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Artyom0805 [142]

4 years ago

6

a triangle poster is twice as long as its height. a rectangular banner is 3 inches longer than its width. both the poster and th

e banner have areas of 648 square inches. what is the length and the width of the banner?

1 answer:

Step2247 [10]4 years ago

8 0

davqueeenwillk will know

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Derive these identities using the addition or subtraction formulas for sine or cosine: sinacosb=(sin(a+b)+sin(a-b))/2

Sergeu [11.5K]

Answer:

The work is in the explanation.

Step-by-step explanation:

The sine addition identity is:

$\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)$ .

The sine difference identity is:

$\sin(a-b)=\sin(a)\cos(b)-\cos(a)\sin(a)$ .

The cosine addition identity is:

$\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$ .

The cosine difference identity is:

$\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)$ .

We need to find a way to put some or all of these together to get:

$\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}$ .

So I do notice on the right hand side the $\sin(a+b)$ and the $\sin(a-b)$ .

Let's start there then.

There is a plus sign in between them so let's add those together:

$\sin(a+b)+\sin(a-b)$

$=[\sin(a+b)]+[\sin(a-b)]$

$=[\sin(a)\cos(b)+\cos(a)\sin(b)]+[\sin(a)\cos(b)-\cos(a)\sin(b)]$

There are two pairs of like terms. I will gather them together so you can see it more clearly:

$=[\sin(a)\cos(b)+\sin(a)\cos(b)]+[\cos(a)\sin(b)-\cos(a)\sin(b)]$

$=2\sin(a)\cos(b)+0$

$=2\sin(a)\cos(b)$

So this implies:

$\sin(a+b)+\sin(a-b)=2\sin(a)\cos(b)$

Divide both sides by 2:

$\frac{\sin(a+b)+\sin(a-b)}{2}=\sin(a)\cos(b)$

By the symmetric property we can write:

$\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}$

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3 years ago

John volunteers at the animal shelter on weekends. One Saturday, John unloaded 27 bags of dog food. Each bag weighed 35 pounds.

romanna [79]

Answer:

945 ounces

Step-by-step explanation:

if you read it closley you will find that if you multiply you will get 945 ounces because all you have to do is multipply.

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3 years ago

Which one has the exact same amount of coins as the one above?

dezoksy [38]

Answer:

its b

count them!

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You would do $5.67 divided by three. one pen is $1.89

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Find the percent increase in the price per cheese stick.

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Take the price of the cheese stick then divide that by the old price. you will get a decimal. New divided by old. You should have some decimal that is 1.something. If its a percent increase of 64 percent you'd have 1.64 as the decimal. good luck.

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