Consider the function and its inverse.
f(x) = x2 + 4 and f-1(x) = -x - 4
When comparing the functions using the equations, which conclusion can be made?
The domain of f(x) is restricted to x 20, and the domain of f'(x) is restricted to x2 0.
The domain of f(x) is restricted to x 20, and the domain off(x) is restricted to xs 0.
O The domain of f(x) is restricted to x s 0, and the domain off'(x) is restricted to x2 4.
O The domain of f(x) is restricted to x s 0, and the domain off'(x) is restricted to x s 4.

Answer:

2

Step-by-step explanation:

f(x)= 2x^5-3x^3+2x^2+1

Let x=1

f(1)= 2(1)^5-3(1)^3+2(1)^2+1

    = 2*1 -3*1+2(1) +1

     = 2-3+2+1

     2

[tex] \tt{if \: \: f(x) = 2 {x}^{5} - 3{x}^{3} + 2 {x}^{2} + 1 \: \: then \: \: f(1) = ?}[/tex]

[tex]\quad \quad \quad \quad \tt{f(x) = 2 {x}^{5} - 3 {x}^{3} + 2 {x}^{2} + 1}[/tex]

[tex]\quad \quad \quad \quad \tt{f(x) = 2 {(1)}^{5} - 3 {(1)}^{3} + 2 {(1)}^{2} + 1}[/tex]

[tex]\quad \quad \quad \quad \tt{f(x) = 2 (1) - 3 (1) + 2 (1) + 1}[/tex]

[tex]\quad \quad \quad \quad \tt{f(x) = 2 - 3 + 2 + 1}[/tex]

[tex]\quad \quad \quad \quad \tt{f(x) = 2 - 3 +3}[/tex]

[tex]\quad \quad \quad \quad \tt{f(x) = 2 \: \: \cancel{ \color{red}- 3 +3}}[/tex]

[tex]\quad \quad \quad \quad \tt{f(x) = 2 }[/tex]

________

#LetsStudy

1234567890233572o7o5y345uo22u.3936584643728284/43794729237932972478864966666666666666666666666666666666663870434573428734907 goood luck!

[tex]\longrightarrow{\green{A.\:5.5 \: n - \frac{1}{2} \: p - 2}}[/tex] ✔

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]1 + 4.25 \: n + \frac{3}{2} \: p - 3 + ( - 2 \: p) + \frac{5}{4} \: n [/tex]

Combining like terms, we have

[tex] = 4.25 \: n + \frac{5}{4} \: n + \frac{3}{2} \: p - 2 \: p + 1 - 3 \\ \\= 4.25 \: n + 1.25 \: n + 1.5 \: p - 2 \: p - 2 \\\\ = 5.5 \: n - 0.5 \: p - 2 \\ \\ = 5.5 \: n - \frac{1}{2} \: p - 2[/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Answer:

below

Step-by-step explanation:

that is the procedure above

Answer:

The volume of the cylinder is defined by the expression .

[tex]V=\pi (x+8)^2 (2x+3) or V=\pi (2x^3 + 35x^2 + 176x +192)[/tex]

The volume of the cylinder where the radius is r = ( x + 8 ) and height is h = ( 2x + 3 ) is given by the expression V = π ( 2x³ + 35x² + 176x + 192 ) units³

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the volume of the cylinder be V

Now , the radius of the cylinder is r = ( x + 8 ) units

The height of the cylinder is h = ( 2x + 3 ) units

And , Volume of Cylinder = πr²h

On simplifying , we get

The volume of cylinder V = π ( x + 8 )² ( 2x + 3 ) units³

The volume of cylinder V = π ( x² + 16x + 64 ) ( 2x + 3 )

The volume of cylinder V = π ( 2x³ + 35x² + 176x + 192 ) units³

Hence , the volume of cylinder is V = π ( 2x³ + 35x² + 176x + 192 ) units³

To learn more about cylinder click :

https://brainly.com/question/16134180

#SPJ7

Answer:

Each student gets 1.75 ft of ribbon

Step-by-step explanation:

r × 4 = 7

First, divide the given factor by itself in order to get the variable by itself.

4 ÷ 4

Next, divide the product by the given factor bc what you do to the left, you must do to other side.

7 ÷ 4

Last, right down your new equation and find you solution.

New Equation: r = 1.75

Answer:

Step-by-step explanation:

Step-by-step explanation:

[tex] \frac{642}{3} \\ [/tex]

Answer:

[tex]214[/tex]

Step-by-step explanation:

[tex] = 642 \div 3 \\ = 214[/tex]

Given:

The equation is:

[tex]\dfrac{x}{y}=\dfrac{2}{9}[/tex]

To find:

The constant of proportionality.

