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:
There are 52 possible outcomes when you draw one card from a standard deck. Hence, 52 is the denominator of your probability fraction.
Colfax:
Add the ratio numbers together:
5 + 4 = 9
Divide total students by that:
270 / 9 = 30
Multiply each ratio by 30:
Boys = 30 *5 = 150
Girls = 30 * 4 = 120
Do the same for Winthrop:
4 +5 = 9
180 /9 = 20
Boys = 20 * 4 = 80
Girls = 20 * 5 = 100
Total students = 270 + 180 = 450
Total Girls = 120 + 100 = 220
Fraction that are girls = 220 / 450 which reduces to 22/45
I hope this helps you
perpendicular lines slopes multiplication -1
M1×M2= -1
1/2×M2= -1
M2= -2
Answer:
y=-\frac{5}{3} x+\frac{10}{3} or what is the same: ![5x+3y=10](https://tex.z-dn.net/?f=5x%2B3y%3D10)
Step-by-step explanation:
First we find the slope of the line that goes through the points (-4,10) and (-1,5) using the slope formula: ![slope=\frac{10-5}{-4-(-1)} =\frac{5}{-3} =-\frac{5}{3}](https://tex.z-dn.net/?f=slope%3D%5Cfrac%7B10-5%7D%7B-4-%28-1%29%7D%20%3D%5Cfrac%7B5%7D%7B-3%7D%20%3D-%5Cfrac%7B5%7D%7B3%7D)
Now we use this slope in the general form of the slope- y_intercept of a line:
![y=-\frac{5}{3} x+b](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B3%7D%20x%2Bb)
We can determine the parameter "b" by requesting the condition that the line has to go through the given points, and we can use one of them to solve for "b" (for example requesting that the point (-1,5) is on the line:
![y=-\frac{5}{3} x+b\\5=-\frac{5}{3} (-1)+b\\5=\frac{5}{3}+b\\5-\frac{5}{3}=b\\b=\frac{10}{3}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B3%7D%20x%2Bb%5C%5C5%3D-%5Cfrac%7B5%7D%7B3%7D%20%28-1%29%2Bb%5C%5C5%3D%5Cfrac%7B5%7D%7B3%7D%2Bb%5C%5C5-%5Cfrac%7B5%7D%7B3%7D%3Db%5C%5Cb%3D%5Cfrac%7B10%7D%7B3%7D)
Therefore, the equation of the line in slope y_intercept form is:
![y=-\frac{5}{3} x+\frac{10}{3}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B3%7D%20x%2B%5Cfrac%7B10%7D%7B3%7D)
Notice that this equation can also be written in an equivalent form by multiplying both sides of the equal sign by "3", which allows us to write it without denominators:
![y=-\frac{5}{3} x+\frac{10}{3}\\3*y=(-\frac{5}{3} x+\frac{10}{3})*3\\3y=-5x+10\\5x+3y=10](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B3%7D%20x%2B%5Cfrac%7B10%7D%7B3%7D%5C%5C3%2Ay%3D%28-%5Cfrac%7B5%7D%7B3%7D%20x%2B%5Cfrac%7B10%7D%7B3%7D%29%2A3%5C%5C3y%3D-5x%2B10%5C%5C5x%2B3y%3D10)