Kareem wants to put up a small corner shelf in his room. The shelf is in the shape of a right triangle. One leg of the triangle is2inches shorter than the other. The longest side of the shelf is10inches long. Kareem needs to find the area of the shelf so that he knows if he has enough paint to cover the top of the shelf. He has enough paint to cover23square inches. a. Let the length of the long leg of the triangle equalx. How can the length of the short leg be expressed in terms ofx?b. How can the Pythagorean Theorem help us to relate the lengths of all three sides of the triangular shelf?c. How can the equation be simplified and set equal to0?d. How can the quadratic expression be rewritten in factored form?e. How can the Zero Product Property help us to solve the factored equation?f. Do both of the answers make sense as side lengths?g. What are the lengths of the two legs of the triangle?h. What is the area of the shelf?i. Does Kareem have enough paint?

At river bank, checking account customers earn 0.75% interest a month on their account balances, pay no service fees for writing checks, and pay a monthly $2.00 financial charge. calculate the income earned in one month on the checking account for a customer with an account balance of $1,000. a. $4.25 b. $5.50 c. $6.75 d. $7.25 checking account earnings at baker’s bank are expressed by the equation: i = -0.09x + 10.2. while the earnings at elite bank are modeled by: i = -0.02x + 7.5. in both cases, x is the number of checks written. at what number of checks will elite bank start generating more checking account income than baker's bank? a. 12 b. 25 c. 39 d. 42 emilio’s checking account had a balance of 728.32 at the beginning of the week. he wrote checks for the following amounts throughout the week: $99.48, $33.50, $18.23, and $72.05. he also deposited his paycheck in the amount of $1,109.90. what is his account balance at the end of the week? a. $1,192.35 b. $1,222.86 c. $1,540.52 d. $1,614.96