Answer:
![\cos(\frac{\pi}{4})\cos(\frac{\pi}{6})=\frac{1}{2}(\cos(\frac{\pi}{12})+\cos(\frac{5\pi}{12}))](https://tex.z-dn.net/?f=%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B6%7D%29%3D%5Cfrac%7B1%7D%7B2%7D%28%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B12%7D%29%2B%5Ccos%28%5Cfrac%7B5%5Cpi%7D%7B12%7D%29%29)
So the blank is cos.
Step-by-step explanation:
There is an identity for this:
![\cos(a)\cos(b)=\frac{1}{2}(\cos(a+b)+\cos(a-b))](https://tex.z-dn.net/?f=%5Ccos%28a%29%5Ccos%28b%29%3D%5Cfrac%7B1%7D%7B2%7D%28%5Ccos%28a%2Bb%29%2B%5Ccos%28a-b%29%29)
Let's see if this is fit by your left hand and right hand side:
So
while
.
Let's plug these in to the identity above:
![\cos(\frac{\pi}{4})\cos(\frac{\pi}{6})=\frac{1}{2}(\cos(\frac{\pi}{4}+\frac{\pi}{6})+\cos(\frac{\pi}{4}-\frac{\pi}{6}))](https://tex.z-dn.net/?f=%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B6%7D%29%3D%5Cfrac%7B1%7D%7B2%7D%28%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cfrac%7B%5Cpi%7D%7B6%7D%29%2B%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B4%7D-%5Cfrac%7B%5Cpi%7D%7B6%7D%29%29)
Ok, we definitely have the left hand sides are the same.
Let's see if the right hand sides are the same.
Before we move on let's see if we can find the sum and difference of
and
.
We will need a common denominator. How about 12? 12 works because 4 and 6 go into 12. That is 4(3)=12 and 6(2)=12.
.
.
Let's go back to our identity now:
![\cos(\frac{\pi}{4})\cos(\frac{\pi}{6})=\frac{1}{2}(\cos(\frac{\pi}{4}+\frac{\pi}{6})+\cos(\frac{\pi}{4}-\frac{\pi}{6}))](https://tex.z-dn.net/?f=%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B6%7D%29%3D%5Cfrac%7B1%7D%7B2%7D%28%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cfrac%7B%5Cpi%7D%7B6%7D%29%2B%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B4%7D-%5Cfrac%7B%5Cpi%7D%7B6%7D%29%29)
![\cos(\frac{\pi}{4})\cos(\frac{\pi}{6})=\frac{1}{2}(\cos(\frac{5\pi}{12})+\cos(\frac{\pi}{12}))](https://tex.z-dn.net/?f=%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B6%7D%29%3D%5Cfrac%7B1%7D%7B2%7D%28%5Ccos%28%5Cfrac%7B5%5Cpi%7D%7B12%7D%29%2B%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B12%7D%29%29)
We can rearrange the right hand side inside the ( ) using commutative property of addition:
![\cos(\frac{\pi}{4})\cos(\frac{\pi}{6})=\frac{1}{2}(\cos(\frac{\pi}{12})+\cos(\frac{5\pi}{12}))](https://tex.z-dn.net/?f=%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B6%7D%29%3D%5Cfrac%7B1%7D%7B2%7D%28%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B12%7D%29%2B%5Ccos%28%5Cfrac%7B5%5Cpi%7D%7B12%7D%29%29)
So comparing my left hand side to their left hand side we see that the blank should be cos.
Answer:
r=-29/20
Step-by-step explanation:
because
-2 1/4 will be -9/4=r-2/5 now you add 2/5 to both sides
witch means you have to increase the denominator to the greatest common denominator of 4 and 5 witch is 20 multiply the number used to combine with the denominator to get 20 to the numerator so itll be -45/20+16/20 witch will be -29/20 so there fore r=-29/20 or 1 9/20.
I hope this helps you
2/3y= 2+6
2/3y=8
2y=8.3
2y=24
y=12
You need to understand Rise over Run (r/r) to find these equations.
Rise over run works by counting how far a point on the line is from another.
You do this by first counting how much higher or lower a point is from another then how far it is from the left or right side.
So to answer the equation for #2,
Your Rise over Run is: 3/4
Which translates to Y = 4x + 3
Finding line #1 is actually much easier. All you need to know is how far up it is, which is 8 units
So that’s just Y = 8
Finding a slope parcel to the 2nd line is a lot easier than you might think.
We know the slope of line #2 is Y = 4x + 3.
Parallel means if two lines were next to each other and kept going, they won’t intercept. Like the equals sign, =.
So to find a parallel line, you can just add or subtract the same number from Y to X
Y = 4x + 3
4x + 2 = 6x
3 + 2 = 5
=
Y = 6x + 5
Answer- your answer would be 5/11