If Marie were to paint her living room alone, it would take 7 hours. Her sister Barbara could do the job in 8 hours. How many hours would it take them working together? Express your answer as a fraction reduced to lowest terms, if needed.

Given: ab ≅ cd and ad ≅ bc prove: abcd is a parallelogram. statements reasons 1. ab ≅ cd; ad ≅ bc 1. given 2. ac ≅ ac 2. reflexive property 3. △adc ≅ △cba 3. ? 4. ∠dac ≅ ∠bca; ∠acd ≅ ∠cab 4. cpctc 5. ∠dac and ∠bca are alt. int. ∠s; ∠acd and ∠cab are alt. int. ∠s 5. definition of alternate interior angles 6. ab ∥ cd; ad ∥ bc 6. converse of the alternate interior angles theorem 7. abcd is a parallelogram 7. definition of parallelogram what is the missing reason in step 3? triangle angle sum theorem sas congruency theorem sss congruency theorem cpctc

Write a function rule for  “the output is  5 less than the input.” let  xx  be the input and let  yy  be the output.

Sarah is collecting recyclables for a science project. on the first day she collected 35 recyclable objects. on the second day she had a total of 52 recyclables. on the third day she had a total of 69 recyclables. determine if the scenario describes an arithmetic or a geometric sequence. then, write the recursive formula for the sequence described.