<h3>
Answer: 49</h3>
Work Shown:
Replace x with 3, replace y with -8. Use order of operations PEMDAS to simplify.
x^2 + y^2 + x*y
3^2 + (-8)^2 + 3*(-8)
9 + 64 - 24
73 - 24
49
A.)
x y
1 1
2 4
3 9
dx=2-1→dx=1 dy=4-1→dy=3
dx=3-2→dx=1 dy=9-4→dy=5 different to 3, then this table can not be represented by a line
B.)
x y
1 2
2 5
3 10
dx=2-1→dx=1 dy=5-2→dy=3
dx=3-2→dx=1 dy=10-5→dy=5 different to 3, then this table can not be represented by a line
C.)
x y
1 3
2 6
3 9
dx=2-1→dx=1 dy=6-3→dy=3
dx=3-2→dx=1 dy=9-6→dy=3, then this table can be represented by a line
D.)
x y
1 0
2 3
3 8
dx=2-1→dx=1 dy=3-0→dy=3
dx=3-2→dx=1 dy=8-3→dy=5 different to 3, then this table can not be represented by a line
Answer: Option C. x 1 2 3 y 3 6 9
The first step to solving a story problem is identifying variables. For this problem, I will identify the variables as:
D = Drew's age
J = Jimmy's age
Once the variables are identified, we need to find as many equations as we have variables. Since we have two variables, we will have to write two equations.
Since Drew is 3 years younger than Jimmy: D + 3 = J
Since the sum of the brothers' ages is 21: D + J = 21
Once I have two equations is two variables, I can solve the system using either substitution method or elimination method. For this problem, I will use substitution method.
D + J = 21 Equation 2
D + (D + 3) = 21 Substitution of value of J from equation 1 into equation 2
D + D + 3 = 21 Associative property of addition
2D + 3 = 21 Simplify
2D + 3 - 3 = 21 - 3 Subtract 3 from each side
2D = 18 Simplify each side
2D/2 = 18/2 Divide each side by 2
D = 9 Simplify each side
Now that we have D, we can substitute it into equation 1 to get the value of J
D + 3 = J Equation 1
9 + 3 = J Substitution
12 = J Simplify
Simple, since you want to find y, in y=mx+b form, move everything to the other side.
1/2x-y=4
Move 1/2x
1/2x-y=4
-1/2x -1/2x
Making it look like,
-y=4-1/2x
Divide by the negative 1 in front of the y,
-y=4-1/2x
/-1 /-1
y=-4+1/2x
or
y=1/2x-4
Thus, this written in y=mx+b form, y=1/2x-4.
You have a rational expression whose numerator's degree is smaller than the denominator's. This tells you you should consider a partial fraction decomposition. We want to rewrite the integrand in the form
You can use the "cover-up" method here to easily solve for 
. It involves fixing a value of 
to make 2 of the 3 terms on the right side disappear and leaving a simple algebraic equation to solve for the remaining one.
- If
, then 
- If
, then 
- If
, then 
So the integral we want to compute is the same as
and each integral here is trivial. We end up with
which can be condensed as
