What is the greatest common factor of x2y and xy2 ?

Which binomial is a factor of x4 − 4x2 − 4x 8?

Anastasy [175]

The given polynomial is

$x^4-4x^2-4x-8$

As this is a fourth degree polynomial, we can not directly use any formula, So here we will use hit and trial method

check whether x=-1 is a zero of the polynomial or not

$(-1)^4-4(-1)^2-4(-1)-8=-7$

Hence x=-1 is not a zero.

Now check whether x=-2 is a zero of the polynomial or not

$(-2)^4-4(-2)^2-4(-2)-8=0$

Hence x=-2 is a zero of the polynomial.

Hence we can re-write the polynomial as

$x^4-4x^2-4x-8=x^4+2x^3-2x^3-4x^2-4x-8\\ \\ =x^3(x+2)-2x^2(x+2)-4(x+2)\\ \\ =(x+2)(x^3-2x^2-4)\\$

Hence the required binomial is (x+2)

6 0

2 years ago

Which expression is equivalent to (x^6y^8)^3\x^2y^2

Damm [24]

Answer:

$\large\boxed{\dfrac{(x^6y^8)^3}{x^2y^2}=x^{16}y^{22}}$

Step-by-step explanation:

$\dfrac{(x^6y^8)^3}{x^2y^2}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=\dfrac{(x^6)^3(y^8)^3}{x^2y^2}=\dfrac{x^{(6)(3)}y^{(8)(3)}}{x^2y^2}=\dfrac{x^{18}y^{24}}{x^2y^2}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=x^{18-2}y^{24-2}=x^{16}y^{22}$

5 0

2 years ago

Read 2 more answers

Rutherford used positively charged particles to investigate the structure of the atom. The results surprised him, and he develop

mel-nik [20]

The answer is (B): A few positive particles bounced back because they were pushed away from the positive center.

3 0

2 years ago

Read 2 more answers

Aiden borrows a book from a public library. He read a few pages on day one. On day two, he reads twice the number of pages than

Fofino [41]

Let the number of pages read on day 1 be = x

Then on day 2 he read twice the pages from day one, it is = 2x

On 3rd day he read 6 pages less than 1st day, it is = x-6

Total pages are = 458

The equation becomes: $x+2x+x-6=458$

$4x-6=458$

$4x=464$

$x=116$

So on the third day, Aiden read $x-6=116-6=110$ pages.

5 0

2 years ago

The time it takes to deliver a pizza (from time of phone call to delivery at door) follows a normal distribution with a mean (µ)

Yuki888 [10]

Answer:

99.87% of the store’s total delivery orders will be delivered to consumers with charge

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 45, \sigma = 5$

If a pizza store’s policy is, "Orders delivered within one hour or they’re free!", what percentage of the store’s total delivery orders will be delivered to consumers with charge?

Within one hour, which is 60 minutes. So this is the pvalue of Z when X = 60.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{60 - 45}{5}$

$Z = 3$

$Z = 3$ has a pvalue of 0.9987

99.87% of the store’s total delivery orders will be delivered to consumers with charge

5 0

2 years ago