Let Mia's score be
. Then, Erick scored 10 more than Mia, so his score is
. Isabelle scored 16 less than twice Mia's score, so her score is
. We can see that
is the sum of these variables, so
the expression represents the total of their scores in this scenario. Moreover, we recall that the variable in the expression,
,
represents Mia's score.To simplify this expression, we add up the variables and the numbers separately, giving us
. Therefore, in simplified form, the expression is equal to
4x - 6. The constant term
in an expression is the term not multiplied by a variable, so in this case, it is
-6.
The area of the ellipse 
is given by
To use Green's theorem, which says
(
denotes the boundary of ), we want to find 
and 
such that
and then we would simply compute the line integral. As the hint suggests, we can pick
The line integral is then
We parameterize the boundary by
with 
. Then the integral is
###
Notice that 
kind of resembles the equation for a circle with radius 4, 
. We can change coordinates to what you might call "pseudo-polar":
which gives
as needed. Then with , we compute the area via Green's theorem using the same setup as before:
Use the FOIL method (First, Outside, Inside, Last)
6r(-8r) = -48r²
6r(-3) = -18r
-1(-8r) = 8r (note: two negatives multiplied together = positive answer)
-1(-3) = 3
-48r² - 18r + 8r + 3
Combine like terms:
-48r² - 18r + 8r + 3
-48r² - 10r + 3
-48r² - 10r + 3 is your answer
hope this helps
Answer: $2.26
10% of $52.50 is 5.25. Then, $52.50-$5.25 is $47.25. $49.99-$47.25 is $2.26
