Given:
cos 120°
To find:
The exact value of cos 120° in simplest form with a rational denominator.
Solution:
We have,

It can be written as

![[\because \cos (90^\circ-\theta)=-\sin \theta]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Ccos%20%2890%5E%5Ccirc-%5Ctheta%29%3D-%5Csin%20%5Ctheta%5D)
![[\because \sin 30^\circ=\dfrac{1}{2}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Csin%2030%5E%5Ccirc%3D%5Cdfrac%7B1%7D%7B2%7D%5D)

Therefore, the exact value of cos 120° is
.
Answer:
k = 4, y = 4x
Step-by-step explanation:
From the question, we get the ratio of :
x : y = 1 : 4
Two variables are proportional to each other if their ration is constant. The constant value is denoted by 'k' and is called as constant of proportionality.
In the question, the two variables are :
x = glasses of lemonade
y = lemons used
From the question, the ratio of y is to x is given by :
y : x is 24 : 6 = 4 : 1 or 24/6 = 4
32 : 8 = 4 : 1 or 32/8 = 4
28 : 7 = 4 : 1 or 28/7 = 4
8 : 2 = 4 : 1 or 8/2 = 4
16 : 4 = 4 : 1 or 16/4 = 4
So here the constant is 4 . Therefore, the constant of proportionality, k is 4.
So we can write the equation as :
y = kx
or y = 4x
Answer: (-2, 1)
Step-by-step explanation:
He is wrong because he didnt fully simplify the answer, and the answer is $13 per hour
Suppose width is X
then length would be X+44
perimeter of rectangle = 2 (length + width)
substitute:
328 = 2 ( X+44 + X )
328 = 2 ( 2X + 44 )
328 = 4X + 88
328 - 88 = 4X
240 = 4X
240/4 = X
X = 60
substitute in the first and second line
width is X so width = 60 feet
length is X + 44 = 60 + 44 = 104 feet