If f(x)= 2x + 5, which of these is the inverse of f(x)

the way I get the subsequent term, nevermind the exponents, the exponents part is easy, since one is decreasing and another is increasing, but the coefficient, to get it, what I usually do is.

multiply the current coefficient by the exponent of the first-term, and divide that by the exponent of the second-term + 1.

so if my current expanded term is say 7a³b⁴, to get the next coefficient, what I do is (7*3)/5   <----- notice, current coefficient times 3 divided by 4+1.

anyhow, with that out of the way, lemme proceed in this one.

[tex]\bf ~~~~~~~~\textit{binomial theorem expansion} \\\\ \qquad \qquad (1+ax)^n\implies \begin{array}{llll} term&coefficient&value\\ \cline{1-3}&\\ 1&+1&(1)^n(ax)^0\\\\ 2&+\frac{(1)(n)}{1}\to n&(1)^{n-1}(ax)^1\\\\ 3&+\frac{n\cdot (n-1)}{2}&(1)^{n-2}(ax)^2 \end{array}[/tex]

so, following that to get the next coefficient, we get those equivalents as you see there for the 2nd and 3rd terms.

so then, we know that the expanded 2nd term is 24x therefore

[tex]\bf n(1)^{n-1}(ax)1 = 24x\implies n(1)(ax)=24x\implies nax=24x\implies n=\cfrac{24}{a}[/tex]

we also know that the expanded 3rd term is 240x², therefore we can say that

[tex]\bf \cfrac{n(n-1)}{2}~~(1)^{n-2}(ax)^2 = 240x^2\implies \cfrac{n(n-1)}{2}(1)(a^2x^2) = 240x^2 \\\\\\ \cfrac{(n^2-n)(a^2x^2)}{2}=240x^2\implies \cfrac{(n^2-n)(a^2)}{2}=\cfrac{240x^2}{x^2}\implies \cfrac{a^2n^2-a^2n}{2}=240 \\\\\\ a^2n^2-a^2n=480[/tex]

but but but, we know what "n" equals to, recall above, so let's do some quick substitution

[tex]\bf a^2n^2-a^2n=480\qquad \boxed{n=\cfrac{24}{a}}\qquad a^2\left( \cfrac{24}{a} \right)^2-a^2\left( \cfrac{24}{a} \right)=480 \\\\\\ a^2\cdot \cfrac{24^2}{a^2}-24a=480\implies 24^2-24a=480\implies 576-24a=480 \\\\\\ -24a=-96\implies a=\cfrac{-96}{-24}\implies \blacktriangleright a = 4\blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ n=\cfrac{24}{a}\implies n=\cfrac{24}{4}\implies \blacktriangleright n=6 \blacktriangleleft[/tex]

Answer:

(y + 6)(4u + a)

Step-by-step explanation:

Given

4u(y + 6) + a(y + 6) ← factor out (y + 6) from each term

= (y + 6)(4u + a) ← in factored form

The scale factor is obviously 7, because the 28 divided by 4 equals 7.

This means that the larger octagon's perimeter will be 7 times the smaller octagon's perimeter.

So 34 * 7 = 238.

To find the perimeter of a larger octagon, add up the lengths of all its sides. The formula for finding the perimeter of any regular polygon is P = ns, where P is the perimeter, n is the number of sides, and s is the length of one side.

An octagon is a polygon with 8 sides. To find the perimeter of an octagon, you need to add up the lengths of all its sides. If you know the length of one side of the octagon, you can multiply it by 8 to get the perimeter. For example, if the length of one side is 5 cm, the perimeter of the octagon would be 5 cm x 8 = 40 cm.

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[tex]1.999999\inf[/tex]

So adding a rational number, like 2, it would be irrational still:

[tex]2+1.999999\inf=3.999999\inf[/tex]

That being said, answer C is wrong

Now, what is 2/2? Or 4/1? Whole numbers are one of the 3 types of rational numbers.

