The steps for determining the center and radius of a circle using the completing the square method are shown below: step 1 [original equation]: x2 − 10x + y2 + 12y = 20 step 2 [group like terms]: (x2 − 10x) + (y2 + 12y) = 20 step 3 [complete the quadratics]: (x2 − 10x + 25) + (y2 + 12y + 36) = 20 + (25 + 36) step 4 [simplify the equation]: (x2 − 10x + 25) + (y2 + 12y + 36) = 64 step 5 [factor each quadratic]: (x − 5)2 + (y + 6)2 = 82 step 6 [identify the center and radius]: center = (5, −6) radius = 8 what is the first incorrect step, and how can it be fixed? step 3, replace 25 with 5 and replace 36 with 6 step 4, replace 64 with 81 step 5, replace − 5 with + 5 and replace + 6 with − 6 all steps are correct.

An annual marathon covers a route that has a distance of approximately 26 miles. winning times for this marathon are all over 2 hours. the following data are the minutes over 2 hours for the winning male runners over two periods of 20 years each. earlier period 14 12 15 22 13 10 19 13 9 14 20 18 16 20 23 12 18 17 6 13 recent period 7 11 7 14 8 9 11 14 8 7 9 8 7 9 9 9 9 8 10 8 (a) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the earlier period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks. for more details, view how to split a stem.) minutes beyond 2 hours earlier period 0 1 2 (b) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the recent period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks.) minutes beyond 2 hours recent period (c) compare the two distributions. how many times under 15 minutes are in each distribution