Answer:
10
Step-by-step explanation:
(x + 2) + (-2 + x) = 20
2x + 0 = 20
2x = 20
x = 20/2
x = 10
12.5%. there is a 1 in 8 chance that all three times it will land on heads.
Answer: 13a-6b
Step-by-step explanation:
Answer:
67
Step-by-step explanation: Given the quadratic equation $z^2 + bz + c = 0$, Vieta's formulas tell us the sum of the roots is $-b$, and the product of the roots is $c$. Thus,
\[-b = (-7 + 2i) + (-7 - 2i) = -14,\]so $b = 14.$
Also,
\[c = (-7 + 2i)(-7 - 2i) = (-7)^2 - (2i)^2 = 49 + 4 = 53.\]Therefore, we have $b+c = \boxed{67}$.
There are many other solutions to this problem. You might have started with the factored form $(z - (-7 + 2i))(z - (-7 - 2i)),$ or even thought about the quadratic formula.
This is the aops answer :)
Well, I'm not completely sure, because I don't know the formal definition
of "corner" in this work. It may not be how I picture a 'corner'.
Here's what I can tell you about the choices:
A). (0, 8)
This is definitely a corner of the feasible region.
It's the point where the first and third constraints cross.
So it's not the answer.
B). (3.5, 0)
This is ON the boundary line between the feasible and non-feasible
regions. But it's not a point where two of the constraints cross, so
to me, it's not what I would call a 'corner'.
C). (8, 0)
Definitely not a corner, no matter how you define a 'corner'.
This point is deep inside the non-feasible zone, and it doesn't
touch any point in the feasible zone.
So tome, this looks like probably the best answer.
D). (5, 3)
This is definitely a corner. It's the point of intersection (the solution)
of the two equations that are the first two constraints.
The feasible region is a triangle.
The three vertices of the triangle are (0,8) (choice-A),
(0,-7) (not a choice), and (5,3) (choice-D) .
region is a triangle
