How do I solve x+1/x-1 >0

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:

210

Step-by-step explanation:

The general formula for picking k items from a total of n is

[tex]_{n}C_{k} = \frac{n! }{(n-k)!k! }[/tex]

Thus, if we want to select a committee of six people from a club with 10 members, the number of combinations is

[tex]_{10}C_{6} = \frac{10! }{(10-6)!6! }[/tex]

[tex]= \frac{10! }{4!6! }[/tex]

[tex]= \frac{10\times9\times8\times7}{4\times3\times2\times1 }[/tex]

[tex]= \frac{5040 }{24 }[/tex]

= 210

The committee can be selected in 210 separate ways.

Answer:

11.7

Step-by-step explanation:

Using the cosine ratio, then

cos40° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{9}{h}[/tex]

Multiply both sides by h , the hypotenuse

h × cos40° = 9 ( divide both sides by cos40° )

h = [tex]\frac{9}{cos40}[/tex] ≈ 11.7 ( to the nearest tenth )

Answer:

I think the answer would be to divide the inches by 4.  So Length would be 3.5 inches and width would be 1.25 inches . I might be wrong but if you have no hope I would go with my answer.

Step-by-step explanation:

Answer:

lenght: 3.5 inches.

width: 1.25 inches.

Step-by-step explanation:

You have the following information:

- The drawing must be 1/4  the size of the original drawing.

- The tree in the original drawing is 14 inches tall and 5 inches wide.

Therefore, keeping the above on mind, you can find the length and width of the tree in Barry's drawing by multiplying the original dimensions by 1/4.

Then, you obtain the result shown below:

[tex]lenght=\frac{1}{4}*14in=3.5in\\\\width=\frac{1}{4}*5in=1.25in[/tex]

Answer:

[tex]6^{\frac{7}{3} }[/tex]

Step-by-step explanation:

Using the rules of exponents

• [tex]\sqrt[n]{a^{m} }[/tex] ⇔ [tex]a^{\frac{m}{n} }[/tex]

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]

Hence

[tex]\sqrt[3]{6}[/tex] = [tex]6^{\frac{1}{3} }[/tex] and

6² × [tex]6^{\frac{1}{3} }[/tex] = [tex]6^{\frac{7}{3} }[/tex]

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!

God bless ❤️

xXxGolferGirlxXx

Answer:

the blue one is 1/2 and the red one is 1/4

Step-by-step explanation:

count the bricks and put a "1/" in front of the number of bricks and... BOOM you have your answer

Answer:

f(x)+1 = x^2 + 1

Step-by-step explanation:

The graph of f(x)+1 will be given by adding 1 to the initial function f(x)

f(x)+1 = x^2 + 1

See the attachment for the graph;

[tex] - 7 {v}^{2} - 25v - 12 \\ = - 7 {v}^{2} - 21v - 4v - 12 \\ = - 7 v (v + 3) - 4(v + 3) \\ = ( - 7v - 4)(v + 3) \\ = - (7v + 4)(v + 3)[/tex]

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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➷ Substitute it into the equation:

3 = 2x + 5

Subtract 5 from both sides:

-2 = 2x

Divide both sides by 2:

x = -1

The other coordinate is -1

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

-1

Step-by-step explanation:

1.We know that the equation of the line is y=2x+5 ( with a gradient of 2 and a

y-intercept of 5) and the y coordinate is 3 so we must work out x (x,3).

2.We know y=3 so

3 = 2x+5

3. Solve the equation

3=2x+5

(-5 from both sides)

-2=2x

(Divide both sides by 2 to isolate x)

-1 = x so x = 1

Hope this helps:)

5INGH

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:

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

➷ 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

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

Step-by-step explanation:

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

There are 7040 yards in 4 miles

Answer:

there is 7040 yards in 4 miles

Step-by-step explanation:

1) 1 Miles = 1760 yards

2) just multiply 1760 times 4 because one Miles is 1760 yards

1760 x 4 = 7040 yards

4 represents miles

Hopes this helps!

Answer:

Part A: 379.94

Part B: 254.34

Part C: 125.6

Step-by-step explanation:

The are for the area of a circle is A = Pi*r^2

So for part A, do

A = 3.14 * 11^2

A = 3.14 * 121

A = 379.94

Same thing for Part B, just change the radius:

A = 3.14 * 9^2

A = 3.14 *81

A= 125.6

And for Part C, Subtract the area of the smaller from the area of the larger circle:

379.97 - 254.34 = 125.6

Answer:

I'm just answering this so that you can give them brainlest

Step-by-step explanation: Have a good day

Answer:

an = -8 +3(n-1)

an = -11 +3n

f(n) = -11 +3n

Step-by-step explanation:

–8, –5, –2, 1, 4, ...

