Let $a_1,$ $a_2,$ $\dots,$ $a_n$ be real numbers such that \[a_1^2+2a_2^2+\cdots+na_n^2 = 1.\]Find the maximum value of $(a_1+2a_2+\cdots+na_n)^2.$

Over which interval is the graph of f(x) = x2 + 5x + 6 increasing?

Barney & noblet customers can choose to purchase a membership for $25 per year members receive 10% off all store purchases 1. how much would a member pay per year if he bought $50 worth of items each year? 2. write a slope-intercept equation that expresses how much a member pays per year using x to represent his purchases per year 3. how much would a member have to spend per year to pay off his membership fee?

Which of the following pair(s) of circles have las a common external tangent? select all that apply. a and b a and c b and c