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4 years ago

If m(x) =x+5/x-1 and n(x) = x - 3, which function has the same domain as (mºn)(x)?

Mathematics

1 answer:

GREYUIT [131]4 years ago

5 0

We have

M(X) = (X + 5)/(X - 1)

N(X) = X - 3

So,

M(N(X)) = [(X - 3) + 5]/[(X - 3) - 1]

The M(N(X)) domain will be:

D = {X / X ≠ 4}

4 ∉ to the M(N(X)) domain, otherwise we would have a/0, which is not possible (a denominator with zero). An equivalent function would be

H(X) = 1/(X - 4)

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It takes three identical water pumps 8 hours to fill a pool, What is the constant of variation?

BaLLatris [955]

Answer:

Constant of variation is 24.

Step-by-step explanation:

Inverse variation states that a relationship between two variables in which the product is remain constant.

If one variable increases then, the other one decreases in proportion so that the product is unchanged,

if y is inversely proportional to x i.e $y \propto\frac{1}{x}$ or

$y =\frac{k}{x}$ ;where k is the constant of variation.

It is given that 3 identical water pumps takes 8 hours to fill a pool,

since, it will take less time with more pumps, so it is an inverse variation.

By definition of inverse variation;

$time = \frac{k}{pump}$

Substitute the values to solve for k;

$8 = \frac{k}{3}$

Multiply by 3 to both sides we get;

$8 \times 3 = \frac{k}{3} \times 3$

Simplify:

k = 24

Therefore, the constant of variation is, 24

3 0

3 years ago

Solve < 2. {x | x > - } {x | x < - } {x | x > } {x | x < }

solmaris [256]

Unfortunately, solving: < 2. {x | x > - } {x | x < - } {x | x > } {x | x < } is impossible.

5 0

3 years ago

What is the slope intercept equation for this

earnstyle [38]

Answer:

I think that it is (3,2)

hope this helped!!

4 0

4 years ago

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized here.

anastassius [24]

Answer:

There is no difference in the mean number of times men and women send a Twitter message in a day

Zmen = 0.4

Zwomen = 0.2

Step-by-step explanation:

Null hypothesis: There is no difference in the mean number of times men and women send a Twitter message in a day

Alternate hypothesis: There is a difference in the mean number of times men and women send a Twitter message in a day

Z = (sample mean - population mean)/(sd ÷ √n)

Zmen = (25 - 23)/(5÷√1) = 2/5 = 0.4

Zwomen = (30 - 28)/(10÷√1) =2/10= 0.2

For a two tailed test, at 0.01 significance level, the critical value is 2.576

0.2 and 0.4 falls within the region bounded by -2.576 and 2.576, so we fail to reject the null hypothesis

There is no difference in the mean number of times men and women send a Twitter message in a day

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3 years ago

R, S, and T represent the lengths of the three sides of a right triangle. Select the equation that represent the relationship be

Anastaziya [24]

Answer:

a. R 2+ S 2= T 2

Step-by-step explanation:

Is this multiple choice? If not, then I will explain my answer.

I would say that it is R² + S² = T² because, the original pythagorean theorem equation is a² + b² = c².

They are put in an alphabetical order, a, b, c.

R goes first in the alphabet, then S and T. So, that's why I say it is:

R² + S² = T²

I hope this helps! Please tell me if I'm incorrect! Have a great day may God bless you!

(Also, if you have a keyboard like mine, then you can make an exponent 2, by doing alt + 0178 )

² <-or just cut and paste this

5 0

3 years ago