Find the 3 × 3 matrix that produces the following composite 2d transformation, using homogeneous coördinates: shift points 2 units in the r-direction and -3 units in the y-direction, then rotate through 45°, then reflect across the origin. (hint: see section 1.9 for some possibly useful information.)

Danny draws a transversal, t, on two parallel lines ab and cd, as shown below: he makes the following table to prove that the alternate interior angles are equal: which is the missing justification? (6 points) corresponding angles formed by a transversal on parallel lines are supplementary. corresponding angles formed by a transversal on parallel lines are congruent. co-interior angles formed by a transversal on parallel lines are congruent. co-exterior angles formed by a transversal on parallel lines are congruent.

What is the value of x in the equation 6(x + 1) – 5x = 8 + 2(x – 1)?

Me! #1 write an equation for the interior angles of this triangle that uses the triangle sum theorem. #2 what is the value of x? #3 what is the measure of #4 classify the triangle above as acute, obtuse, or right. state your reason in a complete sentence.