[tex]2\ /\ 2=1\\\\4\ / 1=\ 4[/tex]

Thus the answer appears to be D

Now lets use the process of elimination to double check the answer:

The wording of your question is what will help us out here:

Which of the statements using operations on rational or irrational numbers always results in a rational number?

Because of that, any of the choices that involve a irrational number can result with another irrational number like so:

[tex]a)\ 1.999\inf+ 1.999\inf=3.888\inf\\\\b)\ 2.999\inf / 1.999\inf= 1.50025\inf[/tex]

And there you go, the only answer that hasn't been proven wrong is answer D.

The statement using operations on rational or irrational numbers always results in a rational number is d) rational ÷ rational​.

We know all the real can be subdivided into two parts one is rational numbers and the other is an irrational number.

Rational numbers are those numbers that have repeating or terminating digit patterns after the decimal place and irrational numbers are those numbers that do not have this property.

a) irrational + irrational is an irrational number, √3 + √3.

b) irrational ÷ irrational is sometimes rational and sometimes irrational,

√3 ÷ √3 = 1 but √6 ÷ √3 = √2.

c) rational + irrational is always an irrational number.

d) rational ÷ rational is always a rational number.

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Answer:

A. all three rectangular faces have the same surface area

B. the surface area of each rectangular face is  [tex]66\ cm^{2}[/tex]

D. the surface area of one base is [tex]15.6\ cm^{2}[/tex]

Step-by-step explanation:

Verify each statement

case A) all three rectangular faces have the same surface area

The statement is true

Because, the equilateral triangle has the three equal sides and the three equal internal angles.

case B) the surface area of each rectangular face is  [tex]66\ cm^{2}[/tex]

The statement is true

Because, the area of each rectangular face is equal to

[tex]6(11)=66\ cm^{2}[/tex]

case C) the combined surface area of both bases is greater than the surface area of one rectangular face

The statement is False

Because

The combined surface area of both bases is [tex]2[\frac{1}{2}(6)(5.2)]=31.2\ cm^{2}[/tex]

The surface area of one rectangular face is [tex]66\ cm^{2}[/tex]

therefore

[tex]31.2\ cm^{2}< 66\ cm^{2}[/tex]

case D) the surface area of one base is [tex]15.6\ cm^{2}[/tex]

The statement is True

Because

The surface area of one base is [tex]\frac{1}{2}(6)(5.2)=15.6\ cm^{2}[/tex]

C.

D.

B.

C.

A.

D.

C.

C.

B.

A. B. and D.

This is the whole practice! 100% percent!

Have an amazing day! :):)

Answer:

y=cos(0.4x)

Step-by-step explanation:

Answer:

The equation of the graph given is:

                  [tex]y=\cos(0.4x)[/tex]

Step-by-step explanation:

Clearly from the graph of the function that is provided to us we see that the graph repeats itself after every 5π.

i.e. the period of the function is: 5π.

Now we will check in each of the given options whose period is 5π.

We know that the period of a cosine function of the type:

[tex]y=cos(bx)[/tex] is given by:

[tex]Period=\dfrac{2\pi}{5}[/tex]

1)

[tex]y=\cos(\dfrac{x}{0.4})[/tex]

The period of this function is:

[tex]Period=\dfrac{2\pi}{\dfrac{1}{0.4}}\\\\\\Period=0.8\pi\neq 5\pi[/tex]

Hence, option: 1 is incorrect.

2)

[tex]y=\cos (5x)[/tex]

The period of this function is:

[tex]Period=\dfrac{2\pi}{5}\\\\\\Period=\dfrac{2}{5}\pi\neq 5\pi[/tex]

Hence, option: 2 is incorrect.

4)

[tex]y=\cos (\dfrac{x}{5})[/tex]

The period of this function is:

[tex]Period=\dfrac{2\pi}{\dfrac{1}{5}}\\\\\\Period=10\pi\neq 5\pi[/tex]

Hence, option: 4 is incorrect.

