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3 years ago

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Mathematics

1 answer:

sergij07 [2.7K]3 years ago

6 0

A because they all something I forgot but a

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Find all roots given that x = 3 + i is a solution. <br><br> x^4 - 10x^3 + 29x^2 - 10x - 50 = 0

Basile [38]

Answer:

x = 3 + i, x = 3 - i , x = 5 , and x = -1

Step-by-step explanation:

We know that given the polynomial with real coefficients, if x = 3 + i is a root, then x = 3 - i must be another root. These two roots can combine multiplicative factors as shown:

(x - 3 - i) * (x - 3 + i) = (x-3)^2 + 1 = x^2 - 6 x + 9 + 1 = x^2 - 6 x + 10

Then we divide the given polynomial: x^4 - 10x^3 + 29x^2 - 10x - 50 by the quadratic one we just found, and get a perfect division:

{x^4 - 10x^3 + 29x^2 - 10x - 50} / {x^2 - 6 x + 10} = x^2 - 4 x - 5

which can be factored out by grouping as shown below:

x^2 - 4 x - 5 = x^2 - 5 x + x - 5 = x (x - 5) + x - 5 = (x - 5 ) * (x + 1)

then the full factor form of the quartic polynomial given is:

(x - 3 - i) * (x - 3 + i) * (x - 5 ) * (x + 1)

and therefore the associated roots are:

x = 3 + i, x = 3 - i , x = 5 , and x = -1

5 0

3 years ago

Mai biked 5 1/4 miles today, and Noah biked 2 1/2 miles. How many times the length of Noah’s bike ride was Mai’s bike ride?

OlgaM077 [116]

Answer:

The length of Mai's bike ride was 2.1 times the length of Noah's ride.

Step-by-step explanation:

Mai biked 5 1/4 miles today

So he biked, in miles:

$5 + \frac{1}{4} = \frac{5*4 + 1}{4} = \frac{20+1}{4} = \frac{21}{4}$

Noah biked 2 1/2 miles.

So, in miles, he biked:

$2 + \frac{1}{2} = \frac{2*2 + 1}{2} = \frac{4+1}{2} = \frac{5}{2}$

How many times the length of Noah’s bike ride was Mai’s bike ride?

We divide the Mai distance by Noah's distance. In a division of fractions, we multiply the numerator by the inverse of the denominator. So

$\frac{\frac{21}{4}}{\frac{5}{2}} = \frac{21}{4} \times {2}{5} = \frac{21*1}{2*5} = \frac{21}{10} = 2.1$

The length of Mai's bike ride was 2.1 times the length of Noah's ride.

5 0

3 years ago

How can you multiply 1/3 so that the fraction you get you can simplify back to 1/3?

Bingel [31]

Answer:

Step-by-step explanation:

Multiply 1/3 x 1 so you can simplify 1/3 to 1/3 but other wise 2/6 is 1/3 3/9 is 1/3 and etc

6 0

3 years ago

PLEASE HELP Find the area of the rectangle, to the nearest hundredth, with a base of 5 inches and a height = 2.5 inches. Type a

il63 [147K]

Answer:

The area of a rectangle with a width of 5 inches, and a height of 2.5 inches, would have an area 12.5 inches!

Step-by-step explanation:

To find the area of a rectangle, simply multiply the width (W) by the length (L) to find the area (A) of the rectangle.

A = W x L

A = 5 inches x 2.5 inches

A = 12.5 inches

Hope this helps! :)

5 0

3 years ago

Pls answer it right ill brainliest u

Rufina [12.5K]

P=10h is the right one i believe

5 0

3 years ago

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