Let D be a region bounded by a simple closed path C in the xy-plane. The coordinates of the centroid ( , ) of D are given below, where A is the area of D. = 1/2A x 2 dy = -1/2A y 2 dx Use the formulas to find the centroid of the triangle with vertices (0, 0), (a, 0), and (a, b), where a > 0 and b > 0. {x, y) = ( )

Perform the required operations on the following functions given: f(x)= 3-x; g(x)= -2x find g[f(x)]

Tim's phone service charges $23.06 plus an additional $0.22 for each text message sent per month. if tim's phone bill was $28.56, which equation could be used to find how many text messages, x, tim sent last month?

Ariana starts with 100 milligrams of a radioactive substance. the amount of the substance decreases by 20% each week for a number of weeks, w. the expression 100(1−0.2)w finds the amount of radioactive substance remaining after w weeks. which statement about this expression is true? a) it is the difference between the initial amount and the percent decrease. b) it is the difference between the initial amount and the decay factor after w weeks. c) it is the initial amount raised to the decay factor after w weeks. d) it is the product of the initial amount and the decay factor after w weeks.