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frutty [35]
3 years ago
8

Can anyone help me with question number 3

Mathematics
1 answer:
ira [324]3 years ago
7 0
The answer is: There are 595 calories in a banana split 

To find this we first need to set up our equation: 

80= \frac{1}{7}x-5, where x= calories in a banana split


85= \frac{1}{7}x----------------Add 5 to both sides

595=x-------------------Multiply 7 to both sides to get rid of the fraction

So, there are 595 calories in a banana split

Hope this helps! :)
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Choose the correct algebraic expression to represent: 7 less than n
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Match each binomial expression with the set of coefficients of the terms obtained by expanding the expression.
user100 [1]

 explanation:

(A) (2x+y)^3=8 x^3 + 12 x^2 y + 6 x y^2 + y^3

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8 0
3 years ago
Read 2 more answers
Prove it please <br>answer only if you know​
deff fn [24]

Part (c)

We'll use this identity

\sin(x+y) = \sin(x)\cos(y) + \cos(x)\sin(y)\\\\

to say

\sin(A+45) = \sin(A)\cos(45) + \cos(A)\sin(45)\\\\\sin(A+45) = \sin(A)\frac{\sqrt{2}}{2} + \cos(A)\frac{\sqrt{2}}{2}\\\\\sin(A+45) = \frac{\sqrt{2}}{2}(\sin(A)+\cos(A))\\\\

Similarly,

\sin(A-45) = \sin(A + (-45))\\\\\sin(A-45) = \sin(A)\cos(-45) + \cos(A)\sin(-45)\\\\\sin(A-45) = \sin(A)\cos(45) - \cos(A)\sin(45)\\\\\sin(A-45) = \sin(A)\frac{\sqrt{2}}{2} - \cos(A)\frac{\sqrt{2}}{2}\\\\\sin(A-45) = \frac{\sqrt{2}}{2}(\sin(A)-\cos(A))\\\\

-------------------------

The key takeaways here are that

\sin(A+45) = \frac{\sqrt{2}}{2}(\sin(A)+\cos(A))\\\\\sin(A-45) = \frac{\sqrt{2}}{2}(\sin(A)-\cos(A))\\\\

Therefore,

2\sin(A+45)*\sin(A-45) = 2*\frac{\sqrt{2}}{2}(\sin(A)+\cos(A))*\frac{\sqrt{2}}{2}(\sin(A)-\cos(A))\\\\2\sin(A+45)*\sin(A-45) = 2*\left(\frac{\sqrt{2}}{2}\right)^2\left(\sin^2(A)-\cos^2(A)\right)\\\\2\sin(A+45)*\sin(A-45) = 2*\frac{2}{4}\left(\sin^2(A)-\cos^2(A)\right)\\\\2\sin(A+45)*\sin(A-45) = \sin^2(A)-\cos^2(A)\\\\

The identity is confirmed.

==========================================================

Part (d)

\sin(x+y) = \sin(x)\cos(y) + \cos(x)\sin(y)\\\\\sin(45+A) = \sin(45)\cos(A) + \cos(45)\sin(A)\\\\\sin(45+A) = \frac{\sqrt{2}}{2}\cos(A) + \frac{\sqrt{2}}{2}\sin(A)\\\\\sin(45+A) = \frac{\sqrt{2}}{2}(\cos(A)+\sin(A))\\\\

Similarly,

\sin(45-A) = \sin(45 + (-A))\\\\\sin(45-A) = \sin(45)\cos(-A) + \cos(45)\sin(-A)\\\\\sin(45-A) = \sin(45)\cos(A) - \cos(45)\sin(A)\\\\\sin(45-A) = \frac{\sqrt{2}}{2}\cos(A) - \frac{\sqrt{2}}{2}\sin(A)\\\\\sin(45-A) = \frac{\sqrt{2}}{2}(\cos(A)-\sin(A))\\\\

-----------------

We'll square each equation

\sin(45+A) = \frac{\sqrt{2}}{2}(\cos(A)+\sin(A))\\\\\sin^2(45+A) = \left(\frac{\sqrt{2}}{2}(\cos(A)+\sin(A))\right)^2\\\\\sin^2(45+A) = \frac{1}{2}\left(\cos^2(A)+2\sin(A)\cos(A)+\sin^2(A)\right)\\\\\sin^2(45+A) = \frac{1}{2}\cos^2(A)+\frac{1}{2}*2\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\\sin^2(45+A) = \frac{1}{2}\cos^2(A)+\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\

and

\sin(45-A) = \frac{\sqrt{2}}{2}(\cos(A)-\sin(A))\\\\\sin^2(45-A) = \left(\frac{\sqrt{2}}{2}(\cos(A)-\sin(A))\right)^2\\\\\sin^2(45-A) = \frac{1}{2}\left(\cos^2(A)-2\sin(A)\cos(A)+\sin^2(A)\right)\\\\\sin^2(45-A) = \frac{1}{2}\cos^2(A)-\frac{1}{2}*2\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\\sin^2(45-A) = \frac{1}{2}\cos^2(A)-\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\

--------------------

Let's compare the results we got.

\sin^2(45+A) = \frac{1}{2}\cos^2(A)+\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\\sin^2(45-A) = \frac{1}{2}\cos^2(A)-\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\

Now if we add the terms straight down, we end up with \sin^2(45+A)+\sin^2(45-A) on the left side

As for the right side, the sin(A)cos(A) terms cancel out since they add to 0.

Also note how \frac{1}{2}\cos^2(A)+\frac{1}{2}\cos^2(A) = \cos^2(A) and similarly for the sin^2 terms as well.

The right hand side becomes \cos^2(A)+\sin^2(A) but that's always equal to 1 (pythagorean trig identity)

This confirms that \sin^2(45+A)+\sin^2(45-A) = 1 is an identity

4 0
3 years ago
9 yd<br> 9 yd<br> 5 yd<br> 3 yd<br> Perimeter:<br> Area:
Kipish [7]

Area:66 Perimeter:36

Step-by-step explanation:

Perimeter: 9+9+5+3+4+6: 36

as 9-5 is 3

and 9-3 is 6

Area: 9*6 +3*4: 66

5 0
2 years ago
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