A swimming club can currently accommodate up to 100 members for a year-long training program. They plan to increase their pool capacity to accommodate up to an additional 75 members into the program every year. To make a profit, the club must have at least 50 members enrolled in the program. The club manager expects the minimum membership requirement for making a profit to increase by 20% every year. The manager modeled this situation with a system of inequalities, where x is time from today, in years, and y is the number of members. She graphed the system to show the solution region when the club is making a profit.

In a graph with several intervals o data how does a constant interval appear? what type of scenario produces a constant interval?

Use the ratio test to determine whether ∑n=14∞n+2n! converges or diverges. (a) find the ratio of successive terms. write your answer as a fully simplified fraction. for n≥14, limn→∞∣∣∣an+1an∣∣∣=limn→∞.

Statement reason 1. δabc is similar to δced. given 2. 3. definition of slope 4. slope of slope of definition of slope 5. slope of × slope of multiplying the slopes 6. slope of × slope of substitution property of equality 7. slope of × slope of simplifying the right side the table contains the proof of the relationship between the slopes of two perpendicular lines. what is the reason for statement 2? a. parallel line segments that meet a common perpendicular line are proportional in length. b. the lengths of vertical and horizontal sides in congruent triangles are in a common ratio. c. trigonometric identities determine the lengths of the legs in a right triangle. d. corresponding side lengths in similar triangles are proportional in length.