Arectangular patio has an area of 91 ft squared. the length is 6 feet longer than the width. find the dimensions of the patio area. solve by completing the square. a. find the width and the length in terms of w b. write the equation for the total area. c. find (b/2)to the second d. find the dimensions.

Ivan and jeff buy a package of 8 pens for $4.00. ivan wants 5 of the pens, and jeff wants 3.how much should each student pay?

Me on this one i will give you 20pts. answer should be in detail . this is the discussion topic. one of the most fiercely debated topics in sports is the hot hand theory. the hot hand theory says that success breeds success. in other words, rather than each shot a basketball player takes or each at-bat a baseball player has being an independent event, the outcome of one event affects the next event. that is, a player can get hot and make a lot of shots in a row or get a lot of hits in a row. the hot hand theory, however, has been shown to be false in numerous academic studies. read this article, which discusses the hot hand theory as it relates to a professional basketball player. state whether you agree or disagree with the hot hand theory, and give reasons for your opinion. be sure to use some of the terms you’ve learned in this unit, such as independent event, dependent event, and conditional probability, in your answer.

In one day there are too high tides into low tides and equally spaced intervals the high tide is observed to be 6 feet above the average sea level after six hours passed a low tide occurs at 6 feet below the average sea level in this task you will model this occurrence using a trigonometric function by using x as a measurement of time assume the first high tide occurs at x=0. a. what are the independent and dependent variables? b. determine these key features of the function that models the tide: 1.amplitude 2.period 3.frequency 4.midline 5.vertical shift 6.phase shift c. create a trigonometric function that models the ocean tide for a period of 12 hours. d.what is the height of the tide after 93 hours?