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Pie
2 years ago
11

Simplify y 2 + 11y - 6y + y 2​

Mathematics
1 answer:
Darya [45]2 years ago
6 0

Answer:

y2+5y+2

Step-by-step explanation:

View picture

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100 points!!! Pre calculus. I need helpppppppppp
Fantom [35]

Answer:

We have function,

y = 3 - 6 \sin {}^{} (2x +  \frac{\pi}{2} )

Standard Form of Sinusoid is

y =  - 6 \sin(2x +  \frac{\pi}{2} )  + 3

Which corresponds to

y = a \sin(b(x + c))  + d

where a is the amplitude

2pi/b is the period

c is phase shift

d is vertical shift or midline.

In the equation equation, we must factor out 2 so we get

y =  - 6(2(x +  \frac{\pi}{4} )) + 3

Also remeber a and b is always positive

So now let answer the questions.

a. The period is

\frac{2\pi}{ |b| }

\frac{2\pi}{ |2| }  = \pi

So the period is pi radians.

b. Amplitude is

| - 6|  = 6

Amplitude is 6.

c. Domain of a sinusoid is all reals. Here that stays the same. Range of a sinusoid is [-a+c, a-c]. Put the least number first, and the greatest next.

So using that<em> rule, our range is [6+3, -6+3]= [9,-3] So our range</em> is [-3,9].

D. Plug in 0 for x.

3 - 6 \sin((2(0) +  \frac{\pi}{2} )

3 - 6 \sin( \frac{\pi}{2} )

3 - 6(1)

3 - 6

=  - 3

So the y intercept is (0,-3)

E. To find phase shift, set x-c=0 to solve for phase shift.

x +  \frac{\pi}{4}  = 0

x =  -  \frac{\pi}{4}

Negative means to the left, so the phase shift is pi/4 units to the left.

f. Period is PI, so use interval [0,2pi].

Look at the graph above,

6 0
3 years ago
What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)?
yawa3891 [41]
The equation of circle is:
(x-a)^2+(y-b)^2=r^2 where C(a, b) is the center.
In order to find r you have to find the distance between C(-2, 1) and let's say A(-4, 1)

The formula for distance is:
\sqrt{  ( y_{A}-y_{C )^{2} + (x_{A}- x_{C )^{2} }
r = 2

The equation of circle is
(x+2)^2+(y-1)^2=4

I hope that this is the answer that you were looking for and it has helped you.

5 0
3 years ago
Which statement is true?
spayn [35]

I’m not sure is D , I’m clueless

8 0
3 years ago
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I only need help on number 6 plzzzz help
Gennadij [26K]
That question is asking for the time so your answer will specifically be in hours. And I'm not sure if you divide or you multiply but I'm pretty sure the correct answer is dividing because tomorrow so cancel the miles they will be left with hours. I don't know if that makes sense to you but it kind of makes sense to me somehow.
4 0
3 years ago
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Prove that A is in the subset B if P(A) is in the subset P(B)
natima [27]
Show that if p(a) ⊂ p(b) then a ⊂ b. 

<span>I will assume p() means power set. </span>

<span>proof: let x∈a, then {x} ∈ p(a) and so by hypothesis {x} ∈ p(b). However {x} could not be in p(b) unless x∈b. This shows that each element of a is an element of b and hence a ⊂ b.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
</span>
5 0
3 years ago
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