We can let x and y represent cups of lemonade and numbers of lemon bars, respectively. Then the constraints are ...
- x ≥ 150
- y ≥ 0
- 2x +1.5y ≥ 500
- 0.25x +0.20y ≤ 100
A graph is shown in the attachment, with the ordered pairs plotted. It is not feasible to sell half cups of lemonade or half lemon bars, so the second and third choices must be excluded. The point (160, 110) falls outside the feasible region, so is not a correct choice.
The correct choices are ...
The law of cosines states that, if 
is the angle between sides b and c,
So, plugging our values, we have
This is equal to
Plug x = 0 into the function
f(x) = x^3 + 2x - 1
f(0) = 0^3 + 2(0) - 1
f(0) = -1
Note how the result is negative. The actual number itself doesn't matter. All we care about is the sign of the result.
Repeat for x = 1
f(x) = x^3 + 2x - 1
f(1) = 1^3 + 2(1) - 1
f(1) = 2
This result is positive.
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We found that f(0) = -1 and f(1) = 2. The first output -1 is negative while the second output 2 is positive. Going from negative to positive means that, at some point, we will hit y = 0. We might have multiple instances of this happening, or just one. We don't know for sure. The only thing we do know is that there is at least one root in this interval.
To actually find this root, you'll need to use a graphing calculator because the root is some complicated decimal value. Using a graphing calculator, you should find the root to be approximately 0.4533976515
MOKL and mHKJ are vertical angles, so they’re congruent
so mHKJ is also 80°
Answer:
11.42 dollars
Step-by-step explanation: since you are adding a percentage turn 20% into a decimal. if you do this you will get .2. Next, multiple .2 by 9.52 and you will get 20% of 9.52. Now add this value to 9.52 and you will get 11.42 dollars.
