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2 years ago

6

Select the correct answer. Which statement is true about this quadratic equation? y=2x^2 + 9x-12 a There is one complex solution

b there are two complex solutions c There is one real solution d There are two real solutions

1 answer:

Yakvenalex [24]2 years ago

5 0

Answer:

There are 2 complex solutions

Step-by-step explanation:

Both imaginary Solutions

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Rewrite with only sin x and cos x.

Annette [7]

Option A

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

<em><u>Solution:</u></em>

Given that we have to rewrite with only sin x and cos x

Given is cos 3x

$cos 3x = cos(x + 2x)$

We know that,

$\cos (a+b)=\cos a \cos b-\sin a \sin b$

Therefore,

$\cos (x+2 x)=\cos x \cos 2 x-\sin x \sin 2 x$ ---- eqn 1

We know that,

$\sin 2 x=2 \sin x \cos x$

$\cos 2 x=\cos ^{2} x-\sin ^{2} x$

Substituting these values in eqn 1

$\cos (x+2 x)=\cos x\left(\cos ^{2} x-\sin ^{2} x\right)-\sin x(2 \sin x \cos x)$ -------- eqn 2

We know that,

$\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x$

Applying this in above eqn 2, we get

$\cos (x+2 x)=\cos x\left(1-2 \sin ^{2} x\right)-\sin x(2 \sin x \cos x)$

$\begin{aligned}&\cos (x+2 x)=\cos x-2 \sin ^{2} x \cos x-2 \sin ^{2} x \cos x\\\\&\cos (x+2 x)=\cos x-4 \sin ^{2} x \cos x\end{aligned}$

$\cos (x+2 x)=\cos x-4 \cos x \sin ^{2} x$

Therefore,

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Option A is correct

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2 years ago

Duffy Duck, If you see this, is Y rational?

oksano4ka [1.4K]

Answer:

i think so

Step-by-step explanation:

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3 years ago

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ratelena [41]

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e^-0.1446t = 0.5

t = ln 0.5 / -0.1446
t = 4.8 days

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3 years ago

Put these in order of size smallest first 60% 0.4 1/2

Ludmilka [50]

.4 is smallest, 1/2 , then 60% is greatest.

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3 years ago

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Which statement is correct about relations and functions?

vitfil [10]

1. all functions are relations.

2.
-7 + 3(-12) ÷ (-3)
-7 - 36 ÷ -3
-7 - (-12)
-7 + 12
5

3.
f(n) = n² - n f(-4)
f(-4) = -4² - (-4)
f(-4) = 16 - (-4)
f(-4) = 16 + 4
f(-4) = 20

hope this helped, God bless!

6 0

2 years ago