An informal survey was taken at a farmer’s market. People were asked whether they liked carrots, turnips, or both. The results are shown in the Venn diagram. A circle labeled carrots 84 overlaps a circle labeled turnips 25. Overlap is labeled 17. 4-column table with 3 rows. First column has no label with entries carrots, not carrots, total. Second column is turnips with entries a, b, blank. Third column is not turnips with entries 60%, blank, blank. Fourth column is labeled total with entries blank, blank, 100%. What are the values of a and b in the relative frequency table for the survey results? Round answers to the nearest percent. a = 12%, b = 17% a = 12%, b = 18% a = 40%, b = 18% a = 41%, b = 63%

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step-by-step explanation:

distance formula is d=√(x2-x1)^2   +   (y2-y1)^2

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.

this is a good question! i’ll do some research and what i find, i’ll contact you asap when i have something! ✊