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Mkey [24]
3 years ago
9

Consider the equation y = 3(x-5)(x +2)

Mathematics
1 answer:
lara31 [8.8K]3 years ago
4 0
-x intercepts: 5, -2
-1/2(x-5)(x+2) is wider than the first equation because the coefficient is smaller
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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}

3 0
3 years ago
The function<img src="https://tex.z-dn.net/?f=f%28x%29%3D-3x%5E%7B3%7D%20%2Bx%5E%7B2%7D%20%2B2x" id="TexFormula1" title="f(x)=-3
musickatia [10]

Answer:

True

Step-by-step explanation:

True.

Like the cubic term -3x^3 is negative, for small values of "x", the dependent variable "y" will rise. All this can be verified by looking at the graph.

6 0
3 years ago
A choir teacher is dividing 3 sopranos and 12 altos into singing groups. he wants each group to have the same combination of sop
Andreyy89
You can have a maximum of 3 groups. This is due to the fact that you only have 3 sopranos to equally divide between groups. Over 3 you would have a group lacking a soprano so 3 is the greatest you can make it.
7 0
3 years ago
What the answer asap
Westkost [7]
The ounces are greater than the pints.  

I do hope I got what you needed and helped!  :)
4 0
3 years ago
The Martin family is comparing the costs of two different cable companies. Direct TV charges a
nikdorinn [45]

Answer:

It would take 5.5 months for the two cable companies to cost the same.

Step-by-step explanation:

50x + 100 = 60x + 45

        -45               -45

50x + 55 = 60x

-50x            -50x

55 = 10x

/10    /10

x = 5.5

 

6 0
3 years ago
Read 2 more answers
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