Consider a geometric progression, where a1 represents the first term, and an represents the nth term. Each term of the progression is defined by the product of the previous term and the common ratio, r. The derivation of the formula for the finite sum of a geometric progression, where r < 1, is shown below, with a mistake at a key step. Steps Derivation Reasons 1 Given 2 Substitution 3 Multiply both sides by r 4 Subtracting Sr from S 5 Factor common terms 6 Division Determine the step where the first mistake occurs.

What is the solution to the equation 9^(x+1) =27

5, 6, 10 question: a. determine whether the side lengths form a triangle. (explain your reasoning) b. if it is a triangle, determine whether it is a right, acute, or obtuse triangle. (show your work)

Arrange the steps to solve this system of linear equations in the correct sequence. x + y = -2 2x – 3y = -9 tiles subtract 3x + 3y = -6 (obtained in step 1) from 2x – 3y = -9 (given) to solve for x. substitute the value of x in the first equation (x + y = -2) to get y = 1. the solution for the system of equations is (-3, 1). x = -15 the solution for the system of equations is (-15, 13). add 3x + 3y = -6 (obtained in step 1) to 2x – 3y = -9 (given), and solve for x. x = -3 substitute the value of x in the first equation (x + y = -2) to get y = 13. multiply the first equation by 3: 3(x + y) = 3(-2) 3x + 3y = -6.