At a particular restaurant, each onion ring has 40 calories and each mozzarella stick has 60 calories. a combination meal with onion rings and mozzarella sticks has a total of 14 onion rings and mozzarella sticks altogether and contains 800 calories. write a system of equations that could be used to determine the number of onion rings in the combination meal and the number of mozzarella sticks in the combination meal. define the variables that you use to write the system.

Step-by-step explanation:

Writing a system of equations is really just writing an equation for each part of the problem.  The parts here being the calories, and number of items.  It's not asking to solve it, so I will not unless you do want me to.

First variables, let's keep it simple.  O will be onion rings and M will be mozzarella sticks.

Now, I mentioned the two parts are the calories and number of items so we'll take it one at a time.  First calories.  

The total calories will equal 800, so we know the answer to the equation.  Now, how would we relate the variables?  if you had two of each item what would the total calories be?  it may be easy to figure out,  but for our purposes we want to think of it as multiplying the calories of each by the number of each item, or in other words 40*O+60*M, where O and M equal 2.  So for the general case we use the same thing, but we know what we want So our first equation is 40*O + 60*M = 800

The second is a bit simpler.  It just wants to know the total amount of things ordered.  So we are just adding O and M together.  So this gets us O + M = 14, since there are 14 things together.  Let me know if there's still something you don't understand though.  

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i