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Mathematics

1 answer:

kotykmax [81]3 years ago

4 0

Answer:

Step-by-step explanation:

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How do you solve this? (#11/#12)

zepelin [54]

$\text{If}\ x_1,\ \text{and}\ x_2\ \text{are zeros of a polynomial function, then the function}\\\text{has equation}:\\\\f(x)=a(x-x_1)(x-x_2).\\----------------------------\\\\11.\ \text{We have the zeros}\ 3\ \text{and}\ i:\\\\f(x)=(x-3)(x-i)=(x)(x)+(x)(-i)+(-3)(x)+(-3)(-i)\\\\=x^2-xi-3x+3i=\boxed{x^2-(3+i)x+3i}\\\\12.\ \text{We have the zeros}\ -2\ \text{and}\ 2i:\\\\f(x)=(x-(-2))(x-2i)=(x+2)(x-2i)\\\\=x^2-(2i)^2=x^2-2^2i^2=x^2-4(-1)=\boxed{x^2+4}\\\\\text{used}\\\\(a-b)(a+b)=a^2-b^2\\\\i=\sqrt{-1}\to i^2=-1$

3 0

3 years ago

Xerxes, Murray, Norah, Stav, Zeke, Cam, and Georgia are invited to a dinner party. They arrive in a random order and all arrive

Nikolay [14]

Answer:

0.143

Step-by-step explanation:

From counting principle, we can say that:

There are 7! ways of the 7 people to arrive first. Any one of them can come first. But, what is the probability that Xerxes with arrive first?

We take that Xerxes is the first one to arrive, then from the 7 - 1 = 6 remaining people, they can arrive in 6! ways. So

Probability Xerxes arrives first = 6!/7! = 0.1429

Rounding to 3 decimal places, it will be:

<u>Probability Xerxes arrives first = 0.143</u>

7 0

3 years ago

Which sentence is true about an angle? A.an angle is formed by two lines that do not cross each other. B.An angle is formed at t

gayaneshka [121]

I believe that the answer is c. An angle forms by two,rays that share the same endpoint. Hope this helps

7 0

4 years ago

PS: WILL GIVE BRANLIEST

Luba_88 [7]

I'm pretty sure it a 3 to 8 and 32 to 12

6 0

3 years ago

Read 2 more answers

Find all solutions to cosx cos3 x-sinx sine3x= 0 on the interval {0,2pi}

fomenos

$\bf \textit{Sum and Difference Identities}
\\ \quad \\
sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}})
\\ \quad \\
sin({{ \alpha}} - {{ \beta}})=sin({{ \alpha}})cos({{ \beta}})- cos({{ \alpha}})sin({{ \beta}})
\\ \quad \\
\boxed{cos({{ \alpha}} + {{ \beta}})= cos({{ \alpha}})cos({{ \beta}})- sin({{ \alpha}})sin({{ \beta}})}
\\ \quad \\
cos({{ \alpha}} - {{ \beta}})= cos({{ \alpha}})cos({{ \beta}}) + sin({{ \alpha}})sin({{ \beta}})\\\\
------------------------$

$\bf cos(x)cos(3x)-sin(x)sin(3x)=0\implies cos(x+3x)=0
\\\\\\
cos(4x)=0\implies cos^{-1}[cos(4x)]=cos^{-1}(0)\implies 4x=cos^{-1}(0)
\\\\\\
4x=
\begin{cases}
\frac{\pi }{2}\\\\
\frac{3\pi }{2}
\end{cases}\implies 
\begin{cases}
4x=\cfrac{\pi }{2}\implies &\measuredangle x=\cfrac{\pi }{8}\\\\
4x=\cfrac{3\pi }{2}\implies &\measuredangle x=\cfrac{3\pi }{8}
\end{cases}$

5 0

3 years ago