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djverab [1.8K]
3 years ago
8

What is the result when the number 10 is decreased by 5.1%?

Mathematics
1 answer:
SashulF [63]3 years ago
6 0

Answer:

(10/100)*94.9 = 9.49

Step-by-step explanation:

Divide by 100 and multiply by 100-5.1 = 9.49

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Briana buys a ring marked $49.99. She receives a 20% discount. Which equation can be used to find the sale price of the ring?
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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

<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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3 years ago
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Answer:

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Bruce pitches for his little brother's baseball team. He has observed that the number of pitches a batter hits varies and is giv
liberstina [14]
Hello!

If Bruce observes that the number of pitches a batter hits varies and is given by the function f(x)=x-11, and the batters get {4, 12, 14, 27, 42}, then Bruce threw {15, 23, 25, 38, 53} pitches. We get this solution set by adding 11 to each element in the set {4, 12, 14, 27, 42}. 
Have a nice day
6 0
3 years ago
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