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Savatey [412]
3 years ago
5

Danielle is x years old. Her sister is five years older and her brother is half Danielle’s age. Write an expression in simplest

form for the sum of their ages
Mathematics
1 answer:
Alborosie3 years ago
7 0
Let x = Danielle, x + 5 = her sister, and .5x = her brother.

x + x + 5 + .5x = the sum of their ages.

Then we simplify to get 2.5x + 5 = the sum of their ages.
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9 in.
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Answer:

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Step-by-step explanation:

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2 years ago
Use the power reduction formulas to rewrite the expression. (Hint: Your answer should not contain any exponents greater than 1.)
Lapatulllka [165]

Some useful relations and identities:

\tan x=\dfrac{\sin x}{\cos x}

\sin^2x=\dfrac{1-\cos2x}2

\cos^2x=\dfrac{1+\cos2x}2

By the first relation, we have

\tan^2x\sin^3x=\dfrac{\sin^5x}{\cos^2x}=\dfrac{(\sin^2x)^2\sin x}{\cos^2x}

Applying the two latter identities, we get

\dfrac{\left(\frac{1-\cos2x}2\right)^2\sin x}{\frac{1+\cos2x}2}=\dfrac{\frac{1-2\cos2x+\cos^22x}4\sin x}{\frac{1+\cos2x}2}=\dfrac{(1-2\cos2x+\cos^22x)\sin x}{2(1+\cos2x)}

We can apply the third identity again:

\dfrac{(1-2\cos2x+\cos^22x)\sin x}{2(1+\cos2x)}=\dfrac{\left(1-2\cos2x+\frac{1+\cos4x}2\right)\sin x}{2(1+\cos2x)}=\dfrac{(3-4\cos2x+\cos4x)\sin x}{4(1+\cos2x)}

and this is probably as far as you have to go, but by no means is it the only possible solution.

8 0
3 years ago
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Answer:

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5 0
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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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