Given a graph for the transformation of f(x) in the format g(x) = f(x) + k, determine the k value. two parabolas open up with f of x passing through negative 3 comma negative 3 and g of x passing through negative 3 comma 5 k = −3 k = 3 k = 5 k = 8

One-third of the people from country a claim that they are from country b, and the rest admit they are from country a. one-fourth of the people from country claim that they are from country a, and the rest admit they are from country b. in a combined census of the two countries, one-half of the total claimed to be from a. what is the ratio of the populations of country a to that of country b.

Since opening night, attendance at play a has increased steadily, while attendance at play b first rose and then fell. equations modeling the daily attendance y at each play are shown below, where x is the number of days since opening night. on what day(s) was the attendance the same at both plays? what was the attendance? play a: y = 8x + 191 play b: y = -x^2 + 26x + 126 a. the attendance was never the same at both plays. b. the attendance was the same on day 5. the attendance was 231 at both plays on that day. c. the attendance was the same on day 13. the attendance was 295 at both plays on that day. d. the attendance was the same on days 5 and 13. the attendance at both plays on those days was 231 and 295 respectively.

The height of a plant, in inches, p years after planting it is given by the polynomial function r(p) = -2p% + 270p. find the height of the plant when p = 90 years.