please show work for both thank you!!

Answer:

f^(-1)(x) = 1/5x

Step-by-step explanation:

[tex] \large{f(x) = mx + b \longrightarrow f^{ - 1} (x) = \frac{x - b}{m} }[/tex]

Inverse Function is when we swap the x-term and y-term. Here is an explanation to the inverse of linear function above.

[tex] \large{f(x) = mx + b}[/tex]

Here we define f(x) = y. It is better to use y instead of f(x)

[tex] \large{y = mx + b}[/tex]

Swap x-term and y-term.

[tex] \large{x = my + b}[/tex]

Arrange/Simplify in the y-isolated equation.

[tex] \large{x - b = my} \\ \large {\frac{x - b}{ m} = y} \\ \large{ y = \frac{x - b}{m} }[/tex]

Since the function is in inverse form. It's recommended to use f^(-1) to point out that the function is an inverse of the original function.

[tex] \large \boxed{ {f}^{ - 1} (x) = \frac{x - b}{m} }[/tex]

Hence, y = (x-b)/m is an inverse of y = mx+b. A one-to-one function can have an inverse form. Back to the question!

We are given the linear function:

[tex] \large{f(x) = 5x}[/tex]

We will be using substitution method by substituting the original function in inverse form.

Since we know that the slope is 5 and doesn't have y-intercept which is b-value. Hence

[tex] \large{ {f}^{ - 1} (x) = \frac{x - 0}{5} } \\ \large{ {f}^{ - 1} (x) = \frac{x }{5} } \\ \large{ {f}^{ - 1} (x) = \frac{1}{5} x}[/tex]

Or we swap x-term and y-term.

[tex] \large{f(x) = 5x} \\ \large{y = 5x} \\ \large{x = 5y} \\ \large{ \frac{x}{5} = y} \\ \large{y = \frac{x}{5} = \frac{1}{5} x} \\ \large{ {f}^{ - 1} (x) = \frac{1}{5} x}[/tex]

Answer:

150 Wh

I guess the question means, how much money is wasted on lighting in a year ?

$0.50

Step-by-step explanation:

3 × 10W × 5 hours = 150 Wh

2 × 10W × 1 hour × 365 × 0.068 / 1000

divided by 1000, because the price is in kWh (1000 Wh), but the rest of the calculation refers to W. so, we need to bring all factors to the same dimension. the division by 1000 either brings the Wh to kWh, or the price to the price for Wh (instead of kWh). it does not matter which one. just one of these 2 things have to happen here, so that all factors have the same dimension.

=> 20 × 365 × 0.068 / 1000 = 7300 × 0.068 / 1000 =

= 7.3 × 0.068 = $0.50 (rounded from 0.4964)

Answer:

3/36

Step-by-step explanation:

Answer:

8 Roses

Step-by-step explanation:

Y = 15 + 4.50X

51 = 15 + 4.50X

51 - 15 = 4.50X

36 = 4.50 X

360 = 45x  

360/45 = x

x = 8

Answer:

That's a right angled Triangle

When viewed upside down

(HINT: 50 can't possibly be the adjacent; Why? Its the longest side(Hypotenuse)... You can also know this by identifying the part of the triangle directly facing the 90° sign)

tanA= Opp/Adj

tanA= 30/40

tanA= 3/4

OPTION D SEEMS LEGIT!!!

The second option should be chosen as it depicts the amount with the lowest interest.

For option 1, the annual interest will be:

= $1300 × 16.5% = $214.50

The monthly finance charge will be:

= $1300 × (0.165/12)

= $17.88

The minimum monthly payment for the first month will be:

= $100 + $17.88 = $117.88

Hence, the total amount paid will be:

= ($117.88 × 12) + $214.50

= $1629.06

For option 2, the simple interest will be:

= (1300 × 12.5%)

= $162.50

The amount that will be paid monthly will be:

= $1000/12

= $83.33.

In this case, the total amount paid will be:

= $162.50 + $1300

= $1462.50

Therefore, the second option is better as it's cheaper.

Learn more about interest on:

https://brainly.com/question/2294792

Answer:

2.44560420

Step-by-step explanation:

Answer:

[tex]a _{n} = a( {r}^{n - 1} ) \\ a _{n} = 80(2 {}^{n - 1} ) \\ a _{n} = \frac{80. {2}^{n} }{ {2}^{ 1} } \\a _{n} = 40( {2}^{n} ) \\ a _{n} = ( {2}^{3} \times 5)( {2}^{n} ) \\ a _{n} = 5( {2}^{n + 3} )[/tex]

[tex]\boxed{4a}[/tex] ✅

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

[tex]a + 3a \\ = 4a[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.ඞ}}}}}[/tex]

Answer:

Step-by-step explanation:

a+3a

since they are like terms u can add them

=4a  

therefore a+3a=4a

Answer:

10/30 is the fraction of the diagram shade

Answer:

x = 18

Step-by-step explanation:

Both angles together make 180, they are essentially supplementary angles thou not on the same line.

Set your formula up as

81 + 5x + 9 = 180

5x = 180 - 81 - 9

5x = 90

x = 90/5

x = 18

Answer:

[tex]y = {(0.7634)}^{4} \\ log(y) = 4 log(0.7634) \\ log(y) = - 0.46899 \\ y = {10}^{ - 0.46899} \\ y = 0.3396[/tex]

Answer:

Precio original= $97.5

Step-by-step explanation:

Dada la siguiente información:

Precio de venta (con descuento)= $39

Porcentage de descuento= 60%

Para calcular el precio orinigal del videojuego, debemos usar la siguiente formula:

Precio original= precio de descuento / (1 - porcentage de descuento)

Precio original= 39 / (1 - 0.6)

Precio original= $97.5

Answer:

x = 77.5

Step-by-step explanation:

1. Use cross-multiplication to find x.

[tex]\frac{13}{21} =\frac{48}{x}[/tex]

[tex]13x =1008[/tex]

2. Divide and round.

x ≈ 77.5

Answer: I and III

Step-by-step explanation:

The origin is at (0,0).

When we look at the graph, we can see that the only visible x and y intercepts are at the origin, (0,0) (an x or y intercept is where the graph intersects the x or y axis). We also know that because the graph is going outwards, it will not have another x or y intercept. So, I is correct.

II would be incorrect because the maximum point would be WAY further up. The maximum point is the highest point the graph will reach.

III is correct because the origin is the lowest point, which means that the origin is the minimum point.

Answer:

How many televisions do the families in your neighborhood own?

Answer:

Step-by-step explanation:

There is no dot plot so I can’t help

Answer:

(2,-7)

Step-by-step explanation:

Answer:

266.386

Step-by-step explanation:

im not shore if its right, i used a surface area calculator

Answer:

56ft

Step-by-step explanation:

Surface area is adding up all the sides multiplied by 2, so:

8 x 2 = 16ft

8 x 2 = 16ft

12 x 2 = 24ft

24ft + 16ft + 16ft = 56ft

Answer:

Ella could make:

2, 3, 4, 6, or 12 fruit baskets.

Step-by-step explanation:

We know that Ella has 48 apples and 60 oranges.

She wants to make N fruit baskets, such that each one of these fruit baskets has the same number of each fruit.

So we can define the variables:

a = number of apples in each one of these baskets

o = number of oranges in each one of these baskets

Then, if we have N baskets, we must have that:

N*a = 48

N*o = 60

a = 48/N

o = 60/N

And the values of a and o must be integers, then N must be a common factor of 48 and 60.

Remember that every number can be written as a product of prime factors, then let's rewrite 48 and 60 in that way:

48 = 2*24 = 2*2*12 = 2*2*2*2*3

60 = 2*30 = 2*3*10 = 2*2*3*5

Then, the common factors between 48 and 60 are the ones we can make with the prime numbers (that appear in both constructions) these are:

2

3

2*2 = 4

2*3 = 6

2*2*3 = 12

These are all the possible numbers of fruit baskets.

Answer:

1800

Step-by-step explanation:

Just find the area of all the triangles and add

Answer:

18 metres squared

Step-by-step explanation:

it looks like you want to find the area of the kite as a whole, and lucky for you, the kite is conveniently cut into right triangles.

to find the area of a right triangle, you use the equation

A = (b × h)/2

where A is the area, b is the base, and h is the height.

now we plug in the numbers for each individual area and solve for the total area.

let's start with the 1st triangle, where it's base is 30cm and the height is 25 cm.

A = (30 × 25)/2

A = 375 cm squared

now the next one whose base is 30 and it's height is also 25 (We just did this last time so the area is the same)

A = 375 cm squared

now we'll do the next one whose base is 30 and height is 35.

A = (30 × 35)/2

A = 525 cm squared

and the last one is the same as the one we just did so I'll just copy the other answer.

A = 525 cm squared

alright now we'll add up all of the areas we just found to get the total area of the kite.

Total A = 375 + 375 + 525 + 525

Total A = 1800 cm squared

now we will divide our total by 100 because it takes 100 centimetres to get 1 metre and what we have right now is centimetres.

1800/100 = 18 metres squared.

Answer:

65 cm

Step-by-step explanation:

16^2 x 63^2 = 65^2

Answer:

y = x-4

Step-by-step explanation:

y = x +4

This has a slope of 1 since it is in the form y = mx+b where m is the slope and b is the y intercept

Parallel lines have the same slope

The line we are interested in passes through the point (0,-4) which means it has a y intercept of -5

y = mx+b

y = 1x-4

y = x-4

Answer:

y=-5x-9

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

y=kx

-12=-4k

k=3

24=3x

x=8

y=kx

-12=-4

k=3

24=3x

X=8

Your Answer..

V=10in³

Hope This Helps You

Answer:

x = 15°

Step-by-step explanation:

First Identify the angle of x by subtracting 180° - 120° = 60°

Always remember when you see a straight line the line measures 180°

So the angle of x = 60° but not the value of x so use the given equation to find the value of x

3x + 15 = 60°

3x  - 15 = -15°

3x = 45

x = 15°

Answer:

There was a mistake in line D

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

Explanation:

Note in the previous line C that Noah multiplied both sides by 5. This is to clear out the fractions, since each have a denominator of 5.

In line D, Noah only multiplied those outer '5's by the first term in each parenthesis group. He didn't use the distributive property correctly.

The distributive property is a*(b+c) = a*b+a*c.

The 'a' is multiplied to everything inside, which are the terms b and c.

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

Here are what the steps should look like from line D and onward. Take note of the 30 and 100. This is from 5*6 = 30 and 5*20 = 100.

We end up with the same thing on both sides. So this confirms that x = 14/5 is the solution to the original equation.

Answer:

ᕼᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᕼᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᕼᓰᓰᓰᓰᓰᕼᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰ

Step-by-step explanation:

ᕼᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᕼᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᓰᕼᓰᓰᓰᓰᓰᕼᓰᓰᓰᓰᓰᓰᓰᓰᓰ