Can somebody help me find the answer to this problem please ?

The pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.

To determine if two functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's analyze the given options:

A. f(x) = 5 + x and g(x) = 5 - x

To check if they are inverses, we compute f(g(x)) = f(5 - x) = 5 + (5 - x) = 10 - x, which is not equal to x. Similarly, g(f(x)) = g(5 + x) = 5 - (5 + x) = -x, which is also not equal to x. Therefore, these functions are not inverses.

B. f(x) = 2x - 9 and g(x) = x + 9/2

By calculating f(g(x)) and g(f(x)), we find that f(g(x)) = x and g(f(x)) = x, which means these functions are inverses of each other.

C. f(x) = 3 - 6 and g(x) = x + 6/2

Similar to option A, we compute f(g(x)) and g(f(x)), and find that they are not equal to x. Hence, these functions are not inverses.

D. f(x) = x/3 + 4 and g(x) = 3x - 4

After evaluating f(g(x)) and g(f(x)), we see that f(g(x)) = x and g(f(x)) = x. Therefore, these functions are inverses of each other.

In summary, the pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.

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Answer:

x+3

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

(x-3)(x-2)(x-4)

Step-by-step explanation:

x+4             x^2 -16

---------------÷ -------------

x^2 - 5x+6     x+3

Copy dot flip

x+4                x+3

--------------- * -------------

x^2 - 5x+6     x^2 -16

Factor

x+4                x+3

--------------- * -------------

(x-3)(x-2)     (x-4)(x+4)

Cancel like terms

1                   x+3

--------------- * -------------

(x-3)(x-2)     (x-4)1

x+3

---------------   x cannot equal 3,2,4 -4

(x-3)(x-2)(x-4)

Answer:

Step-by-step explanation:

To find the times that the height is 26 feet, we set the position equation equal to 26 and solve for t:

[tex]26=-16t^2+40t+4[/tex] and

[tex]0=-16t^2+40t-22[/tex] and factor that however you are factoring in class to solve a problem like this. When you do that you get

t = .86 seconds and t = 1.68 seconds. That means that .86 seconds after the ball is thrown into the air, it reaches a height of 26 feet; it goes up to its max height and then gravity takes over and pulls it back down. When this happens, it will pass 26 feet again on its way back down. This second time is after 1.68 seconds.

Answer:

x = 3

Step-by-step explanation:

First, use trigonometric function to find RT.

θ = 60°

Opposite = 2√3

Hypotenuse = RT

Apply SOH:

Sin θ = Opp/Hyp

Plug in the values

Sin 60° = 2√3/RT

RT*Sin 60° = 2√3

Divide both sides by Sin 60°

RT = 2√3/sin 60°

RT = 2√3 × √3/2 (sin 60° = √3/2)

RT = (2√3 × √3)/2

RT = (2 × 3)/2

RT = 3

✔️Find x

θ = 45°

Opposite = x

Adjacent = 3

Apply TOA:

Tan θ = Opp/Adj

Substitute

Tan 45° = x/3

3 × Tan 45° = x

3 × 1 = x (tan 45° = 1)

3 = x

x = 3

I don't know sorry I am weak in math

Answer:

Indication of Actual Quantity and Estimated Quantity

Actual Quantity:

Registered students in the university = 25,000

Sample of students = 400

Students living at home = 317

Estimated Quantity:

317 out of 400 students

79%

Step-by-step explanation:

An actual quantity does not require to be estimated.  It is usually given in the question or scenario.  For example, the number of registered students in the university is an actual quantity.  The percentage of students who live at home from the simple random sample of 400 is an estimated quantity.

Answer:

C

Step-by-step explanation:

The slope of the line will be (2) and the equation will be C

9514 1404 393

Answer:

  (b) ∠STU

Step-by-step explanation:

Transversal UT between parallel sides RU and ST creates alternate interior angles RUT and STU. These are congruent.

  ∠STU has the same measure as ∠RUT

_____

The figure shown is a trapezoid, not a parallelogram.

