102999566398 = 1 + r

1.0717734625 = 1 + r

Subtract 1 from both sides

0.0717734625 = r

r ≈ 7.18%

----------------------------------

Alternate method

2 = (1 + r)^(10)

Take 10th root of both sides

1.0717734625 = 1 + r

Subtract 1 from both sides

0.0717734625 = r

r = 7.18%

Answer:

50-32*8

Step-by-step explanation:

Answer:

50-32<8

Step-by-step explanation:

Answer:

the answer is A:)

Step-by-step explanation:

Answer:

diameter = the distance from one edge of the circle, through the center, to the other edge

pi = long irrational number commonly written as 3.14

circle = a 2d shape where all points are the same distance from the center

radius = the distance from the center of a circle to the outer edge

circumference = the length of the outside of a circle or a circle's perimeter

hope that helps