Alex needs to borrow 10,000 dollars from the bank. the bank gives him two options.
1. a ten-year loan with an interest rate of 10% compounded quarterly, with the condition that at the end of 5 years alex must make a payment equal to half of his balance. at the end of the ten years, alex will pay off the remaining balance.
2. a ten-year loan with a simple annual interest rate of 12%, with just one lump-sum payment at the end of the ten years. find the positive difference between the total amounts alex has to pay back under the two schemes. round your answer to the nearest dollar.

Based on the situation in part a, the width of a rectangular garden is x feet, and its length is 5 feet more than twice its width. the right side of the equation, g(x) = 2x2 − 13x + 6, can be factored to g(x) = (2x − 1)(x − 6). this function could represent an inner region of the garden from the first equation, such as a vegetable garden with a border around it. the length of this inner garden would be 2x − 1 feet, and the width would be x − 6, which would leave a 3-foot border around the garden. part d what is the value of g(8) for the function g(x) in part c? what does this value mean in the context of the situation you described in part c?