Solution:

If y is directly proportional to x, then

[tex]y\propto x[/tex]

[tex]y=kx[/tex]                        ...(i)

Where, k is the constant of proportionality.

We have,

[tex]\dfrac{x}{y}=\dfrac{2}{9}[/tex]

On cross multiplication, we get

[tex]9x=2y[/tex]

Divide both sides by 2.

[tex]\dfrac{9}{2}x=y[/tex]

Interchange the sides.

[tex]y=\dfrac{9}{2}x[/tex]                ...(ii)

On comparing (i) and (ii), we get

[tex]k=\dfrac{9}{2}[/tex]

The constant of proportionality is [tex]\dfrac{9}{2}[/tex]. Therefore, the correct option is B.

Answer:

y = 2x + 14

Step-by-step explanation:

Hope this helps!!!

First, you have to find the slope by using

In other words,

The slope is 2.

Then you plug the rest into point-slope form (you can use either of the points, I used the first one)

Remember that m is the slope.

Distribute the slope to the parenthesis

Isolate the y variable

Answer:

2x+14

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [ 3, 4 ] , then

f(b) = f(4) = - 1 ← from table

f(a) = f(3) = - 5 ← from table , then

average rate of change = [tex]\frac{-1-(-5)}{4-3}[/tex] = [tex]\frac{-1+5}{1}[/tex] = 4

Answer:

Yes, of course

Step-by-step explanation:

Corollary simply means the similar case or alike. So we can apply same theorem. Although it may be lengthy and bit tricky but its easy to prove.

Answer:

72

Step-by-step explanation:

67+5= 72

Answer:

The answer is negative, the one you chose in the picture.

Step-by-step explanation:

Positive slope would be going upwards.

Negative slope would be going downwards.

Slopes that are zero would be horizontal.

Slopes that are undefined would be vertical.

So, the reason why the slope is negative is that the line is going downhill.

Hope this is helpful

=======================================================

There are a few ways to do this.

One way is to slice horizontally to break up the L shape into two separate rectangular blocks. Refer to the diagram below to see what I mean.

The block on top has length 80-60 = 20 mm (horizontal), width 10 mm, and height 40 mm.

The volume of this block on top is L*W*H = 20*10*40 = 8000 mm^3, where mm^3 means "cubic millimeters"

The block down below has a length of 80 mm, width of 10 mm, and height of 60-40 = 20 mm (vertical). Its volume is L*W*H = 80*10*20 = 16000 mm^3

Add up the two volumes to get the overall volume: 8000+16000 = 24000 mm^3

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

Another approach you could take is to do a vertical slice to form two separate blocks. You would follow similar steps mentioned in the section above to find the two volumes, and add up the smaller pieces.

Yet another way to find the answer is to find the area of the L shape, and then multiply that by the depth of 10 mm.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \huge \mathrm{ \underbrace{Answer}}[/tex]

The given equation is :

[tex] \huge \boxed{ y = 2x + 6 }[/tex]

Now, let's solve for each value of "x"

[tex]\mathrm {\hookrightarrow \:1. \: \: when \: \: x = 0}[/tex]

[tex]\mathrm{\hookrightarrow 2.\: \: when \: \: x = 1}[/tex]

[tex]\mathrm {\hookrightarrow \: 3. \: \: when \: \: x = 2}[/tex]

[tex]\mathrm{\hookrightarrow \: 4. \: \: when \: \: x = 3}[/tex]

[tex] \mathrm{✌TeeNForeveR✌}[/tex]

Answer:

[tex]\huge\boxed{Answer\hookleftarrow}[/tex]

Equation = [tex]\large\bold{y = 2x + 6}[/tex]

a) [tex]x = 0[/tex]

Substitute the value of x as 0 in the equation.

[tex]y = 2x + 6 \\ y = 2(0) + 6 \\ y = 0 + 6 \\ y = 6[/tex]

✐ Answer of a) is [tex]\large\bold{y = 6}[/tex]

____________________

b) [tex]x = 1[/tex]

Substitute the value of x as 1 in the equation.

[tex]y = 2x + 6 \\ y = 2(1) + 6 \\ y = 2 + 6 \\ y = 8[/tex]

✐ Answer of b) is [tex]\large\bold{y = 8}[/tex]

____________________

c) [tex]x = 2[/tex]

Substitute the value of x as 2 in the equation.

