Which dimensions cannot create a triangle?
three angles measuring 25°, 65°, and 90°
three angles measuring 50°, 30°, and 100°
three sides measuring 5 in., 12 in., and 13 in.
three sides measuring 4 ft, 8ft, and 14 ft

three sides measuring 4 ft, 8ft, and 14 ft

Step-by-step explanation:

Verify each case

case 1) three angles measuring 25°, 65°, and 90°

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

in this problem

25°+65°+90°=180° > is correct

therefore

I can create a triangle

case 2) three angles measuring 50°, 30°, and 100°

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

in this problem

50°+30°+100°=180° > is correct

therefore

I can create a triangle

case 3) three sides measuring 5 in., 12 in., and 13 in.

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

so

1) 5+12 > 13 > is true

2) 5+13 > 12 > is true

3) 12+13 > 5 > is true

therefore

I can create a triangle

case 4) three sides measuring 4 ft, 8ft, and 14 ft

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

so

1) 4+8 > 14 > is not true

therefore

cannot create a triangle

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: