The side lengths 10, 14, and 15 form a triangle. Explain why.

Therefore, the side lengths 10, 14, and 15 form a triangle.

Step-by-step explanation:

The Triangle Inequality Theorem defines that if we are given the three sides of a triangle, then the sum of any 2 sides of a triangle must be greater than the measure of the third side of the triangle.

The three conditions that need to be met for any triangle with the side lengths A, B, and C.

Given the side lengths of a triangle

Let us check whether it satisfies the three conditions.

10+15 > 14     →  TRUE

10+14 > 15     →  TRUE

14+15 > 10    →  TRUE

As all the conditions are met. Therefore, the side lengths 10, 14, and 15 form a triangle.

practice. practice. practice.

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