Jen is investigating a quadratic function g(x). She writes four different forms of the function, as shown below. Select the form that reveals the maximum value of g(x) without having to be rewritten.

Answer: 1,4,5

Step-by-step explanation:

The correct options are, The simplified expression for g(f(x)) is x.

The functions are not inverses of each other.

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Given, f(x) = 1/(8x³).

f(x) = 1/(2x)³.

y = 1/(2x)³.

(2x)³ = 1/y.

[tex]2x = \frac{1}{y^\frac{1}{3}}[/tex].

[tex]x = \frac{1}{2y^\frac{1}{3}}[/tex].

[tex]f^{-1}(x) = \frac{1}{2x^\frac{1}{3}}[/tex] and g(x) = [tex]2x^\frac{1}{3}[/tex] so, they are not inverses of each other.

Now, f(g(x)) = [tex]\frac{1}{8((2x)^\frac{1}{3})^3}[/tex].

f(g(x)) = 1/16x.

g(f(x)) = [tex]2(1/8x^3)^\frac{1}{3}[/tex].

g(f(x)) = x

learn more about the inverse of functions here :

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Answer:

María solamente debe venderle al cliente 10 unidades

Step-by-step explanation:

Explicación paso a paso:

Una docena representa un total de doce (12) unidades. Los huevos se empacan por docena, por lo tanto si nos piden solo 5/6 de la docena, multiplicamos dicha fracción por 12 unidades:

5/6 · 12 = (12 · 5)/6 = 60/6 = 10 unidades

Por lo tanto, María solamente debe venderle al cliente 10 unidades, es decir 5/6 representa 10 unidades de los huevos

Usando conceptos de proporción, se encuentra que Martha debe vender 10 huevos al cliente.

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

1 docena - 12 huevos

5/6 de docena - x huevos

Aplicando multiplicación cruzada:

[tex]x = 12 \times \frac{5}{6} = \frac{12 \times 5}{6} = 2 \times 5 = 10[/tex]

Martha debe vender 10 huevos.

A similar problem is given at https://brainly.com/question/23926715

Answer:

The wire is about 18.44 feet long.

Step-by-step explanation:

From the question:

The wire is √340 feet long.

This implies that the length of the wire is √340 feet.

Converting the value of this length (√340) to decimal gives;

√340 = 18.439

Now, let's convert 18.439 to the nearest hundredth of a foot.

18.439 ≅ 18.44

Therefore, the length of the wire to the nearest hundredth of a foot is 18.44 feet.

In other words, the wire is about 18.44 feet long.

Answer:

5 and 3/5

Step-by-step explanation:

sorry if it is wrong

Answer:

1.c

2.e

3.d

3.a

5.b

best of luck!

Answer: Answer is in the steps read carefully

Step-by-step explanation:

1.   y = -3x  It has a slope of -3 and y intercept of 0 so it goes with  C

2.  y =2x+ 5   It has a slope of 2 and y intercept of 5 so it goes with  E

3.  y = 1/2x - 3   It has a slope of 1/2 and y intercept of -3 so it goes with  D

4. y= -1x + 2    It has a slope of -1 and y intercept of 2 so it also goes with A

5. y = 1x   It has a slope of 1 and y intercept of 0 so it goes with  B

Step-by-step explanation:

Yes it is

20 Characters needed but thank me later. Wouldnt mind if you marked me as brainliest

Answer:

1280

Step-by-step explanation:

32x4=128

320x4=1280

Answer:

30-42x

Step-by-step explanation:

Use the distributive property to multiply 6 by 5-7x.

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{30 - 42x}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{6(5 - 7x)}[/tex]

Distribute 6 through the parentheses

[tex] \dashrightarrow{\sf{6 \times 5 - 6 \times 7x}}[/tex]

[tex] \dashrightarrow{ \sf{30 - 42x}}[/tex]

Hope I helped!

Best regards! :D

Answer:

5.4

Step-by-step explanation:

vhtx

It is a difference of squares, so we can factor this to

[tex](x+2)(x-2)=0[/tex]

Then, we can solve for [tex]x[/tex].

[tex]x=-2,2[/tex]

Hope this helps.

頑張って!

Answer:

Actually, this is referring to matrix equations, so it's -3  1  4  2-

Step-by-step explanation:

Hey, so I got this from the comments and wanted it to be a real answer, so please give them lot's of thanks if you can. They are keatonmorehouse0727.

Answer:

The variable X represents:

X = the number of books

The real world situation can be:

1.) Jennie reads books. She reads each books for

2.) Jennie wants to read book at least 5 books today.

Write an inequality that models the minimum number of books that Jennie needs to read.

The inequality for this situation is:

[tex]2x \: \geqslant \: 5[/tex]

Answer:

72 is your answer mate...

Answer:

46.9333 feet per second

Step-by-step explanation:

Answer:

i rthink i understand your question but im not sure- I think you forgot to add a little bit of the question but im pretty sure your question is what  is a parrllel line. IM going to answer that sorry if its wrong but im trying to be helpfull.

