All categories

3 years ago

Which expression is equivalent to x^8-256

Mathematics

1 answer:

Evgesh-ka [11]3 years ago

3 0

Answer:

$\large\boxed{x^8-256=(x^4+16)(x^2+4)(x+2)(x-2)}$

Step-by-step explanation:

$x^8-256\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=x^{(4)(2)}-16^2=(x^4)^2-16^2\qquad\text{use}\ (a+b)(a-b)=a^2-b^2\\\\=(x^4+16)(x^4-16)=(x^4+16)(x^{(2)(2)}-4^2)\\\\=(x^4+16)\bigg((x^2)^2-4^2\bigg)=(x^4+16)(x^2+4)(x^2-4)\\\\=(x^4+16)(x^2+4)(x^2-2^2)\\\\=(x^4+16)(x^2+4)(x+2)(x-2)$

You might be interested in

A roulette wheel has 38 slots, numbered 0, 00, and 1 to 36. the slots 0 and 00 are colored green, 18 of the others are red, and

sammy [17]

There are 38 slots so P(any 1 slot) = 1/38

6 0

3 years ago

A chemist examines 15 geological samples for potassium chloride concentration. The mean potassium chloride concentration for the

NikAS [45]

Answer:

$0.376-2.145\frac{0.0012}{\sqrt{15}}=0.375$

$0.376+2.145\frac{0.0012}{\sqrt{15}}=0.377$

And we are 95% confident that the true mean of chloride concentration is between 0.375 and 0.377 cc/ cubic meter

Step-by-step explanation:

Data provided

$\bar X=0.376$ represent the sample mean for the chloride concentration

$\mu$ population mean (variable of interest)

s=0.0012 represent the sample standard deviation

n=15 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

Since we need to find the critical value first we need to begin finding the degreed of freedom

$df=n-1=15-1=14$

The Confidence is 0.95 or 95%, the significance would be $\alpha=0.05$ and $\alpha/2 =0.025$ , and the critical value for this case with a t distribution with 14 degrees of freedom is $t_{\alpha/2}=2.145$

And the confidence interval is:

$0.376-2.145\frac{0.0012}{\sqrt{15}}=0.375$

$0.376+2.145\frac{0.0012}{\sqrt{15}}=0.377$

And we are 95% confident that the true mean of chloride concentration is between 0.375 and 0.377 cc/ cubic meter

7 0

3 years ago

Please Help!! what value of b makes the trinomial below a perfect square?

Anna [14]

Remember, you take 1/2 of b and square it to get c

c=100
(b/2)^2=c
(b/2)^2=100
sqrt oth sides
b/2=+/-10
times both sides by 2
b=+/-20
it is 20 or -20

answe ris B
yo is right

4 0

3 years ago

Two of your friends go bowling. One friend rents a pair of bowling shoes for $3 and bowls 3 games. The other friend brings his o

Nesterboy [21]

Answer: The cost of each game is $2.50

Step-by-step explanation:

Let's find the equations for each friend:

Friend 1:

Pays $3 for the shoes, and plays 3 games, then if X is the cost of each game, Friend 1 pays a total of:

$3 + 3*X

Friend 2:

This friend buys a soda for $0.50, and he plays 4 games, remember that the cost of each game was X. then this friend pays:

$0.50 + 4*X

And we know that both friends pay the exact same amount, then we can write:

$3 + 3*X = $0.50 + 4*X

And solve this for X.

We need to isolate X, then we can move all the terms with X to the right, and all the terms without X to the left:

$3 - $0.50 = 4*X - 3*X

$2.50 = (4 - 3)*X = X

This means the cost of each game is $2.50

4 0

2 years ago

An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholde

kherson [118]

Answer:

Step-by-step explanation:

Given that X is the number of months between successive payments

Cumulative distribution function of X is

$F(x) =0, x$

a) PMF of x would be

$P(x) =0, x$

b) $P(3 ≤ X ≤ 6) =0.86-0.44=0.42\\ P(4 ≤ X)=1-0.44=0.56\\P(3 < X < 6) =0.6\\P(4 < X) =1-0.48=0.52$

4 0

2 years ago