The first thing to do with these problems is to convert them into y=mx+b form; this will literally show you the answer to slope and y intercept since m=slope and b=y intercept.
To convert, isolate the y and the rest should fall into place. Subtract 2x from 4y and the other side of the equation to get the equation 4y= -2x+9 (put the x first because of mx+b). Then Divide the 4 from y and do the same to the other side to get y= -1/2x+9/4. M= -1/2 so that is the slope. B=9/4 so that is the y intercept
The result of expanding the trigonometry expression
is ![cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)](https://tex.z-dn.net/?f=cos%5E0%28%5Ctheta%29%20%2B%20%5Ccos%28%5Ctheta%29%20-%20%5Ccos%5E2%28%5Ctheta%29%20-%20%5Ccos%5E3%28%5Ctheta%29)
<h3>How to evaluate the expression?</h3>
The expression is given as:
![\sin^2(\theta) * (1 + \cos(\theta))](https://tex.z-dn.net/?f=%5Csin%5E2%28%5Ctheta%29%20%2A%20%281%20%2B%20%5Ccos%28%5Ctheta%29%29)
Express
as
.
So, we have:
![\sin^2(\theta) * (1 + \cos(\theta)) = (1- \cos^2(\theta)) * (1 + \cos(\theta))](https://tex.z-dn.net/?f=%5Csin%5E2%28%5Ctheta%29%20%2A%20%281%20%2B%20%5Ccos%28%5Ctheta%29%29%20%3D%20%20%281-%20%5Ccos%5E2%28%5Ctheta%29%29%20%2A%20%281%20%2B%20%5Ccos%28%5Ctheta%29%29)
Open the bracket
![\sin^2(\theta) * (1 + \cos(\theta)) = 1 + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)](https://tex.z-dn.net/?f=%5Csin%5E2%28%5Ctheta%29%20%2A%20%281%20%2B%20%5Ccos%28%5Ctheta%29%29%20%3D%20%201%20%2B%20%5Ccos%28%5Ctheta%29%20-%20%5Ccos%5E2%28%5Ctheta%29%20-%20%5Ccos%5E3%28%5Ctheta%29)
Express 1 as cos°(Ф)
![\sin^2(\theta) * (1 + \cos(\theta)) = cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)](https://tex.z-dn.net/?f=%5Csin%5E2%28%5Ctheta%29%20%2A%20%281%20%2B%20%5Ccos%28%5Ctheta%29%29%20%3D%20%20cos%5E0%28%5Ctheta%29%20%2B%20%5Ccos%28%5Ctheta%29%20-%20%5Ccos%5E2%28%5Ctheta%29%20-%20%5Ccos%5E3%28%5Ctheta%29)
Hence, the result of expanding the trigonometry expression
is ![cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)](https://tex.z-dn.net/?f=cos%5E0%28%5Ctheta%29%20%2B%20%5Ccos%28%5Ctheta%29%20-%20%5Ccos%5E2%28%5Ctheta%29%20-%20%5Ccos%5E3%28%5Ctheta%29)
Read more about trigonometry expressions at:
brainly.com/question/8120556
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Answer:
25%
Step-by-step explanation:
Since there are 24 apples, and 6 are bad, to find the percentage of the bad apples, you do bad apples/total apples
6/24=.25
0.25 is 25%
The denominator of the raised fraction is what goes on the outside of the square root. So if you had 2 raised to 1/3, you'd put the 3 raised outside to the left of the radical and the 2 inside. They give the same answer, so if you know one, you can always play with the other until you get the same answer. My teacher told us in Calculus a funny/weird way to remember it is the "bottom (of the raised fraction) goes in the crack (of the radical)." Does this help??
![2.32\cdot10^3=2.32\cdot1,000=2,320\\\\4.2\cdot10^4=4.2\cdot10,000=42,000\\\\4.2\cdot10^{-2}=4.2\cdot0.01=0.042](https://tex.z-dn.net/?f=2.32%5Ccdot10%5E3%3D2.32%5Ccdot1%2C000%3D2%2C320%5C%5C%5C%5C4.2%5Ccdot10%5E4%3D4.2%5Ccdot10%2C000%3D42%2C000%5C%5C%5C%5C4.2%5Ccdot10%5E%7B-2%7D%3D4.2%5Ccdot0.01%3D0.042)
Multiplication by 10ⁿ → move decimal n places to the right.
Multiplication by 10⁻ⁿ → move decimal n places to the left.
For n ∈ N