Both siblings are cleaning the house. Lily can clean the house in 40 minutes and Jake can clean the house in 30 without stopping. Suppose lily takes a five minute break from cleaning the house after 15 minutes of cleaning but Jake takes no breaks. How long will it take for them to finish cleaning the house together.

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

Three numbers x, y, and z are in the ratio 2: 7: 8. if 12 is subtracted from y, then three numbers form a geometric sequence (in the order x, y–12, z). find x, y, and z. there are 2 sets.

The equation ip| = 2 represents the total number of points that can be earned or lost during one turn of a game. which best describes how many points can be earned or lost during one turn?