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Degger [83]
3 years ago
6

At a concession​ stand, three hot dogs and 4 hamburgers cost ​$11.50​; 4 hot dogs and three hamburgers cost $11.25 Find the cost

of one hot dog and the cost of one hamburger.
What is the cost of one hot dog​? ​
Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
7 0

Answer:11.50/4=2.87

2.87×3=8.61

11.25-8.61=2.62

one hamburger$ 2.87

one hot dog $2.64

Step-by-step explanation:

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Step-by-step explanation:

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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

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7 0
3 years ago
AXY Zand AABCare similar triangles. Given the dimensions shown in the diagram, what is the
Lady bird [3.3K]

Answer:

3.528

Step-by-step explanation:

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6 0
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Step-by-step explanation:

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