The specifications for machining a piece of metal state that it must be 12 cm long, within a 0.01-cm tolerance. What is the longest the piece is allowed to be? What is the shortest? Express the range of acceptable values for the length of the piece using inequalities.

Which of the following correctly justifies statement four of the two column proof? a. corresponding angles theorem b. transitive property of equality c. vertical angle theorem d. substitution property of equality

What are the solutions of the system? solve by graphing. y = -x^2 - 3x + 2 y = -2x + 2

Raj encoded a secret phrase using matrix multiplication. using a = 1, b = 2, c = 3, and so on, he multiplied the clear text code for each letter by the matrix to get a matrix that represents the encoded text. the matrix representing the encoded text is . what is the secret phrase? determine the location of spaces after you decode the text. yummy is the corn the tomato is red the corn is yummy red is the tomato