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2 years ago

9

The polynomials P(x)=x^3−x−2 and Q(x)=x^2+2x+1 are multiplied and the result is completely simplified.

1 answer:

GarryVolchara [31]2 years ago

6 0

Answer:

C. 2x^4; E. -5x

Step-by-step explanation:

P(x) = x^3 − x − 2 and Q(x) = x^2 + 2x + 1

P(x) * Q(x) = (x^3 − x − 2)(x^2 + 2x + 1) =

= x^5 + 2x^4 + x^3 - x^3 - 2x^2 - x - 2x^2 - 4x - 2

= x^5 + 2x^4 - 4x^2 - 5x - 2

Answer: C. 2x^4; E. -5x

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3 years ago

Please solve 5 f <br> (Trigonometric Equations)<br> #salute u if u solved it

Zanzabum

Answer:

$\beta=45\degree\:\:or\:\:\beta=135\degree$

Step-by-step explanation:

We want to solve $\tan \beta \sec \beta=\sqrt{2}$ , where $0\le \beta \le360\degree$ .

We rewrite in terms of sine and cosine.

$\frac{\sin \beta}{\cos \beta} \cdot \frac{1}{\cos \beta} =\sqrt{2}$

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Use the Pythagorean identity: $\cos^2\beta=1-\sin^2\beta$ .

$\frac{\sin \beta}{1-\sin^2\beta}=\sqrt{2}$

$\implies \sin \beta=\sqrt{2}(1-\sin^2\beta)$

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$\implies \sqrt{2}\sin^2\beta+\sin \beta- \sqrt{2}=0$

This is a quadratic equation in $\sin \beta$ .

By the quadratic formula, we have:

$\sin \beta=\frac{-1\pm \sqrt{1^2-4(\sqrt{2})(-\sqrt{2} ) } }{2\cdot \sqrt{2} }$

$\sin \beta=\frac{-1\pm \sqrt{1^2+4(2) } }{2\cdot \sqrt{2} }$

$\sin \beta=\frac{-1\pm \sqrt{9} }{2\cdot \sqrt{2} }$

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When $\sin \beta=\frac{\sqrt{2}}{2}$ , $\beta=\sin ^{-1}(\frac{\sqrt{2} }{2} )$

$\implies \beta=45\degree\:\:or\:\:\beta=135\degree$ on the interval $0\le \beta \le360\degree$ .

When $\sin \beta=-\sqrt{2}$ , $\beta$ is not defined because $-1\le \sin \beta \le1$

4 0

3 years ago

F(t)=212-6t<br>what is the value of t when F (t) = 140?<br><br>

Sladkaya [172]

Answer: -628

Step-by-step explanation:

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8 0

3 years ago

Can someone please help??

Vsevolod [243]

Answer:

let the number of cows = x

let the number of chickens = y

since there are 42 heads:

x + y = 42

and since a cow has 4 legs, and a chicken has 2

4x + 2y = 144

from first equation:

x + y = 42

x = 42 - y (now, we will substitute this in the second equation)

4(42 - y) + 2y = 144

168 - 4y + 2y = 144

2y = 168 - 144

2y = 24

y = 12

now, we know the number of chickens. we will replace y with 12 in the first equation since it is more simpler

x + 12 = 42

x = 30

So, there are 30 cows and 12 chickens

Brainly it if you find the answer helpful

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