Step-by-step explanation:

Parallel lines are two lines that never intersect they start off beside each other and they stay where you can conect them with one line but they will never intercet.

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and

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Answer:

Literally, parallel lines are lines that extend in both directions without meeting.

The three definitions of parallel lines are correct, but Rachel's and Briana's definitions have flaws

Step-by-step explanation:

                            Rachel

The definition implies that two lines are said to be parallel if they are both perpendicular to another line.

This definition is correct, but the definition brings a new concept; it introduces the concept of line transversal.

Because the parallel lines can be defined without introducing the concept of line transversal (which was not part of the required definition), then we can conclude that the definition has a drawback.

                                             Alex

Alex's definition is correct, and it has no drawback because the definition can  be applied to concepts where parallel lines are used.

                                            Briana

Here, Brianna introduced the concept of slopes.

Ideally, parallel lines have the same slope; but the concept is limited to slopes only; and cannot be applied to other concepts such as transversal of lines.

Answer:

Step-by-step explanation:

Plug in 4 for x

2(4) + 5y = 28

8 + 5y = 28 (subtract both sides by 8)

5y = 20 (divide both sides by 5)

y = 4

Answer:

(a) The linear depreciation function of the car which gives the worth of the car y after a number of years, t is given as follows;

y = 25,425 - 2,739 × t

(b) The value of the car 7 years from now is $6,252

(c) $2,739 per year

Step-by-step explanation:

The manufacture's suggested retail price (MSRP) for the car = $25,425

The amount the car is expected to be worth in 5 years = $11,730

(a) The linear depreciation is given as follows;

[tex]Depreciation \ Per \ Year \ = \dfrac{Cost \ of \, Asset - Salvage \ Value}{Life \ of \, Asset \ in \ use}[/tex]

Where;

Cost of Asset = $25,425

Salvage Value = $11,730

Life of Asset in use = 5 years

We get;

[tex]Depreciation \ Per \ Year \ = \dfrac{\$ 25,425 - \$11,730}{5} = \$2,739/year[/tex]

Therefore, the linear depreciation function, can be written as follows;

y - 25,425 = -2,739×(t - 0)

y = -2,739·t + 0 + 25,425 = 25,425 -2,739·t

y = 25,425 - 2,739 × t

Where;

y = The expected worth of the car after a given number of years

t = The number of years used for the calculation of the depreciation

(b) The value of the car 7 years from now is given by substitution as follows;

Whet t = 7, we have;

y = 25,425 -2,739·t = y = 25,425 -2,739 × 7 = $6,252

The value of the car 7 years from now = $6,252

(c) [tex]Depreciation \ Per \ Year \ = \dfrac{\$ 25,425 - \$11,730}{5} = \$2,739/year[/tex]

The car is depreciating at a rate of $2,739 per year.

That is ver very sad

yes,

abcdefghijklmnopqrstuvwxyz

Since the diver is 19 metres below the surface of the water, then he will need to travel 19 metres to reach the surface.

Answer:

Step-by-step explanation:

[tex]d_{FG}=\sqrt{(x_G-x_F)^2+(y_G-y_F)^2}\\\\d_{FG}=\sqrt{(5-2)^2+(16-11)^2}=\sqrt{3^2+4^2}=\sqrt{25}=5[/tex]

Answer:

0.65 x 20 = 13  0.15  x 20 = 3 so 13 + 3 =16  20 - 16 = 4

Step-by-step explanation:

Answer:

[tex]d=\sqrt{218}[/tex]

Step-by-step explanation:

Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Simply plug our coordinates into the distance formula to find the distance between the points:

[tex]d=\sqrt{(3 - (-4))^2+(-7 - 6)^2}[/tex]

[tex]d=\sqrt{(3 +4)^2+(-13)^2}[/tex]

[tex]d=\sqrt{(7)^2+169}[/tex]

[tex]d=\sqrt{49+169}[/tex]

[tex]d=\sqrt{218}[/tex]

Answer:

Step-by-step explanation:

The question lacks appropriate diagram. Find the diagram attached below;

From the diagram GK = GH+HJ+JK

Given GH = GJ-HJ

GH = 2x+2-x

GH = x+2

HJ = x

JK = HK - HJ

JK = 6x-1-x

JK = 5x-1

GK = x+2+x+5x-1

collect like terms

GK = x+x+5x+2-1

GK = 7x+1

Given GK = 24, then;

7x+1 = 24

7x = 24-1

7x= 23

x = 23/7

Since GH =  x+2

GH = 23/7 + 2

GH 23+14/7

GH = 37/7

Also JK = 5x-1

JK = 5(23/7)-1

JK = 115/7 - 1

JK = 115-7/7

JK = 108/7

Answer:

[tex]\frac{x}{2}+5[/tex]

Step-by-step explanation:

[tex]\frac{x+10}{2}[/tex]

To solve, you will have to divide.

[tex]\frac{x}{2}+5[/tex]

Hope this helps!

Answer:

D) -6

Step-by-step explanation: