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Semenov [28]
2 years ago
12

Subtract the rational expression 1/x^2-x-6 - x/x+2.

Mathematics
1 answer:
Aleksandr [31]2 years ago
4 0

Answer:

Step-by-step explanation:

x² - x -6 = x²  + 2x - 3x - 3*2

            =x(x + 2) - 3(x + 2)

            = (x + 2 )(x - 3)

\frac{1}{x^{2}-x-6}+\frac{x}{x+2}=\frac{1}{(x +2 )(x - 3)}-\frac{x}{x + 2}\\

                      = \frac{1}{(x+2)(x-3)}-\frac{x(x-3)}{(x+2)(x-3)}\\\\=\frac{1-x(x-3)}{(x+2)(x-3)}\\\\=\frac{1-x^{2}+3x}{(x+2)(x-3)}\\\\

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Determine the lengths of the sides of the rectangle using the given area. Give answers both exactly and
Degger [83]

Answer:

Part a) Exactly values

The width of the rectangle is \frac{\sqrt{70}}{2}\ cm

The length of the rectangle is 2\sqrt{70}\ cm

Part b) Approximately values

The width of the rectangle is 4.2\ cm

The length of the rectangle is 16.7\ cm

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The area of rectangle is equal to

A=LW

we have

L=4x\ cm\\W=x\ cm

substitute the values in the formula

A=4x(x)

A=4x^2

A=70\ cm^2

so

70=4x^2

Solve for x

Divide by 4 both sides

\frac{70}{4}=x^2

square root both sides

x=(+/-)\frac{\sqrt{70}}{2}

The solution is the positive value

x=\frac{\sqrt{70}}{2}

therefore

<em>Exactly values</em>

L=4\sqrt{70}}{2}=2\sqrt{70}\ cm\\\\W=\frac{\sqrt{70}}{2}\ cm

<em>Approximately values</em>

L=4\sqrt{70}}{2}=16.7\ cm\\\\W=\frac{\sqrt{70}}{2}=4.2\ cm

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Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.
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For a binomial experiment in which success is defined to be a particular quality or attribute that interests us, with n=36 and p as 0.23,  we can approximate p hat by a normal distribution.

Since n=36 , p=0.23 , thus q= 1-p = 1-0.23=0.77

therefore,

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n*q = 36*0.77=27.22>5

and therefore, p hat can be approximated by a normal random variable, because n*p>5 and n*q>5.

The question is incomplete, a possible complete question is:

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

Suppose n = 36 and p = 0.23. Can we approximate p hat by a normal distribution? Why? (Use 2 decimal places.)

n*p = ?

n*q = ?

Learn to know more about binomial experiments at

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