Given the following funtions: f (x) = x^2 g (x) = x-3 find the composition of the two functions and show your process: f (g(x))

Answer:

Option C

Step-by-step explanation:

[tex]f(x)=40( \frac{1}{4} )^{x} \\ x = 0\\ y = 40( \frac{1}{4} )^{0} = 40

[/tex]

Part A

Answers:

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

Explanation:

The variables are simply letters. They are placeholders for numbers to be plugged in later. Think of them like empty boxes where numbers will go. In this case, the variable h represents the number of hours Tyler works, and c is the number of new accounts she opens.

The coefficients are the numbers multiplied with the variables. They are to the left of the variable.

The constant 50 is not attached to any variable.

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

Part B

Answer: She earns $618.5

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

Explanation:

We're told she worked 37 hours. So we'll replace h with 37.

Also, she opened 12 new accounts. So c = 12

This means...

10.50*h + 15*c + 50

10.50*37 + 15*12 + 50

388.5 + 180 + 50

618.5

is the amount she earns

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

Part C

Answer: The coefficient changes. Specifically, the coefficient 10.50 changes to 11.25

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

Explanation:

The constant never changes (hence the name) no matter how much of a raise Tyler gets. The other coefficient doesn't change either because she would still get $15 per new account. All that's changed is the hourly wage.

If we're told that Tyler got a raise to $11.25 per hour and she now earned $20 per new account, then both coefficients would change and the new equation would be 11.25h+20c+50

Answer:

32

Step-by-step explanation:

Answer:

Step-by-step explanation:

okay so if we lay it out...,

f(x)              6-5x                x-9           x³           2x-5            12x+3

f(-3)              21                   12            -27           -11               -33

f(-2)              16                   -11           -8              -9                -21

f(0)                6                   -9             1                -5                 3

f(1)                 1                    -8             1                -3                 15

f(2)               -4                    -7            8               -1                   27

okay so the left side is all the f(x) values. So the numbers in the "()" represents "x". Now you just substitute the numbers in the"()" for the "x"'s on the top margins. so...,

f(-3)= 6-5x            f(-2)= 6-5x                 f(0)=6-5x               f(1)=6-5x        f(2)=6-5x

f(-3)= 6-5(-3)         f(-2)= 6-5(-2)             f(0)=6-5(0)            f(1)=6-5(1)       f(2)=6-5(2)

f(-3)= 6+15            f(-2)= 6+10                 f(0)=6-0                f(1)=6-5          f(2)=6-10

f(-3)= 21                f(-2)= 16                      f(0)=6                   f(1)= 1              f(2)= -4

f(-3)=x-9               f(-2)=x-9                      f(0)=x-9               f(1)=x-9            f(2)=x-9

f(-3)=(-3)-9            f(-2)=(-2)-9                  f(0)=0-9              f(1)=1-9             f(2)=2-9

f(-3)=-12                f(-2)=-11                       f(0)= -9                f(1)= -8            f(2)= -7

f(-3)=x³                 f(-2)=x³                        f(0)=x³                f(1)= x³              f(2)=x³

f(-3)=(-3)³             f(-2)= (-2)³                    f(0)=0³               f(1)=1³                f(2)=2³

f(-3)= -27             f(-2)= -8                        f(0)= 1                f(1)= 1                 f(2)=8

f(-3)= 2x-5           f(-2)= 2x-5                 f(0)= 2x-5            f(1)= 2x-5      f(2)=2x-5

f(-3)=2(-3)-5         f(-2)=2(-2)-5              f(0)= 2(0)-5          f(1)= 2(1)-5     f(2)=2(2)-5

f(-3)= -6-5            f(-2)= -4-5                  f(0)=0-5               f(1)=2-5         f(2)=4-5

f(-3)= -11               f(-2)= -9                      f(0)= -5                f(1)= -3          f(2)= -1

f(-3)=12x+3            f(-2)=12x+3              f(0)=12x+3          f(1)=12x+3     f(2)=12x+3

f(-3)= 12(-3)+3        f(-2)=12(-2)+3          f(0)=12(0)+3        f(1)=12(1)+3    f(2)=12(2)+3

f(-3)= -36+3          f(-2)= -24+3              f(0)= 0+3             f(1)=12+3       f(2)=24+3

f(-3)= -33                f(-2)= -21                  f(0)=3                 f(1)=15           f(2)= 27

Don't know if you wanted all the work. But I just did it for you so you can see.

Answer: 25

Step-by-step explanation: got it wrong and got the answer Took 1 for the team

Answer:

25

Step-by-step explanation:

khan academy :D

Hi there!

~

⇒ Graph : [tex]y=6x^2+1[/tex]

∴ Rewrite the equation in vertex form.

