Can someone please help me

Find a degree 3 polynomial with real coefficients having zeros 2 and 2 − 2 i and a lead coefficient of 1. Write P in expanded fo

Zanzabum

Answer:

The polynomial with real coefficients having zeros 2 and 2 - 2i is

x³ - 6x² + 16x - 16 = 0

Step-by-step explanation:

Given that a polynomial has zeros at 2 and 2 - 2i, we want to write this polynomial.

We have

x - 2 = 0

x - (2 - 2i) = 0

=> x - 2 + 2i = 0

Since the polynomial has real coefficients, and 2 - 2i is a zero of the polynomial, the conjugate of 2 - 2i, which is 2 + 2i is also a polynomial.

x - (2 + 2i) = 0

=> x - 2 - 2i = 0

Now,

P(x) = (x - 2)(x - 2 + 2i)(x - 2 - 2i) = 0

= (x - 2)((x - 2)² - (2i)²) = 0

= (x - 2)(x² - 4x + 8) = 0

= x³ - 4x² + 8x - 2x² + 8x - 16 = 0

= x³ - 6x² + 16x - 16 = 0

This is the polynomial required.

6 0

3 years ago

The circumference of a circle is 50.24 centimeters. Find the area of the circle. (Use 3.14 for π.)

Usimov [2.4K]

Answer:

help me first

Step-by-step explanation:

5 0

3 years ago

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One of the authors with too much time on his hands weighed each chocolate candy in a bag of 463 plain chocolate candies. Complet

wel

Answer:

a. One of the chocolate candies weighed 0.776 gram and it was heavier than 25 of the other chocolate candies. What is the percentile of this particular value?

It is the 5th percentile.

b. One of the chocolate candies weighed 0.876 gram and it was heavier than 329 of the other chocolate candies. What is the percentile of this particular value?

It is the 71th percentile.

c. One of the chocolate candies weighed 0.856 gram and it was heavier than 229 of the other chocolate candies. What is the percentile of this particular value?

It is the 49th percentile.

Step-by-step explanation:

So when we are talking about percentile, what it means is the point below a certain score or percentage lies, or the rank.

The formula is simple:

Let's call percentile pth, pth= $\frac{p}{100}*(n+1)$

where p is the position in the data set you want to evaluate (in statistical analysis, these are called quartiles, and they are useful for evaluating groups, so 3 quartiles would divide sample into 25th, 50th and 75th, four quartiles would be 20th, 40th, 60th, 80th, and so on).

and n is the number of elements in the set

For this problem there are no quartiles specified, but we can then work with the definition of percentile, meaning, if you are the 5th percentile, then 95% of the group are above you.

a. So 0.776 was heavier than 25 others, meaning it is in the 26th position out of 463. But we need that in relation to 100, so $\frac{26}{463}$ is 0.0562 or about 5/100, (rounded down). That would mean that the percentile is:

pth= $\frac{26}{463}$ *100=5.62 or 5, rounded down

b. 0.876 was heavier than 329 others, meaning it is in the 330th position out of 463. In relation to 100, so $\frac{330}{463}$ is 0.7127 or about 71/100, (rounded down). That would mean that the percentile is:

pth= $\frac{330}{463}$ *100=71.27 or 71, rounded down

c. 0.856 was heavier than 229 others, meaning it is in the 230th position out of 463. In relation to 100, so $\frac{230}{463}$ is 0.4967 or about 49/100, (rounded down). That would mean that the percentile is:

pth= $\frac{230}{463}$ *100=49.67 or 49, rounded down

3 0

4 years ago

A high school booster club is selling raffle tickets for three different prizes. The tickets are $1 for the small prize, $2 for

Ivan

Answer:

x+y+z=15

x+2y+5z=15

-x+y+z=1

Step-by-step explanation:

4 0

3 years ago

CAN SOMEINE PLEASE ANSWER THIS FOR ME TY

kirza4 [7]

Answer:

80 units

Step-by-step explanation:

When a figure is dilated by 2, its side measurements are halved. The figure you're seeing shows the quadrilateral after dilation (we can tell by the apostrophes); if U'R' is 40, UR will have to be 80.

6 0

3 years ago

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