The graph shows the vertical displacement y, in centimeters, that a weight bouncing from a spring would achieve if there were no friction, for a given number of seconds, x. (a) what is the weight’s maximum displacement? (b) from its resting position, how long does it take the weight to bounce one direction, then the other, and then return to its resting position? (c) what are the period and the amplitude of the function? (d) what is the graph’s frequency and what does it indicate in this situation? (e) how is the weight moving during the time period x = 4 to x = 5?

Atriangular field has sides of lengths 21, 39, and 41 yd. find the largest angle. (round your answer to the nearest degree.)

Questions 9-10. use the table of educational expenditures to answer the questions. k-12 education expenditures population indiana $9.97 billion 6.6 million illinois $28.54 billion 12.9 million kentucky $6.58 billion 4.4 million michigan $16.85 billion 9.9 million ohio $20.23 billion 11.6million 9. if the amount of k-12 education expenses in indiana were proportional to those in ohio, what would have been the expected value of k-12 expenditures in indiana? (give the answer in billions rounded to the nearest hundredth) 10. use the value of k-12 education expenditures in michigan as a proportion of the population in michigan to estimate what the value of k-12 education expenses would be in illinois. a) find the expected value of k-12 expenditures in illinois if illinois were proportional to michigan. (give the answer in billions rounded to the nearest hundredth) b) how does this compare to the actual value for k-12 expenditures in illinois? (lower, higher, same? )

Match the following reasons with the statements given to create the proof. 1. do = ob, ao = oc sas 2. doc = aob given 3. triangle cod congruent to triangle aob vertical angles are equal. 4. 1 = 2, ab = dc if two sides = and ||, then a parallelogram. 5. ab||dc if alternate interior angles =, then lines parallel. 6. abcd is a parallelogram cpcte