Which sequence of transformations on preimage ∆abc will not produce the image ∆a'b'c'? reflection across the line y = -x followed by a rotation 180° counterclockwise about the origin reflection across the y-axis followed by a rotation 90° clockwise about the origin reflection across the x-axis followed by a reflection across the y-axis reflection across the line y = x rotation 180° clockwise about the origin followed by a reflection across the line y = -x

1234567891011 match the reasons with the statements in the proof. given: j | | k m 1 = m 3 prove: l | | m 1. j||k, m∠3 = m∠1 if lines are ||, then corresponding angles are =. 2. m∠1 = m∠2 if alternate interior angles are =, then lines are ||. 3. m∠2 = m∠3 substitution 4. l||m given

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."

The base of a triangle is 8 1 3 meters and the height of the triangle is the fourth root of 16 meters meters. what is the area of the triangle?