⇒ [tex]y = 6 ( x + 0)^2 + 1[/tex]

∴ Use the vertex form, [tex]y = a(x - h)^2 + k[/tex] , to determine the values of [tex]a , h ,[/tex] and [tex]k[/tex]

[tex]a = 6 \\h = 0\\k = 1[/tex]

∴ Since the value of [tex]a[/tex] is positive, the parabola opens up.

⇵

∴ Find the vertex [tex]( h,k)[/tex].

[tex](0,1)[/tex]

∴ Find [tex]p[/tex], the distance from the vertex to the focus.

[tex]\frac{1}{24}[/tex]

∴ Find the focus.

[tex]( 0 , \frac{25}{24} )[/tex]

∴ Find the axis of symmetry by finding the line that passes through the vertex and the focus.

[tex]x = 0[/tex]

∴ Find the directrix.

[tex]y = \frac{23}{24}[/tex]

∴ Use the properties of the parabola to analyze and graph the parabola.

Direction: Opens Up

⇒ Vertex: [tex]( 0 , 1)[/tex]

⇒ Focus: [tex]( 0 , \frac{25}{24} )[/tex]

⇒ Axis of Symmetry: [tex]x = 0[/tex]

⇒ Directrix: [tex]y = \frac{23}{24}[/tex]

∴ Select a few [tex]x[/tex] values, and plug them into the equation to find the corresponding [tex]y[/tex]  values. The [tex]x[/tex] values should be selected around the vertex.

[tex]x : -2 , -1 , 0 , 1 , 2 \\y : 25 , 7 , 1 , 7 , 25[/tex]

Hope this helped you!

Answer:n ÷ 7 = 6n

Step-by-step explanation:

Answer:

76 + n

Step-by-step explanation:

Answer:

The slope is 1/3. Rise over run. It goes up 1 and over 3.

Answer:

1.   The star's mass is 3.0 x 10^32 kg.

2.  The star's mass is 3.0 x 10^32 kg.

Step-by-step explanation:

1.

given:

The sun's mass is 2.0×10^30 kg.

mass of a star = 1.5×10^2 kg times the mass of the sun.

find:

Express the answer in Scientific notation.

mass of a star =  1.5×10^2 kg X 2.0×10^30 kg

mass of a star = 3.0 X 10^32 kg

therefore,

The star's mass is 3.0 x 10^32 kg.

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

2.

(2.0 X 10^30) X (1.5 X 10^2)

Multiply the coefficients.

= (2.0 X 1.5)

= 3.0

then add the exponents

= 10^30 + 10^2

= 10^32

Combine the results of the two operations.

(2.0 X 10^30) X (1.5 X 10^2) = 3.0 X 10^32

therefore,

The star's mass is 3.0 x 10^32 kg.

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

Answer:

1.   The star's mass is 3.0 x 10^32 kg.

2.  The star's mass is 3.0 x 10^32 kg.

Step-by-step explanation:

i got them correct on exam

Answer:

rectangle

Step-by-step explanation:

Answer:

17.3 in

Step-by-step explanation:

Given the following :

Length of tank = 20 inches

Width of tank = 10 inches

Amount of water poured into tank = 15 gallons

Volume(V) of tank (rectangular prism)

V = Length × width × height

Height = h

1 gallon = 231 inch³

15 gallons = (231 × 15) = 3465 in³

Hence V = 3465 in³

3465in³ = 20 in × 10 in × h

3465 in³ = 200h

h = 3465 / 200

h = 17.325 in

Height = 17.3 in ( nearest tenth)

Answer:

- 1

Step-by-step explanation:

Step 1:

- 10 + x + 4 - 5 = 7x - 5

Step 2:

- 11 + x = 7x - 5

Step 3:

- 11 = 6x - 5

Step 4:

- 6 = 6x

Answer:

- 1 = x

Hope This Helps :)

Answer:

17

Step-by-step explanation:

i am in doubt with the answer

Answer:

[tex]\huge\boxed{KL = 17}[/tex]

Step-by-step explanation:

If L lies on the line segment KM. It means that:

K_____?__________L___2__M

|<--------------------19------------------->|

Given that:

LM = 2

KM = 19

So,

KM = KL + LM

19 = KL + 2

Subtracting 2 to both sides

KL = 19-2

KL = 17

Answer:

12-6

Step-by-step explanation:

You multiply 3 by the number on the inside. 3x4= 12. 3x2=6.

Answer:

true

Step-by-step explanation:

Answer: True.

Make sure you check each triangle, not all of them are right ones.

Answer:

13527.82

Step-by-step explanation:

A =  1/2 bh

Let's simplify the right side.

A = (bh) / 2

Multiply both sides by 2

2A = bh

Divide both sides by b

(2A) / b = h

Step-by-step explanation:

First, replace f(x) with y . ...