[tex]y = 2x + 6 \\ y = 2(2) + 6 \\ y = 4 + 6 \\ y = 10[/tex]

✐ Answer of b) is [tex]\large\bold{y = 10}[/tex]

____________________

d) [tex]x = 3[/tex]

Substitute the value of x as 3 in the equation.

[tex]y = 2x + 6 \\ y = 2(3) + 6 \\ y = 6 + 6 \\ y = 12[/tex]

✐ Answer of d) is [tex]\large\bold{y = 12}[/tex]

____________________

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

# ꧁❣ RainbowSalt2²2² ࿐

Answer:

P’ is (2,-2)

Step-by-step explanation:

For us to get the appropriate translation, we have to add 9 to the x-coordinate value and subtract 3 from the y-coordinate value

so, we have the transformation as follows;

(-7+9, 1-3)

= (2,-2)

Answer:

I believe that the answer is either C or D

Step-by-step explanation:

Jake forgot his snack, which could mean that he was hungry at school. But it could be logical to assume that he forgot his breakfast. I may be wrong in both cases, but these are my best guesses!

Answer: yeah looks logically correct

Step-by-step explanation: I he got the watch he was 1st

Fact is he didn't get the watch therefore he wasn't first

Therefore 2nd holds true also - if not first then not in station

No watch = not in station

Answer:

n = 116.2 ≈ 117  

Option E) 117 is the correct answer.

Step-by-step explanation:

Given the data in the question;

Exceed = 0.1

{ 1 - 0.1 = 0.9 }

normal table value at 0.9 = - 1.285

Normal table;

hence

( y - 400 ) / 40 = -1.285

y - 400  = -51.4

y = 400 - 51.4

y = 348.6

so,

348.6 = ∈(y) = ∈[ ⁿ∑[tex]_{i=1[/tex] X[tex]_i[/tex] ]

348.6 = n.∈( X[tex]_i[/tex]  )

we substitute

348.6 = n × 3

n = 348.6 / 3

n = 116.2 ≈ 117  { roundup since we talking of number of cars i.e sample size }

Option E) 117 is the correct answer.

Answer:

A

Step-by-step explanation:

Hope this helps!

Answer:

115

Step-by-step explanation:

Given :

Mean of intelligence score = 100

Standard deviation of intelligence score = 15

Since both are perfectly correlated,

The Zscore ON SAT = +1.0

Using the standard normal interpretation, Xcore on SAT of +1.0 means 1 standard deviation to the right

This means :

Mean + 1 standard deviation

100 + 1*15

= 115

We could use the Zscore formula directly too:

Zscore = (x - mean) / standard deviation

Zscore = +1 ; x = score

Hence, we have

1 = (x - 100) / 15

1 * 15 = x - 100

15 = x- 100

x = 15 + 100

x = 115

Answer:

154 inches tall.

Step-by-step explanation:

In this scenario, the sun's angle is the same for both objects. Since we have three values and 1 variable (height of the pole) we can use the Rule of Three to solve this. In this, we simply multiply the diagonal values of the ratios and divide by the third value to get the value of the variable like so...

55 in.  <=====>  70 in.

x  <=========>  196 in.

(55 * 196) / 70 = x

10,780 / 70 = x

154 in. = x

Finally, we can see that the flagpole is 154 inches tall.

Answer:

165 cm

Step-by-step explanation:

We solve using the rule

Shadow of ruler/Length of ruler = Shadow of the girl /Length of the girl

Shadow of ruler = 20cm

Length of ruler = 30cm

Shadow of the girl = 110cm

Length of the girl = x

Hence:

20/30 = 110/x

Cross Multiply

20x = 30 × 110

x = 30 × 110/20

x = 165 cm

Therefore, Sierra(the girl) is 165cm tall

Answer:

around 200.96

Step-by-step explanation:

circle area = pir^2

pi*8^2

pi*64

=around 200.96

Answer:

50%

Step-by-step explanation:

Example of Aa crossed with Aa (both hetero).

Outcomes are:

AA (homo)

Aa (hetero)

aA (hetero)

aa (homo)

So the ratio of hetero to all outcomes = 2:4 = 50%

Answer:

Both m^2 and cm^2 are given below. Take your pick.

Step-by-step explanation:

Area = L * W

L = 1.57 m * 100 cm / 1 meter = 157 cm

W = 45 cm

Area = 157 cm * 45 cm = 7065 cm^2

In meters, the width would be 45 cm * 1 m / 100 cm = 0.45 m

Area = L * W

L = 1.57 m

W = 0.45 M

Area = 1.57 * 0.45

Area = 0.7065 m^2