Note: enter your answer and show all the steps that you use to solve this problem in the space provided. triangle a b c is shown with an angle bisector and two congruent sides. side a b is congruent to side a c. segment a d is the bisector of angle a. point d is on side b c. angle b a d is labeled y degrees. angle b d a is labeled x degrees. angle a c d is labeled 47 degrees. find the values of x and y.

The image of the point (-6, -2)under a translation is (−7,0). find the coordinates of the image of the point (7,0) under the same translation.

Carla was trying to decide what to do saturday evening. she has $100 available to spend for the evening. she has narrowed her choices down to these events: braves game, a concert of an artist she likes, or the georgia aquarium. admission to the braves game is $25, hot dogs cost $10, sodas cost $5. the concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. the georgia aquarium has the show of a lifetime with an all you can eat and drink that costs $100. carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her uber/lyft, which is $15 each way. which option should carla choose if she wants to spend the least? based on that choice, what then is carla's oppotunity cost? fully explain your answer in at least one paragraph.

Aprobability experiment is conducted in which the sample space of the experiment is s={7,8,9,10,11,12,13,14,15,16,17,18}, event f={7,8,9,10,11,12}, and event g={11,12,13,14}. assume that each outcome is equally likely. list the outcomes in f or g. find p(f or g) by counting the number of outcomes in f or g. determine p(f or g) using the general addition rule.