Polygons efhg and e′f′h′g′ are shown on the following coordinate grid:

what set of transformations is performed on efhg to form e′f′h′g′?

a.) a translation 1 unit to the right followed by a 90-degree counterclockwise rotation about the origin
b.) a translation 1 unit to the right followed by a 270-degree counterclockwise rotation about the origin
c.) a 270-degree counterclockwise rotation about the origin followed by a translation 1 unit to the right
d.) a 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the right

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."

Arley is building a model of a city map. in one part of the city, three roads form a right triangle, which harley draws as triangle abc, with the following measures: m∠b=90° and m∠a=30°. in his scale model, the hypotenuse of triangle abc, ac¯¯¯¯¯¯¯¯, has a length of 817−−√ cm. what is the value of a (the length of bc¯¯¯¯¯¯¯¯)?

What is the range for 31,39,29,34,37,24,36,33,34,28