Kate and mateo are on a hill by a river. kate throws a stick into the river. her stick’s path is described by the equation y = –5x^2 + 10x + 9. mateo is higher on the hill than kate. he also throws a stick into the river. the path of his stick is shown in the graph. in each function, x is the stick's horizontal distance from the hill and y represents its height. both are measured in feet. whose stick reached a higher point above the river? a. mateo’s stick reached a higher point. b. kate’s stick reached a higher point. c. the two sticks reached the same height.

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

If t8 = 4 and t12 = −2, find the first three terms of the arithmetic sequence.

Ican interpret and represent the remainder in division calculations sensibly for the context (eg if we wont to know how many 40 seat buses will be needed to transport 170 students for on excursion, we divide 170 by 40 and realise buses and another smaller vehicle to that we need 4 transport 10 more students) solve the following questions. show your work! 11) the zoo had 420 butterflies that needed to be transported to a new enclosure. the boxes that the butterflies would be moved in only hold 80 butterflies in each. how many boxes would they need? 2 12) each classroom in the school can have exactly 25 students, if there are 345 students in the school how many full classrooms are there?