Replace every x with a y and replace every y with an x .

Solve the equation from Step 2 for y . ...

Replace y with f−1(x) f − 1 ( x ) . ...

Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.

The steps for finding the inverse of a function are given below.

A function accepts values, performs particular operations on these values and generates an output. The inverse function agrees with the resultant, operates and reaches back to the original function.

Steps for finding the inverse of a function f.

Replace f(x) by y in the equation describing the function.

Interchange x and y. In other words, replace every x by a y and vice versa.

Solve for y.

Replace y by f⁻¹(x).

Learn more about inverse of a function click;

https://brainly.com/question/29141206

#SPJ2

Answer:

[tex] - 1 \frac{1}{10} [/tex]

Step-by-step explanation:

[tex] - \frac{7}{10} - \frac{4}{10} [/tex]

The two fraction have the same denominator , so put them under a common denominator

[tex] \frac{ - 7 - 4}{10}[/tex]

Simplify

-7-4=-11

[tex] \frac{ - 11}{10} = - \frac{11}{10} [/tex]

write in mixed fraction form

[tex] - 11 \div 10 = 1 \: remainder \: 1 \\ = - 1 \frac{1}{10} [/tex]

Answer:

90 hour

Step-by-step explanation:

300 minutes is for 1 school week

so if you multiply 300 minutes for 18 weeks it results as 5400 minutes.

300 × 18 = 5400 minutes

To get the number of hours you should divide 5400 minute by 60 minutes      ( which is one hour )

5400 ÷ 60 =. 90 hours

You spent a total of 90 hours studying math in 18 weeks.

Answer:

144°

Step-by-step explanation:

let the smaller angle be x then the larger angle is 4x

The sum of a linear pair of angles = 180°, thus

x + 4x = 180 , that is

5x = 180 ( divide both sides by 5 )

x = 36

Thus the larger angle = 4x = 4 × 36 = 144°

Answer:

let the smaller angle be x.Then the bigger angle will be 4x.

x+4x= 180

or, 5x=180

or, x=180/5

there fore, x=36

Again,

4x=4×36

=144

The larger angle is 144.

Answer:

25 questions

Step-by-step explanation:

First set up the equation.

[tex]\frac{20}{x} = \frac{80}{100}[/tex]

To get from 20 to 80 you have to multiply by a scale factor of 4, so do the same to the bottom as well.

Do the inverse and divide 100 by 4 to get x = 25.

There were 25 questions on Victoria's test.

Anwser

25

Step-by-step explanation:

because 5 x 10 is 50 so 5 x 16 is 80 so she got an 80 but 5x 20 equals 100 so Victoria got 5 points per questions so multiply and youll find out  i has to be 25 tho

Answer:

Option C is the correct answer.

C.  5•(-20)

Step-by-step explanation:

We are told that the insurance payment for the car follows a certain pattern that can be represented through an expression. The payment is decreasing by $20 every year. As we don't know the total payment amount per period, so we cannot calculate how much is paid per period/year for insurance but we can calculate the rate at which this payment is decreasing.

Change in payment = t * (-20)

The above expressions can be used to calculate the amount of change in payment i payment is decreasing by a constant $20 every year, after t years.

So, if we want to calculate the change in payment after say 5 years, we can replace t with 5 in the equation and calculate the change,

Change in payment = 5 * (-20)

Change in payment = - $100

Answer:

Step-by-step explanation:

oh im late-......

Answer:

The height of her screen on her drawing must be 30 inches.

Step-by-step explanation:

The scale factor is obtained by dividing the drawn width by real width of the movie screen:

[tex]k = \frac{9\,in}{60\,ft}[/tex]

[tex]k = \frac{3\,in}{20\,ft}[/tex]

The drawn height of movie screen is the product of the scale factor and the real height of the movie screen:

[tex]h_{s} = \left(\frac{3\,in}{20\,ft} \right)\cdot (200\,ft)[/tex]

[tex]h_{s} = 30\,in[/tex]

The height of her screen on her drawing must be 30 inches.

Steps to solve:

2(3n - 9); n = 13

~Substitute

2(3(13) - 9)

~Simplify

2(39 - 9)

~Subtract

2(30)

~Multiply

60

Best of Luck!

Answer:

[tex]\Huge \boxed{60}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

[tex]2(3n-9)[/tex]

The value of n is 13.

[tex]\Longrightarrow \ \ 2(3(13)-9)[/tex]

Solving for brackets,

[tex]\Longrightarrow \ \ 2(39-9)[/tex]

[tex]\Longrightarrow \ \ 2(30)[/tex]

Multiplying,

[tex]\Longrightarrow \ \ 60[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

c 1:3

Step-by-step explanation:

2/6 divide it by 1/3 and u get 1:3