For the triangle, the shaded part, both the height and base are 12, so the area of it is:
1/2 (12 x 12) = 72
And the area of the whole square is 144
But what we’re looking for is the area of the unshaded region. So to find it, we’ll need to subtract the shaded from the total. So:
144 - 72 = 72
Thus, the area of the unshaded region is 72
Answer:
3/1
Step-by-step explanation:
The average rate of change is the distance between y values divided by the distance between x values. We know this as rise/run or slope for linear equations. For non-linear equations, we calculate the average over an interval.
This function has y-values of -1 at x=0 and 5 at x=2.
We add -1+5=6 and divide this by 2-0=2.
6/2=3.
The y-values on average change 3 units for every 1 unit of the x-values.
let's make p stand for popcorn and d for drinks. Using those variables, we can create our equations:
2p + 3d = 18.25
4p + 2d = 27.50
From this, we can use substitution or elimination to solve:
For substitution, in the second equations, we could factor out a 2, divide both sides by 2, and then move the left over 2p to the other side to isolate d to put into the first equation.
For elimination, we can multiply the first equation by -2 so that we can remove the 4p and focus on solving for d.
I'll be using elimination in this case:
-2(2p + 3d = 18.25) --> -4p - 6d = -36.50
-4p - 6d = -36.50
4p + 2d = 27.50
-4d = -9.00
d = 2.25
4p + 2 * 2.25 = 27.50
4p + 4.50 = 27.50
4p = 23.00
p = 5.75
Now let's check our answer:
2 * 5.75 + 3 * 2.25 = 18.25
11.50 + 6.75 = 18.25
18.25 = 18.25
So drinks cost $2.25 and popcorn $5.75
