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2 years ago

Can you help me with 4, 5, 6?I don't even know if number 4 is right.

Mathematics

1 answer:

Lerok [7]2 years ago

4 0

Answer:

see explanation

Step-by-step explanation:

f(- 4) = means what is the value of f(x) when x = - 4

locate x = - 4 on the x- axis, go vertically down to the graph at (- 4, - 1 )

that is f(- 4) = - 1

f(1) means what is the value of f(x) when x = 1

locate x = 1 0n the x- axis, go vertically down to the graph at (1, - 2 )

that is f(1) = - 2

f(x) = - 4 means what is the value of x when f(x) = - 4

locate - 4 on the vertical axis, go across to the right to the graph at (4, - 4 )

that is when f(x ) = - 4 then x = 4

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Which transformation can you use to show that these shapes are congruent?

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Answer:

Rotations, reflections, and translations are isometric. That means that these transformations do not change the size of the figure. If the size and shape of the figure is not changed, then the figures are congruent.

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3 years ago

Rewrite with only sin x and cos x.

Annette [7]

Option A

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

Solution:

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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3 years ago

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3 years ago

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3 years ago

Solve: 3x - 9 = 5(x-3)

Viefleur [7K]

Hi,

$3x - 9 = 5(x-3)\\3x - 9 - 5(x-3)= 0\\3x -9 -5x +15 =0\\6-2x=0\\6=2x\\x=3$

Have a good day.

3 0

3 years ago

Can you help me with 4, 5, 6?I don't even know if number 4 is right.​

Can you help me with 4, 5, 6?I don't even know if number 4 is right.