The logician Raymond Smullyan describes an island containing two types of people: knights who always tell the truth and knaves who always lie. You are visiting the island and have the following encounters with natives. (a) Two natives A and B address you as follows. A says: Both of us are knights. B says: A is a knave.

A is a knave

B is a knight

Step-by-step explanation:

If A is telling the truth, then both are knights and B cannot be lying. However, since B claims that A is a knave, they can't be both knights, and there is no possible way that A is a knight.

If A is knave and thus is lying, they aren't both knights. Since B claims A is a knave, his statement can be true and thus B can be knight and A will be knave.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

i think the answer is 90 hope this