Answer:
Step-by-step explanation:
![\sin\theta + 1 = \cos(2\theta)\\\sin\theta + 1 = \cos^2\theta - \sin^2\theta\\\sin\theta + \sin^2\theta + \cos^2\theta = cos^2\theta -\sin\theta^2\\2\sin^2\theta +\sin\theta = 0\\\sin\theta[2\sin\theta + 1] = 0\\\sin\theta = 0 || 2\sin\theta + 1 = 0\\\theta \in \{0, \pi, \frac{11\pi}{6}\}](https://tex.z-dn.net/?f=%5Csin%5Ctheta%20%2B%201%20%3D%20%5Ccos%282%5Ctheta%29%5C%5C%5Csin%5Ctheta%20%2B%201%20%3D%20%5Ccos%5E2%5Ctheta%20-%20%5Csin%5E2%5Ctheta%5C%5C%5Csin%5Ctheta%20%2B%20%5Csin%5E2%5Ctheta%20%2B%20%5Ccos%5E2%5Ctheta%20%3D%20cos%5E2%5Ctheta%20-%5Csin%5Ctheta%5E2%5C%5C2%5Csin%5E2%5Ctheta%20%2B%5Csin%5Ctheta%20%3D%200%5C%5C%5Csin%5Ctheta%5B2%5Csin%5Ctheta%20%2B%201%5D%20%3D%200%5C%5C%5Csin%5Ctheta%20%3D%200%20%7C%7C%202%5Csin%5Ctheta%20%2B%201%20%3D%200%5C%5C%5Ctheta%20%5Cin%20%5C%7B0%2C%20%5Cpi%2C%20%5Cfrac%7B11%5Cpi%7D%7B6%7D%5C%7D)
Hello,
As the question states, let r be the number of hours worked at the restaurant, and y be the number of hours of yard work. We know that she can only work a maximum of 15 hours per work total, and that at she must work at least 5 hours in the restaurant. Therefore:r + y ≤ 15r ≥ 5We also know that she wants to earn at least 120 dollars, earning $8/hr in the restaurant and $12/hr in the yard:8r + 12y ≥ 120
What is the maximum of hours Lia can work in the restaurant and still make at leas 120 hours? Lia's parents won't let her work more than 15 hours, so we know that the answer won't be higher than 15.If she worked all 15 hours in the restaurant, she would make 8*15 = 120.The maximum number of hours she can work in the restaurant is therefore 15 hours
What is the maximum amount of money Lia can earn in a week? Lia has to work a minimum of 5 hours in the restaurant. She makes more money doing yard work, so she should devote the rest of her available work hours to yard work. That means that, given her 15 hour work limit, she will maximize her income by working 5 hours in the restaurant and 10 hours in the yard. 5*8 + 10*12 = 40 + 120 = 160The most she can make is 160 dollars, working 5 hours in the restaurant and 10 hours in the yard
Hope this helps
~Girlygir101~
Answer:
1) y=18
2)y=-0.18
Step-by-step explanation:
1) y-15=3. Add 15 on both sides.
y=18
2)-2.1+5y=-3. Add 2.1 on both sides
5y=-0.9. Divide 5 on both sides
y=-0.18
Answer:
Step-by-step explanation:
It was given that, the graph of the bicycle ramp contains the points (-6,0) and (3,3).
We want to find the slope.
We use the formula:
We substitute the points into the formula to get;
Add in the denominator
The slope of the ramp is 1/3.
