Which of the following sets of lengths can be used to form the sides of a triangle? explain your reasoning. 5 inches, 8 inches, 20 inches 3 inches, 16 inches, 18 inches 2 inches, 5 inches, 7 inches

3 inches, 16 inches, 18 inches

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Verify each case

case 1) we have

5 inches, 8 inches, 20 inches

Applying the triangle Inequality Theorem

1) 5+8 > 20

13 > 20 > is not true

therefore

The set of lengths cannot be used to form the sides of a triangle

case 2) we have

3 inches, 16 inches, 18 inches

Applying the triangle Inequality Theorem

1) 3+16 > 18

19 > 18 > is true

2) 3+18> 16

21 > 16 > is true

3) 16+18 > 3

34 > 3 > is true

therefore

The set of lengths can be used to form the sides of a triangle

case 3) we have

2 inches, 5 inches, 7 inches

Applying the triangle Inequality Theorem

1) 2+5 > 7

7 > 7 > is not true

therefore

The set of lengths cannot be used to form the sides of a triangle

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation: