Triangles Q R S and T U V are shown. Triangle Q R S is translated across S Q and then is shifted down and to the right to form triangle T U V. Can a translation and a reflection map TriangleQRS to TriangleTUV? Explain why or why not.

No, the triangles are not congruent.
Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map
△QRS to △TUV.
No, the triangles are obtuse.
Yes, a translation mapping vertex S to vertex T and a reflection across the line containing RS will map
△QRS to △TUV. Which of these triangle pairs can be mapped to each other using a single translation?

Paul’s car is 18 feet long. he is making a model of his car that is 1/6 the actual size. what is the length of the model?

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24

White shapes and black shapes are used in a game. some of the shapes are circles. while the rest are squares. the ratio of the number of white shapes to the number of black shapes is 5: 11. the ratio of the number of white cicrles to the number of white squares is 3: 7. the ratio of the number of black circles to the number of black squres is 3: 8. work out what fraction of all the shapes are circles.