3)

[tex]y=\cos(0.4x)[/tex]

The period of this function is:

[tex]Period=\dfrac{2\pi}{0.4}\\\\\\Period=5\pi[/tex]

        Hence, option: 3 is the correct option.

Answer:

5

Step-by-step explanation:

17x -8x -9 = 76 - 40

17x -8x  = 76 - 40 + 9

9x = 45

x = 45/9

x=5

Answer:

x = 5

Step-by-step explanation:

17x - 8x - 9 = 76 - 40

       9x - 9 = 36

               +9  +9

              9x = 45

              /9     /9

               x = 5

Answer:

V = 321 m^3

Step-by-step explanation:

Volume of a sphere

V = 4/3 pi r^3

The radius is equal to

r = d/2

r = 8.5/2 =4.25

V =4/3 (3.14) (4.25)^3

V =321.3920833 m^3

Rounding to the nearest whole number

V = 321 m^3

Answer:

V = 321 m^3

V = 4/3 pi r^3      diameter is double of radius (radius is half of diameter)

V = 4/3 pi (4.25)^3

V= 75.66 meters squared (rounded)

Answer:

-3.5

Step-by-step explanation:

Remember that mean is the average.

Add all 4 numbers together and divide them by 4.

-9 + -8 + 4 + -1 = -14

-14/4 = -3.5

The expression equivalent to 8x - 12y + 32 is 4(2x - 3y + 8) after factorization by the greatest common factor.

To find an expression equivalent to 8x - 12y + 32, we can primarily factor by finding common factors in this expression. One of the significant aspects in factorizing expressions is searching for the greatest common factor which is 4 in this case. We divide each term in the expression by the greatest common factor to obtain the equivalent expression.

So, "4(2x - 3y + 8) is an equivalent expression to 8x - 12y + 32".

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There are 6 numbers on a die.

The probability of rolling a 6 would be 1/6 for each time you roll the die.

Multiply the number of rolls by 1/6.

30 rolls x 1/6 probability = 5 times.

The answer is B. 5

Answer:

58.6

Step-by-step explanation:

To find the area of the figure by splitting it into two shapes - a trapezoid and a rectangle.

The area of a rectangle is A = b*h where b = 8 and h = 4.

So the area is A = 8*4 = 32

The area of a trapezoid is A = 1/2 (a+b)h where a = 8 and b = 5.3 and h = 4.

So the area is A = 1/2(8+5.3)*4 = 1/2(13.3)(4) = 26.6.

The area of the whole figure is these two areas added together.

32 + 26.6 = 58.6

The cost of 4 notebooks should be 24.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio.

Given that,

Price of 2 notebooks = $12

Price of 3 notebooks = $18

And the price of 5 notebooks = $30

To determine the price of 4 notebooks,

First find the price of 1 notebook = 12 / 2 = 6

The price of 4 notebooks = 6 x 4 = 24

The required price of 4 notebooks is $24.

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Answer:    

3.78 cubic yards or just 4 to make things simple.

20 x 30 = 600 sqft x .17 or (2/12) = 102 cubic feet / 27 (cubic feet in a yard) = 3.78 cubic yards

Step-by-step explanation:

To cover a 27 ft by 34 ft garden with a 2 inch thick layer of topsoil, we would need approximately 5.75 cubic yards of topsoil from the store.

This question involves understanding dimensions and volume. In this case, the dimensions of the garden are given in feet (27 ft by 34 ft), and the desired thickness of the topsoil is 2 inches, which is approximately 0.167 feet. To calculate the volume in cubic feet, we multiply the length, width, and height.

The formula to calculate volume is: Volume = Length * Width * Height.

So, Volume = 27 ft * 34 ft * 0.167 ft = 153.234 cubic feet

Now, to convert this volume into cubic yards (since the store sells soil in cubic yards), we use the fact that 1 cubic yard = 27 cubic feet.

So, Volume = 153.234 cubic feet / 27 = approximately 5.676 cubic yards.

