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alex41 [277]
3 years ago
9

Is x^4-1 a factor of P(x)=x^5+5x^4-x-5

Mathematics
1 answer:
sasho [114]3 years ago
7 0

Answer:

  yes

Step-by-step explanation:

The other factor is (x+5), so the product is ...

  (x^4 -1)(x +5) = x^5 +5x^4 -x -5 = P(x)

(x^4 -1) is a factor of P(x).

_____

It is not a <em>primitive</em> factor, because it can be factored as ...

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

The complete factorization of P(x) to real numbers is ...

  P(x) = (x -1)(x +1)(x +5)(x^2 +1)

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A nanometer (nm) is 10⁻⁹ m.

Therefore
10⁶ x 1 nm = 10⁶(10⁻⁹ m) = 10⁻³ m

By definition,
10⁻³ m = 1 mm (millimeter)

Answer: 1 millimeter
8 0
3 years ago
An estimated regression equation that was fit to estimate ductility in steel using its carbon content was found to be significan
AnnZ [28]

Answer:

At a level of 95%, it is expected that the interval [0.45; 11.59] contains the value of the ductility in steel when its carbon content is 0.5%.

Step-by-step explanation:

Hello!

Considering the dependent variable:

Y: Ductility in steel.

And the independent variable:

X: Carbon content of the steel.

The linear regression was estimated and a prediction interval was calculated.

The prediction interval is calculated to predict a value that the variable Y (response variable) can take for a given value of the variable X (predictor variable) in the definition range of the linear regression line. Symbolically [Y/X=x_{0}]

In this case 95% prediction interval for Y/X=0.5

At a level of 95%, it is expected that the interval [0.45; 11.59] contains the value of the ductility in steel when its carbon content is 0.5%.

I hope it helps!

6 0
3 years ago
Linn is making cookies. Each batch of cookies
Pachacha [2.7K]

Answer:

4 cups of sugar require 14 cups of sugar

Step-by-step explanation:

Given

\frac{7}{8}\ cup\ flour = \frac{1}{4}\ cup\ sugar

Required

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First, we need to determine the unit rate for 1 cup of sugar.

This is done by multiplying both sides by 4

4 * \frac{7}{8}\ cup\ flour = \frac{1}{4}\ cup\ sugar * 4

\frac{7}{2}\ cup\ flour = 1\ cup\ sugar

Next, we determine cup of flour for 4 cups of sugar.

This is done by multiplying both sides by 4

4 * \frac{7}{2}\ cup\ flour = 1\ cup\ sugar * 4

2 * 7\ cup\ flour = 4\ cup\ sugar

14\ cup\ flour = 4\ cup\ sugar

<em>Hence;4 cups of sugar require 14 cups of sugar</em>

8 0
3 years ago
2/3 divided by 5 please help me I'm bad at math (it needs to be a fraction)
Viefleur [7K]

Answer:

The answer is 4

Step-by-step explanation: I did the work and it works out like that I hope this helps

3 0
3 years ago
The ages of three cousins are consecutive even whole numbers. The sum of the youngest and oldest is 16. How old is the oldest co
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The oldest cousin should be 10. If their ages are consecutive even whole numbers, then the younger cousins should be 2 & 4. 2+4=6+10=16
4 0
3 years ago
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