C is the incenter of isosceles triangle ABD with vertex angle ∠ABD. Does the following proof correctly justify that triangles ABC and DBC are congruent? It is given that C is the incenter of triangle ABD, so segment BC is an altitude of angle ABD.

Angles ABC and DBC are congruent according to the definition of an angle bisector.
Segments AB and DB are congruent by the definition of an isosceles triangle.
Triangles ABC and DBC share side BC, so it is congruent to itself by the reflexive property.
By the SAS postulate, triangles ABC and DBC are congruent.

There is an error in line 1; segment BC should be an angle bisector.
The proof is correct.
There is an error in line 3; segments AB and BC are congruent.
There is an error in line 5; the ASA Postulate should be used.

An electronics manufacturer wants to know if customers would be interested in a detachable keyboard for their tables and if so, what the most important features would be. the manufacturer partners with an electronics store to include copies of the survey with every purchase at that store for one week. which of the following best explains why this random sample is unlikely to be a good representative sample of tablet owners' preferences for a detachable keyboard? a) one week is likely not enough time to get a large enough sample. b) most people won't bother to send in the survey, which is likely to skew the results c) there is no way to verify whether the responders to the survey actually own a tablet d) the survey is biased because it was conducted through an electronics store, not the general population

Which expression is equivalent to (3^2)^-2 a.-81 b.-12 c.1/81 d.1/12

Bugs bunny was 33 meters below ground, digging his way toward pismo beach, when he realized he wanted to be above ground. he turned and dug through the dirt diagonally for 80 meters until he was above ground