Fatou has $150 in her bank account. She buys a bike for $200. What is Fatou’s account balance now? Show your work.

Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial

Use the ratio test to determine whether ∑n=14∞n+2n! converges or diverges. (a) find the ratio of successive terms. write your answer as a fully simplified fraction. for n≥14, limn→∞∣∣∣an+1an∣∣∣=limn→∞.

(50 points) drag each description to the correct location on the table. each description can be used more than once. some systems of equations and their graphs are given in the table. for each system, place the description(s) in the box that correctly describe the type of system shown. :