Answer:

15.4 degrees

Step-by-step explanation:

b= 53

h = 55

cos -¹( 53/53)= 15.4

Answer:

width = 7, length = 11

Step-by-step explanation:

area = 77

length = 3w - 10

width = w

w(3w - 10) = 77

3w^2 - 10w - 77 = 0

(3w + 11)(w - 7) = 0

we rule out 3w + 11 = 0 because w would be negative

so we use w - 7 = 0

so the width = 7

length = 3w - 10

length = 21 - 10

length = 11

Answer:

10% gain

Step-by-step explanation:

[P2-P1]/P1

(33-30)/30=3/30=.1 or 10% gain.

Answer:

10%

Step-by-step explanation:

→ Minus the new share from the old one

33 - 30 = 3

→ Divide the answer by the original price

3 ÷ 30 = 0.1

→ Multiply the answer by 100

0.1 × 100 = 10%

Answer:

The answer is "Option D"

Step-by-step explanation:

In a rotation, an item is rotated around with a known location. Clockwise or anticlockwise spinning is possible. Rotation centers are spherical geometry in space where rotation occurs. The direction of inclination is the indicator of the total rotation made. Rotary point refers to that part point of a figure around which it is revolved.

Answer:

Pretty sure it's 0.528

I believe the answer is B!

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Answer:

[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]

Step-by-step explanation:

There's a handy formula we can use to find the sum of a geometric sequence, and here it is

[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]

The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.

First lets visualize this sequence

[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]

Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.

[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]

Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.

[tex]S_n = \sum{a*r^{n-1}}[/tex]

To finish up lets plug these coefficients in and get our sum after 10 terms.

[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]

Answer:

BD = 4.1

Step-by-step explanation:

DA is an angle bisector which also divides the opposite side of the angle it bisects in a way that it is proportional to tye other two sides.

By implication, we would have the following:

AB/BD = AC/DC

AB = 5.3

AC = 5.5

DC = 4.3

BD = ?

Plug in the values

5.3/BD = 5.5/4.3

Cross multiply

BD*5.5 = 4.3*5.3

BD*5.5 = 22.79

Divide both sides by 5.5

BD = 22.79/5.5

BD = 4.1 (to 1 decimal place)

Let x(t) denote the amount of salt (in kg) in the tank at time t. The tank starts with 18 kg of salt, so x (0) = 18.

The solution is drained from the tank at a rate of 90 L/min, so that the amount of salt in the tank changes according to the differential equation

dx(t)/dt = - (x(t) kg)/(9000 L) × (90 L/min) = -1/100 x(t) kg/min

or, more succintly,

x' = -1/100 x

This equation is separable as

dx/x = -1/100 dt

Integrating both sides gives

∫ dx/x = -1/100 ∫ dt

ln|x| = -1/100 t + C

x = exp(-1/100 t + C )

x = C exp(-t/100)

(a) Using the initial condition x (0) = 18, we find

18 = C exp(0)   ==>   C = 18

so that

x(t) = 18 exp(-t/100)

(b) After 20 minutes, we have

x (20) = 18 exp(-20/100) = 18 exp(-1/5) ≈ 14.74

so the tank contains approximately 14.74 kg of salt after this time.

Answer:

$32

Step-by-step explanation:

Multiply $40*3000 students. Subtract 2 students that might receive a $12000 policy each. Divide by 3000 students to find average payout.

Answer: y = x - 7

Slope intercept form: y = mx + b

[tex]2x-2y=14\\\\-2y=-2x+14\\\\y=\frac{-2x+14}{-2} =\frac{-2(x-7)}{-2} =x-7[/tex]

Answer:

2/23

6/23

5/23

Step-by-step explanation:

60 only want chilis

20 wants both

100 only want red lobster

50 want neither

The right solution to the given question is "[tex]\frac{2}{23}[/tex]", "[tex]\frac{6}{23}[/tex]" and "[tex]\frac{5}{23}[/tex]".

