A triangle has sides with lengths of 12 miles, 84 miles, and 85 miles. Is it a right triangle?

Step-by-step explanation:

If a triangle is a right triangle, it can satisfy Pythagorean Theorem.

where a and b are the legs and c is the hypotenuse.

12 and 84 are the legs because are they shortest. 85 is the hypotenuse because it is the longest side.

Substitute the values into the formula.

Solve the exponents.

Add on the right side.

7220 is not equal to 7225, so these sides cannot be a right triangle.

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