Together, david and carol have a total of 35,000 frequent flyer miles with an airline. carol has 19,000 miles. after going on a business trip, david has 1200 more miles than he had last month. how many frequent flyer miles did david have last month?

In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.

It is saturday morning and jeremy has discovered he has a leak coming from the water heater in his attic. since plumbers charge extra to come out on the weekends, jeremy is planning to use buckets to catch the dripping water. he places a bucket under the drip and steps outside to walk the dog. in half an hour the bucket is 1/5 of the way full. what is the rate at which the water is leaking per hour?

One number is 4 less than 3 times a second number. if 3 more than two times the first number is decreased by 2 times the second number, the result is 11. use the substitution method. what is the first number?