Given that the store only sells in increments of 1/4 cubic yards, we will need to round 5.676 up to the nearest quarter yard. This gives us 5.75 cubic yards.

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Answer:

x=3

Step-by-step explanation:

93x-92x=2+1

x=3

Answer:

x=3

Step-by-step explanation:

i did in edge right now

Answer:

since we dont know the variable it isnt very easy to anser..

Step-by-step explanation:

Lets assume the variable is V okay?

5 time we know times means multiplication so

5 x

The quotients is division so

5 x V divided 10

Answer:

use pythagorean theroem lol a²+b²=c²

Answer:

I think the answer would be 4.5 miles

Step-by-step explanation:

➷ 1st side = x - 3

2nd side = x

3rd side = x - 1

Form an equation:

x - 3 + x + x - 5 = 28

Simplify:

3x - 8 = 28

Add 8 to both sides:

3x = 36

Divide both sides by 3:

x = 12

first length = 12 - 3 = 9 inches

second length = 12 inches

third length = 12 - 5 = 7 inches

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Answer: Any number times zero is zero, it can never equal something else.

Step-by-step explanation: My teacher taught me this before so i know :)

The statement is false.

Statement given,

Any number raised to the power of zero is zero.

The following statement is false, as, any number raised to the power of zero is one always. Thus,

[tex]\bold{x^0 =1}[/tex],

where x is any real number, except zero.

So, x is defined for any number except 0.

Hence, the statement is false.

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Answer - No because a door is around 5 feet

Answer:

Step-by-step explanation:

7.8 is the distance from n to lm

Answer:

E. 7.8

Step-by-step explanation:

We have been given an image of a triangle and we are asked to find the distance from point N to line LM.

We can see that NO is the altitude for our given triangle, so the distance from point N to line LM will be equal to length of segment NO.

We can see from our given attachment that length of segment NO is 7.8 units, therefore, option E is the correct choice.

Answer:

= 0.75

Step-by-step explanation:

-3x-9+15x = 0

12x = 9

x = 3

4

= 0.75

Hey there!

The answer is 12x - 9

Hope this helps you!

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xXxGolferGirlxXx

Answer:  √y  

Step-by-step explanation:

[tex]\sqrt[6]{y^3}=y^{\frac{3}{6}}=y^{\frac{1}{2}}=\boxed{\sqrt y}[/tex]

The mathematical formula to solve this is :

f(n)= f1 + (n-1)d

We have:f(n)= 11 + (n-1)-4

f(n)= 11 -4n +4

f(n)=15 -4n

The right answer is D.

Answer:

Step-by-step explanation:

you have to make 4 rows and 36 column then solve 36 divided by 4=9

Answer:

The area of the parallelogram is 117.

Step-by-step explanation:

You do 9x13= area

9x13=  117

Answer:

Debit card

Step-by-step explanation:

Got it right on TTM

Answer:

Debit card

Step-by-step explanation:

Hope this helps :)

Answer:

54 I think

Step-by-step explanation:

I just did 15 divided by 9 and got 5/3 and then did 90 divided by 5/3 and got 54

Final answer:

To find out how many sandwiches would have to be sold for 90 of the total number of sandwiches to be club sandwiches, set up a proportion using the given information: 9 club sandwiches out of 15 total sandwiches is equal to 90 club sandwiches out of x total sandwiches. Solve for x to find that 150 sandwiches would need to be sold in total for 90 of them to be club sandwiches.

Explanation:

To find out how many sandwiches would have to be sold for 90 of the total number of sandwiches to be club sandwiches, we can set up a proportion using the information given.

First, we know that out of the first 15 sandwiches sold, 9 were club sandwiches. This can be written as a ratio:

9 club sandwiches / 15 total sandwiches = 90 club sandwiches / x total sandwiches

Cross-multiplying, we get 9x = 90 * 15

Dividing both sides by 9, we find that x = 150

Therefore, if 150 sandwiches are sold, 90 of them would be club sandwiches.