This is an arithmetic sequence.

We are increasing by 3 each time

-8 +3 = -5

-5+3 = -2

-2 +3 = 1

The common difference is 3

The formula for an arithmetic sequence is

an = a1 +d (n-1)

an = -8 +3(n-1)

an = -8 +3n -3

an = -11 +3n

The nth term is -11 +3n

f(n) = -11 +3n

D. an = an-1+3; a1 = -8

EG. 2020

Answer:

b

Step-by-step explanation:

Answer:

a. [tex]8^{8}\sqrt{8}[/tex]

Step-by-step explanation:

The given expression is

[tex]\sqrt{8^{17}}[/tex]

We rewrite the radicand to obtain;

[tex]\sqrt{8^{16}\times 8}[/tex]

Split the radicand;

[tex]\sqrt{8^{16}}\times \sqrt{8}[/tex]

[tex]\sqrt{(8^{8})^2}\times \sqrt{8}[/tex]

[tex]8^{8}\sqrt{8}[/tex]

Answer:

The answer is A. [-4/3]

For the second part the answer is a rotation 90 CCW about origin

Hope this helped!

Answer:

The correct option is B.

Step-by-step explanation:

From the given graph it is clear the x-coordinate of the vector is 3 and y-coordinate of the vector is 4 in the coordinate plane.

The given vector can be defined as

[tex]A=\begin{bmatrix}3 & 4\end{bmatrix}[/tex]

Translation vector is

[tex]B=\begin{bmatrix}0 & -1\\ 1 & 0\end{bmatrix}[/tex]

We need to find the resulting vector,

[tex]AB=\begin{bmatrix}3 & 4\end{bmatrix}\cdot \begin{bmatrix}0 & -1\\ 1 & 0\end{bmatrix}[/tex]

[tex]AB=\begin{bmatrix}3(0)+4(1) & 3(-1)+4(0)\end{bmatrix}[/tex]

[tex]AB=\begin{bmatrix}4& -3\end{bmatrix}[/tex]

Therefore the correct option is B.

Answer:

y intercept is 1  1/3

equation is y = -1/6x + 4/3

x coordinate is -70  (-70,13)

Step-by-step explanation:

find M

m = 1 - (-1)/ 2 -1 4

m = -2/12 = -1/6

Find y intercept--Plug m and one point from above into y = mx + b

1 = - 1/6 (2) + b

1 = -2/6 + b

1  2/6 = b

1  1/3 = b

4/3 = b

To find the x coordinate if y is 13

13 = -1/6 x + 4/3

11 2/3 = -1/6 x

-70 = x

The y intercept of line AB = [tex](0,\dfrac{4}{3})[/tex]

The equation of line AB will be

[tex] y=\dfrac{-1}{6}x+\dfrac{4}{3}[/tex]

The x-coordinate of C = 4

The slope of line AB with coordinates of A and B are (14, -1) and (2, 1)

[tex]m_1=\dfrac{1-(-1)}{2-14}=\dfrac{2}{-12}=\dfrac{1}{-6}[/tex]

The equation of line AB will be

[tex](y-1)=\dfrac{1}{-6}(x-2)\\\\\Rightarrow y=\dfrac{1}{-6}(x-2)+1\\\\\Rightarrow\ y=\dfrac{-1}{6}x+\dfrac{1}{3}+1\\\\\Rightarrow y=\dfrac{-1}{6}x+\dfrac{4}{3}[/tex]

Put x=0, we get the [tex]y=\dfrac{4}{3}[/tex] i.e. [tex](0,\dfrac{4}{3})[/tex] is the y intercept of line AB.

Since, Line AB and Line BC form a right angle at their point of intersection, B. The the product of their slope must be -1.

Therefore, the slope of BC =[tex]m_2=\dfrac{-1}{m_1}=6[/tex]

Let x coordinate of C be a,then the coordinates of C = (a,13)

Now, slope of BC with points B(2,1) and C(a,13) will be

[tex]\dfrac{13-1}{a-2}=6\\\\\Rightarrow\ a-2=\dfrac{12}{6}\\\\\Rightarrow\ a-1=2\\\\\Rightarrow\ a=4[/tex]

Hence, the x-coordinate of C = 4

Answer:D)78

Step-by-step explanation:70+71+75+75+88+89/6

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.

Answer: $15.92*6= $95.52

$175.72 - $ 95.52= $ 80.20

Step-by-step explanation:

Answer:

[tex]\frac{3}{10}[/tex]

Step-by-step explanation:

step 1

Find the ratio of the height of shape A to the height of shape B

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z-----> the scale factor

x----> surface area shape A

y----> surface area shape B

so

[tex]z^{2} =\frac{x}{y}[/tex]

substitute

[tex]z^{2} =\frac{4}{25}[/tex]

[tex]z =\frac{2}{5}[/tex]

therefore

the ratio of the height of shape A to the height of shape B is equal to

[tex]\frac{hA}{hB}=\frac{2}{5}[/tex]

step 2

Find the ratio of the height of shape B to the height of shape C

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x----> volume shape B

y----> volume shape C

so

[tex]z^{3} =\frac{x}{y}[/tex]

substitute

[tex]z^{3} =\frac{27}{64}[/tex]

[tex]z =\frac{3}{4}[/tex]

therefore

the ratio of the height of shape B to the height of shape C is equal to

[tex]\frac{hB}{hC}=\frac{3}{4}[/tex]

step 3

Find the ratio of the height of shape A to the height of shape C

we have

[tex]\frac{hA}{hB}=\frac{2}{5}[/tex]

[tex]\frac{hB}{hC}=\frac{3}{4}[/tex]

Multiply

[tex](\frac{hA}{hB})(\frac{hB}{hC})=\frac{hA}{hC}[/tex]

so

[tex](\frac{2}{5})(\frac{3}{4})=\frac{6}{20}=\frac{3}{10}[/tex]

In this problem, we're working with the geometric property of similarity to compare the heights and volumes of different shapes. Using the ratios of their surface areas and volumes, we found that the ratio of the height of Shape A to Shape C is 15:8.

In order to solve this problem, it is necessary to first know that, for similar shapes, the ratio of the areas is actually the square of the ratio of the corresponding length measurements (this includes dimensions such as the height). In this particular case, since shapes A and B are similar, the ratio of their surface areas will give the square of the ratio of the heights:

√(25/4) : 1 => 5 : 2

Now, for shapes B and C, we have the volume ratio given as 27 : 64. Since, for similar shapes, the ratio of the volumes is the cube of the ratio of the corresponding length measurements, the cube root of the volume ratio will give the ratio of the heights:

∛(27/64 : 1) => 3 : 4

Using these two ratios, we can find the ratio of height from shape A to shape C by multiplying together the heights of shape A to B and shape B to C: (5/2) * (3/4) => 15 : 8.

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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.

$16 / $80 * 100% = 20%.

$16/$80 *100= 20%

answer is 20%

Answer:

The correct answer is third option

(10x² - 4) - (7x² + 3)

Step-by-step explanation:

From the given option we get the correct answer is  third option.

(10x² - 4) - (7x² + 3)

Check the correct answer

(10x² - 4) - (7x² + 3) = 10x² - 4 - 7x² - 3)

 = 10x² - 7x² - 4 - 3 = 3x² - 7

Therefore the correct answer is third option

(10x² - 4) - (7x² + 3)

The correct answer is C on edg

:)

[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:

Step-by-step explanation:

The general equation for a circle of radius r with center at (h, k) is

(x - h)² + (y - k)² = r²

Here, this equation becomes:

(x - 1)² + (y - 2)² = 3²

Equation of the circle way to represent the circle in the coordinate plane using its center points and the radius. The equation of the circle centered at the point (1,2) and has a radius of length 3 can be given as,

[tex]x^2+y^2-2x-4y-4=0[/tex]

The center point of the given circle is (1,2).

The length of the radius of the circle is 3 units.

Equation of the circle way to represent the circle in the coordinate plane using its center points and the radius.

The standard form of the equation of the circle is,

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Here,

(h,k) is the center of the circle.

[tex]r[/tex] is the radius of the circle.

Put the values given in the problem in the standard form of the equation of the circle. Thus,

[tex](x-1)^2+(y-2)^2=3^2[/tex]

[tex]x^2+1-2x+y^2+4-4y=9[/tex]

[tex]x^2+y^2-2x-4y+5-9=0[/tex]

[tex]x^2+y^2-2x-4y-4=0[/tex]

Thus the equation of the circle centered at the point (1,2) and has a radius of length 3 can be given as,

[tex]x^2+y^2-2x-4y-4=0[/tex]

Learn more about the equation of the circle here;

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