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Alexeev081 [22]
3 years ago
15

The area of a square is 75 inches squared. A student correctly wrote the length of each side of the square as a√3. What is the v

alue of a?
Mathematics
1 answer:
aev [14]3 years ago
6 0

Answer: 5 in.

Step-by-step explanation:

Given

The area of the square is 75\ in.^2

The side length of the square is a\sqrt{3}

Area of square=(\text{length})^2

\therefore 75=(a\sqrt{3})^2\\\Rightarrow 75=3a^2\\\Rightarrow a^2=25\\\Rightarrow a=5\ in.

Thus, value of a is 5 inch

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32 water bottles

Step-by-step explanation:

8x=425-175

425-175=250

250 is how much more they need.

8x=250

x=31.25

You can't have half of a bottle... so round up to at least 32 water bottles

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3 years ago
Which expression is equivalent to 7 3/4 - 1/2 Choose one answer A: 1/2 + 7 3/4 B: 7 3/4 + (-1/2) C: 1/2 + (-7 3/4) D: -7 3/4 + (
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D

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What are the amplitude, period, and phase shift of the given function? f(t)=-2/3 cos (3t-3pi)
dybincka [34]

Answer:

amplitude; \frac{2}{3}

Phase shift; \pi units right

Period;\frac{2\pi}{3}

Step-by-step explanation:

The given function is

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This function is of the form;

y=A\sin (Bt+C)

The period is given by:

|A|=|-\frac{2}{3}|= \frac{2}{3}

The period is given by:

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The phase shift is given by;

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4 0
3 years ago
<img src="https://tex.z-dn.net/?f=%28%20%5Csin%5E%7B2%7D%20%28%20%5Cfrac%7B%5Cpi%7D%7B%204%20%7D%20%20-%20%20%5Calpha%20%29%20%2
guapka [62]

Step-by-step explanation:

\sin^2 (\frac{\pi}{4} - \alpha) = \frac{1}{2}(1 - \sin 2\alpha)

Use the identity

\sin^2 \theta = \dfrac{1 - \cos 2\theta}{2}

on the left side.

\dfrac{1 - \cos [2(\frac{\pi}{4} - \alpha)]}{2} = \frac{1}{2}(1 - \sin 2\alpha)

\dfrac{1 - \cos (\frac{\pi}{2} - 2\alpha)}{2} = \frac{1}{2}(1 - \sin 2\alpha)

Now use the identity

\sin \theta = \cos(\frac{\pi}{2} - \theta)

on the left side.

\dfrac{1 - \sin 2\alpha}{2} = \frac{1}{2}(1 - \sin 2\alpha)

\frac{1}{2}(1 - \sin 2\alpha) = \frac{1}{2}(1 - \sin 2\alpha)

4 0
3 years ago
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