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3 years ago

11

There are 40 houses in a neighborhood.Company X provides electricity to 1/8 of the houses ,how many houses does Company X provid

e electricity to?

1 answer:

Sedaia [141]3 years ago

7 0

Answer:

5 houses

Step-by-step explanation:

40 × 1/8

40/8

5 houses

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James divided 144 ounces of water evenly among 4 containers. One of the containers leaked 8 ounces.

Verdich [7]

Answer:

I dont understand your question rither

Step-by-step explanation:

sorry I would help is I neew

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3 years ago

An electronics store sells remote control dinosaurs for $395 each. About how much do four remote control dinosaurs cost?

svp [43]

Just multiply $395 by 4. This is because $395 is the cost of one and if we're buying four, we would multiply by 4.

So,

395 x 4 = 1580

Therefore, four remote control dinosaurs will cost $1580.

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2 years ago

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Hello! Verify the identity. Please show your work! Use trigonometric identities to verify each expression is equal.

RSB [31]

Answer:

See Below.

Step-by-step explanation:

We want to verify the identity:

$\displaystyle \csc^2 x -2\csc x \cot x +\cot ^2 x = \tan^2\left(\frac{x}{2}\right)$

Note that the left-hand side is a perfect square trinomial pattern. Namely:

$a^2-2ab+b^2=(a-b)^2$

If we let <em>a</em> = csc(x) and <em>b</em> = cot(x), we can factor it as such:

$\displaystyle (\csc x - \cot x)^2 = \tan^2\left(\frac{x}{2}\right)$

Let csc(x) = 1 / sin(x) and cot(x) = cos(x) / sin(x):

$\displaystyle \left(\frac{1}{\sin x}-\frac{\cos x }{\sin x}\right)^2=\tan^2\left(\frac{x}{2}\right)$

Combine fractions:

$\displaystyle \left(\frac{1-\cos x}{\sin x}\right)^2=\tan^2\left(\frac{x}{2}\right)$

Square (but do not simplify yet):

$\displaystyle \frac{(1-\cos x)^2}{\sin ^2x}=\tan^2\left(\frac{x}{2}\right)$

Now, we can make a substitution. Let <em>u</em> = <em>x</em> / 2. So, <em>x</em> = 2<em>u</em>. Substitute:

$\displaystyle \frac{(1-\cos 2u)^2}{\sin ^22u}=\tan^2u$

Recall that cos(2u) = 1 - sin²(u). Hence:

$\displaystyle \frac{(1-(1-2\sin^2u))^2}{\sin ^2 2u}=\tan^2u$

Simplify:

$\displaystyle \frac{4\sin^4 u}{\sin ^2 2u}=\tan^2 u$

Recall that sin(2u) = 2sin(u)cos(u). Hence:

$\displaystyle \frac{4\sin^4 u}{(2\sin u\cos u)^2}=\tan^2 u$

Square:

$\displaystyle \frac{4\sin^4 u}{4\sin^2 u\cos ^2u}=\tan^2 u$

Cancel:

$\displaystyle \frac{\sin ^2 u}{\cos ^2 u}=\tan ^2 u$

Since sin(u) / cos(u) = tan(u):

$\displaystyle \left(\frac{\sin u}{\cos u}\right)^2=\tan^2u=\tan^2u$

We can substitute <em>u</em> back for <em>x</em> / 2:

$\displaystyle \tan^2\left(\frac{x}{2}\right)= \tan^2\left(\frac{x}{2}\right)$

Hence proven.

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3 years ago

Is the value of the 8 in 12.984 the same as the value of the 8 in 7.38? Justify your response.

FinnZ [79.3K]

Answer:

Yes because they are both in the hundredths place

Step-by-step explanation:

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3 years ago

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Which one of the following is an equation?<br> O 3m + 2<br> 3m<br> 2<br> 3m +2 = 11

AVprozaik [17]

Answer:

3m+2=11

Step-by-step explanation:

Because equation is joined with equal sign

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3 years ago