According to the question,

By putting the value of "b", we get

                [tex]a = 80-20[/tex]

                [tex]a = 60[/tex]

By putting the value of "b", we get

      [tex]20+c=120[/tex]

              [tex]c = 120-20[/tex]

              [tex]c = 100[/tex]

By putting the values of "a", "b", "c" and "d", we get    

       [tex]d = 50[/tex]

(a)

P(both Chili's and Red lobster),

= [tex]\frac{b}{a+b+c+d}[/tex]

= [tex]\frac{2}{23}[/tex]

(b)

P(only chili's),

= [tex]\frac{a}{a+b+c+d}[/tex]

= [tex]\frac{6}{23}[/tex]

(c)

P(neither),

= [tex]\frac{d}{a+b+c+d}[/tex]

= [tex]\frac{5}{23}[/tex]

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Answer:

C

Step-by-step explanation:

Given

[tex]\frac{x}{3}[/tex] < 5 ( multiply both sides by 3 to clear the fraction )

x < 15 → C

Answer:

84.60

Step-by-step explanation:

We can write a ratio to solve

18.80             x

---------   = --------------

2 shirts    9 shirts

Using cross products

18.80 *9 = 2x

169.2 =2x

Divide each side by 2

169.2/2 =2x/2

84.60 =x

Vertex is the point where the function is at its maximum/ minimum.

Answer:

"ob" is the answer of this long question

Answer:

D

Step-by-step explanation:

reason:

not A cuz the customer has to wait for a long time, and she feel waste of time

not B cus it's the store's responsiblity, not customer. if she said that, the customer would feel be disrespected. and i swear she never comes back that store.

C if she said that, customer also feel waste of time when she has to talk with Aliana who cant solve her problem

and the boss will think Ali couldnt have no problem-solving skills

Answer:

Assuming order does not matter, the probability of selecting all midsize cars is 0.000277373, or [tex]\frac{4}{14421}[/tex].

Step-by-step explanation:

First, we must find the n(Total arrangements of selections)=(8+15)C6

n(Total arrangements of selections)=23C6

n(Total arrangements of selections)=100,947

Second, we must find the n(Arrangements where all are midsize cars)=8C6

n(Arrangements where all are midsize cars)=28

To find the probability of selecting all midsize cars, we divide the n(Arrangements where all are midsize cars) by the n(Total arrangements of selections):

P(All midsize cars)= [tex]\frac{28}{100,947}[/tex]

P(All midsize cars)= [tex]\frac{4}{14421}[/tex]=0.000277373.

Answer:

-2

Step-by-step explanation:

5 + (-7)

Since the 7 is larger than 5, the 7 will overpower the 5 in a way. So, all you do is subtract 7 and 5.

7 - 5 = 2

But the 7 has a negative with it (since it's larger), so you add the negative to the 2.

7 - 5 = -2

The answer will be -2.

Answer:

The t value for 99% CI for 21 df is 2.831.

The critical value that should be used in constructing the confidence interval is (64.593, 86.407).

Step-by-step explanation:

Now the sample size is less than 30 and also population standard deviation is not known.

Then we will use t distribution to find CI

t value for 99% CI for 21 df is TINV(0.01,21)=2.831

The margin of error is [tex]E=t\times\frac{s}{\sqrt{n}}\\\\=2.831\times\frac{18.07}{\sqrt{22}}\\\\=10.907[/tex]

Hence CI is[tex]CI=\overline{x} \pm E\\\\ =75.50 \pm 10.907\\\\=(64.593,86.407 )[/tex]

Answer:

y=3x+6

Step-by-step explanation:

in a line graph, y=mx+c

m refers to gradient, c refers to y-intercept.

since lines are parallel, both lines have the same gradient.

the line intersects (1,9)

x=1,y=9

9=3(1)+c

c=6

so y=3x+6

Answer:

y = 3x+6

Step-by-step explanation:

Parallel lines have the same slope

y = 3x+2 is in slope intercept form (y=mx+b where m is the slope and b is the y intercept)

So the slope is 3

Y = 3x+2

Using the point given substitute into the equation and solve for b

9 = 3(1)+b

9 =3+b

9-3 =b

6=b

y = 3x+6