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3 years ago

A polynomial has one root that equals 2+i.Name one other root of this polynomial.

Mathematics

2 answers:

weeeeeb [17]3 years ago

8 0

2-i. Complex roots always come in pairs (complex conjugates)

andrew11 [14]3 years ago

4 0

ANSWER

One other root of this polynomial is
$2 - i$

EXPLANATION

One property of the complex root of a polynomial is the conjugate root property.

If one root of a polynomial is
$a + bi$
then the conjugate is also a root of this polynomial.

The conjugate of
$a + bi$
is
$a - bi$

Also the conjugate of
$a - bi$

is
$a + bi$

Therefore if
$2 - i$
is a root of the polynomial, then its complex conjugate
$2 + i$
is also a root of that polynomial.

The same applies to purely imaginary complex roots too.

Thus, if
$bi$
is a root then its conjugate
$- bi$
is also a root.

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A rectangle has a perimeter of 26 units. The length of the rectangle is 2X+3 and the width is 3X. What is the width of the recta

densk [106]

Answer:

X = 2

Step-by-step explanation:

Divided 26 (total perimeter) by 4 = maximum side length possible = 26÷4 =.6.5

I used the trial and error technique

Guessed it was 2 working out to see if i was right or wrong:

Length: 2(2) + 3 = 4+3 = 7

Width: 3(2) = 6

7+7+6+6 = 26

Therefore X = 2

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3 years ago

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3 years ago

If Upper X overbar equals 62, Upper S equals 8, and n equals 36, and assuming that the population is normally distributed, c

marishachu [46]

Answer:

The 99% confidence interval would be given by (58.373;65.627)

We are 99% confident that the true mean for the variable of interest is between 58.373 and 65.627.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=62$ represent the sample mean

$\mu$ population mean (variable of interest)

s=8 represent the sample standard deviation

n=36 represent the sample size

Part a: 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)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=36-1=35$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,35)".And we see that $t_{\alpha/2}=2.72$

Now we have everything in order to replace into formula (1):

$62-2.72\frac{8}{\sqrt{36}}=58.373$

$62+2.72\frac{8}{\sqrt{36}}=65.627$

So on this case the 99% confidence interval would be given by (58.373;65.627)

We are 99% confident that the true mean for the variable of interest is between 58.373 and 65.627.

3 0

3 years ago

Find the area of the shaded region

Basile [38]

Answer:

16 square units

Step-by-step explanation:

→ Find the area of the whole triangle

0.5 × ( 5 + 4 ) × 8 = 36

→ Find the area of the small triangle

0.5 × 5 × 8 = 20

→ Minus the area's of the triangles

36 - 20 = 16 square units

6 0

3 years ago

Aaron has a triathlon. Sunday he bikes 12 5/8 miles and swims 5 2/3 miles. Monday, he runs 6 3/8 miles. How many total miles Aar

Alla [95]

Let’s put these into one fraction each:

Biking:
= (12*5)/8 miles
= 60/8 miles
This can be reduced to,
= 15/2 miles

Swimming:
= (5*2)/3 miles
= 10/3 miles

Running:
= (6*3)/8 miles
= 18/8 miles
This can be reduced to,
= 9/4

Now we add all the distances up:
= (15/2) + (10/3) + (9/4)

Now we just can add the numerators and the denominators. We must find the lowest common factor (LCF) for our 3 denominators (2,3,4). Our LCF turns out to be 12. *Remember what we do to the denominator we must do to the numerator. So:
= (15/2) + (10/3) + (9/4)
= [(15*6)/12] + [(10*4)/12] + [(9*3)/12]
= (90/12) + (40/12) + (27/12)
= (157/12)
Therefore Aaron Ran 157/12 miles or 13.08 miles.

Hope this helps!

4 0

3 years ago