Determine whether the given lengths can be sides of a right triangle. which of the following are true statements. a. the lengths 7, 40 and 41 can not be sides of a right triangle. b. the lengths 12, 16, and 20 can not be sides of a right triangle. c. the lengths 7, 40 and 41 can not be sides of a right triangle. d.the lengths 12, 16, and 20 can be sides of a right triangle. the lengths 7, 40 and 41 can be sides of a right triangle.

Given sides 12, 16 and 20 can be the sides of right triangle.

Step-by-step explanation:

Sides of right triangle always follow the Pythagoras theorem.

i.e

For the given Lengths 7, 40 and 41

We need to check if

That means,

hence 7,40 and 41 can not be the sides of right triangle.

Next,

Given sides 12,16 and 20.

Again follow the similar process used in the above problem.

Therefore given sides 12,16 and 20 can be the sides of right 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:

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.