To find the distance between (-2,-3) and (4,1), Peggy's teacher drew a diagram and marked blue lines to represent the legs of a right triangle. Peggy then used 4² and 6² to find the distance represented by the red segment. What distance did she find?

20
√114
25
√52

lets say that the unknown distance is x so:

x²=4²+6²

x²=16+36

x²=52

x=√52

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: