complete the proof, word bank at bottom

Answer:

The two functions are inverses.

Step-by-step explanation:

Recall what an inverse is:

When you inverse an equation, like y = 2x for example, you switch, the y and x values. So you'd now have x = 2y, then x/2 = y.

In a case like that we'd say that, y = 2x, and y = x/2 are inverses of each other.

Now looking at your question, all we'd need to do is take the inverse of 1, and see if it matches up with the other one. So pick a function. I'll choose g(x) and I'll inverse it.

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

get rid of the g(x), as it doesn't help you anymore.

[tex]y = 2x + 6[/tex]

then, switch the x and the y.

[tex]x = 2y + 6[/tex]

then isolate for y.

[tex]x - 6 = 2y[/tex]

[tex]\frac{x-6}{2} = y[/tex]

Now let's see, does [tex]f(x) = \frac{1}{2}x - 3[/tex] equal [tex]\frac{x-6}{2}[/tex] ? Well actually yes.

We just didn't simplify all the way.

[tex]\frac{x-6}{2} = y\\[/tex]

divide each term by 2

[tex]\frac{x}{2} - 3 = y[/tex]

[tex]\frac{x}{2}[/tex] can be written as [tex]\frac{1}{2}x[/tex] so we get

[tex]\frac{1}{2}x - 3[/tex] which is equal to f(x)

Therefore the 2 functions are inverses.

Q.E.D

Answer:

The perimeter is 50.

The area is 150.

Step-by-step explanation:

To calculate perimeter, add the length and width, then multiply the sum by 2.

( 15+10=25. 25*2=50 )

To calculate area, multiply the length and width.

( 15*10=150 )

Answer:

x ≥ -2

Step-by-step explanation:

6x-2 ≥ 4x-6

2x ≥ -4

x ≥ -2

PLEASE RATE!! I hope this helps!!

If you have any questions comment below...

(I have verified this answer on an online calculator)

The future value of Danielle's account in 3 years given the amount invested monthly and the APR is $1909.06.

The formula that can be used to determine the future value of the annuity is: monthly deposits x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$50 x [(1.003333^36) - 1] / 0.003333 = $1909.06

To learn more about future value, please check:  https://brainly.com/question/24108530

Answer:

the answer will be 14

Step-by-step explanation:

Hope this helps:)...if not then sorry for wasting your time and may God bless you:)

Answer:

The mean is 14

Step-by-step explanation:

Mean = The sum of all Numbers Divided by the count of Numbers

In this case there are 5 numbers and adding them together = 69

69/5 = 13.8

Rounding up because it ends in above 5

= 14

Answer:

10

Step-by-step explanation:

2(3)+4 = 10

Answer:

63.6

Step-by-step explanation:

63.625

63.6

Answer:

63.6

Step-by-step explanation:

The tenth's place is one after the decimal point, and since 2 is closer to zero than ten, the 6 stays the same, making the answer 63.6.

Hopefully this helps- let me know if you have any questions!

Answer:

Positive

Step-by-step explanation:

Negative over a negative cancel out and become positive.

Answer:

About 113,097.34 units

Step-by-step explanation:

           The volume of a sphere can be found with the equation V = [tex]\frac{4}{3}[/tex]πr³ when r is the radius.

V = [tex]\frac{4}{3}[/tex]πr³

V = [tex]\frac{4}{3}[/tex]π(30)³

V ≈ 113,097.34 units

Answer:

The probability of him pulling a red marble is 12 to 30. The probability of him pulling a blue or purple marble is also 12 to 30.

Step-by-step explanation:

7+5+12+6=30 (all colors)

12 to 30 red ones

7+5+12+6=30 (all colors) and

7+5=12 (blue + purple)

12 to 30 blue or purple

Answer:

2

Step-by-step explanation:

The scake factor is 2

Answer is 2

Answer:

119 is correct answer.

Step-by-step explanation:

angle GHI+90+151=360 (being complete turn angle)

angle GHI =360-119

angle GHI =119

Answer:

BC = 24

Step-by-step explanation:

FD = 36, FE = 15 and CD = 18

By secant theorem.

DE • DF = CD • DB

(36 - 15) • 36 = 18 • DB

DB = 42

BC = DB - CD

BC = 42 - 18

BC = 24

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)

Hunter can make a total of 40 cups before he runs out of budget.

We know his total budget was $50 but he already spent $20 on a pitcher and cups.

This means the total of money just for the lemonade is $30.

To find this number divide the budget for lemonade by the cost of a lemonade cup $0.75.

Based on this, the total of cups he can make is 40 cups.

