Catie is trying to determine the height that a ladder reaches as it leans against a wall. she walks under the ladder and touches her forehead to it as shown. if her feet are 16 inches from the ladder's base, the ladder's base is 4.5 feet from the bottom of the wall, and catie is 5 feet 6 inches tall, then come up with an estimate for how high the ladder reaches up the wall to the nearest tenth of a foot. watch your units on this problem and show all work

Pete is making decorations for a dinner party. the instructions tell him to use 9 flowers for a medium-sized decoration. complete each statement to adjust the flowers for different-sized decorations based on these instructions.

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

What are the solutions of the system? y = x^2 + 2x +3y = 4x - 2a. (-1, -6) and (-3, -14)b. (-1, 10) and (3, -6)c. no solutiond. (-1, -6) and (3, 10)