Modeling and solving a problem: an isosceles triangle has two sides of equal length. the third side is 5 less than twice the length of one of the other sides. if the perimeter of the triangle is 23 cm, what is the length of the third side? explain how you would define a variable for this problem.

Simplify 5 square root of 7 end root plus 12 square root of 6 end root minus 10 square root of 7 end root minus 5 square root of 6 . (1 point) 5 square root of 14 end root minus 7 square root of 12 5 square root of 7 end root minus 7 square root of 6 7 square root of 12 end root minus 5 square root of 14 7 square root of 6 end root minus 5 square root of 7

The amount spent on food and drink by 20 customers is shown below what is the modal amount spent and the median amount spent? 40 25 8 36 18 15 24 27 43 9 12 19 22 34 31 20 26 19 17 28

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? )