Learn more about budget in: https://brainly.com/question/15712390

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

The distributive property states that:-

[tex]\bigstar{\underline{\boxed{\pmb{a(b+c)=ab+ac}}}[/tex]

Simplify:-

[tex]\bigstar{\boxed{\pmb{5(7h+3m)}}}[/tex]

[tex]\longmapsto\sf{(5~times~7h)+)5*3m)[/tex]

[tex]\longmapsto\sf{35h*15m}[/tex]

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

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

I believe that x is equal to 6. x=6

Answer:

A

Step-by-step explanation:

Hope this helped

Answer:

∠B = 84

Step-by-step explanation:

Supplementary angles add up to 180°, You would subtract 96 from 180 to find angle B.

Answer:

=> ∠B = 84

Step-by-step explanation:

Given :

∠A + ∠B = 180°

∠A = 96°

=> 96° + ∠B = 180

=> ∠B = 180-96

=> ∠B = 84

Answer

When a input uses two outputs, say we have

5,6

5,8

3,4

6,2

9,1

Notice how 5 uses two instead of one meaning the function is unfunctional

Step-by-step explanation:

The equation which John solve to find w, the greatest width in centimeters he can use for the mosaic, is w(w + 2) = 48.

Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,

[tex]A=a\times b[/tex]

Here, (a)is the length of the rectangle and (b) is the width of the rectangle

The area of the tile is 48 square cm. John wants to make the mosaic with this tile having the length 2 cm longer than the width.

Let suppose the width of the rectangle mosaic is w cm. Thus the length of it is,

[tex]l=w+2[/tex]

As the area of a rectangle is the product of its length and width and Tte area of the tile is 48 square cm. Thus,

[tex]48=(w+2)\times w\\48=(w+2)w\\[/tex]

The equation which John solve to find w, the greatest width in centimeters he can use for the mosaic is

[tex]w(w + 2) = 48[/tex]

Learn more about the area of rectangle here;

https://brainly.com/question/11202023

Answer:

B. w(w + 2) = 48

Step-by-step explanation:

I just took the quiz.

Have the day you deserve :)

Answer:

681 m^3

Step-by-step explanation:

Winder only found part of the volume. He also needs to find the volume of the hemisphere.

I would first find the volume of the cylinder like Winder, then proceed to calculate the volume of the hemisphere, which is V = 4/3π(4^3)=27.16 m^3. The total volume inside the storage tank is 681 m^3 when rounded to the nearest cubic meter.

A transversal line is a line that crosses through two lines on the same plane.

Example:

I attached a photo below showing the Transversal line (the line in red) crossing two lines located on the same plane. Note: The Transversal line is only the red line, not the whole diagram below.

I am open to corrections if I unintentionally added false information :).

#learnwithbrainly

Answer:

-2 * 3 = -6

-2 * h = -2 h

C) is equivalent to this result

Answer:

answer is 19/9.

Step-by-step explanation:

give me brielient.

Answer:

They given expresión is Pd y no mi al

Answer:

0

Step-by-step explanation:

Since B = 16  and C = 9 we can plug into the equation.

(9) + 3 (6 - 9)

Since order of operations we subtract 9 from 6

6 - 9 = -3

Now we do -3 x 3 = -9

Now add -9 to 9

-9 + 9 = 0

Answer:

Step-by-step explanation:

3(6 - 9)

3(-3)= -9

9 + (-9) = 0

Answer:

A. We are given that the length of the box is equal to 24 as indicted in the "24-inch long". From the given, it is also stated that the width of the box is 7 inches less than the height. If the height of the box is x, the width is then x - 7. The equation that would let us solve the problem is,

                           2880 = 24(x)(x - 7)

Simplifying,

                           2880 = 24x² - 168x

B. The value of x from the equation is 15. Thus, the answer is YES.

Step-by-step explanation:

a) The equation that models the volume of the box in terms of its height will be 2880 = 24x² - 168x.

b)Yes, it is possible for the height of the box to be 15 inches

Volume is the three-dimensional space bounded by a boundary or inhabited by an item.

The given data in the problem is;

L is the length of the box= 24-inch

V is the volume = 2,880 cubic inches.W

W is the width of the box

h is the height

Let the side of the box is x then volume V is found as;

V=LWh

2880 = 24(x)(x - 7)

2880 = 24x² - 168x

Hence the equation that models the volume of the box in terms of its height will be 2880 = 24x² - 168x.

b)Yes, it is possible for the height of the  box to be 15 inches

The value of x obtained from the equation is 15.

Hence yes, it is possible for the height of the  box to be 15 inches

To learn more about the volume refer to the link;

https://brainly.com/question/1578538