By the triangle inequality theorem which set of side lengths could create a triangle?
a) 4, 8, 2
b) 5, 9, 6
c) 6, 8, 16
d) 10, 4, 3

B

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

So, let's test each of the points:

A) We have the points: 4, 8, 2. If we sum 4 and 2, the result is 6. Which is not greater than the third side which is 8. So it does not qualify for a triangle.

B) We have the points 5, 9, 6. If we sum 5+6 = 11 which is greater than 9. The sum of any two sides from this set is greater than the third side. It could create a triangle.

C) We have the points 6, 8, 16. If we sum  6+8 = 14 which is not greater than the third side 16. So it could not create a triangle.

D) we have the points 10, 4, 3. If we sum 4+3 = 7 which is not greater than 10. For that reason, it could not create a triangle.

5+2x=a

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