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iren2701 [21]
2 years ago
5

3 1/3 - 2 2/5 what is the answer?

Mathematics
1 answer:
AURORKA [14]2 years ago
7 0
One way to solve this is by changing the mixed numbers to improper functions. 
3 1/3 = 10/3
2 2/5 = 12/5

The next step I would take is to find a common denominator.
10/3 = 50/15
12/5 = 36/15

Now we can solve the original equation: 
50/15 - 36/15 = 14/15

Since 14/15 is already simplified this is your final answer.
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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

7 0
3 years ago
Selena's gross annual salary as the Content editor of a fashion Magazine is Rs 40000 she contribute 10% of her salary. before sh
aalyn [17]

Answer:

Selena's annual intake home salary is $ 26,640.

Step-by-step explanation:

Since Selena's gross annual salary as the content editor of a fashion Magazine is $ 40,000, and she contributes 10% of her salary before she pays taxes to a retirement account, and 25% of her remaining salary is then consumed in state and federal taxes, To determine what is Selena's annual intake home salary if she also has to pay $ 30 for health Insurance each month, the following calculation must be performed:

40,000 - (40,000 x 0.1) - (40,000 x 0.9 x 0.25) - (30 x 12) = X

40,000 - 4,000 - 9,000 - 360 = X

26.640 = X

Therefore, Selena's annual intake home salary is $ 26,640.

7 0
3 years ago
Tiffany used 2/5 kg of cherries to bake pies Linda used 1/10 kg of cherries to bake Tarts how many kilograms of cherries did the
kari74 [83]
1/2 Kg of Cherries

Give both 2/5 and 1/10 a common denominator- 10
4/10 + 1/10 = 5/10 = 1/2
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3 years ago
Please answer this correctly
erastovalidia [21]

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<em>Good</em><em> </em><em>luck</em><em> </em><em>on</em><em> </em><em>your</em><em> </em><em>assignment</em>

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Domino's offers the following “deals”:
tia_tia [17]

Answer: Deal one: 5x+10

Deal two: 6x

3 0
3 years ago
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