Darius owns a business that manufactures and sells record players, now that vinyl records have resurged in popularity. The graph shows Darius's expected revenue and cost in relation to the price he sets for each record player,
у
+7,000
(52, 6,570)
C(x)
+6,000
(32,5,539)
5,000
+4,000
R(x)
(85, 4,062)
Total (dollars)
+3,000
+2,000
+1,000
10
20
30
40
50
60
70
80
90
100
+-1,000
Price (dollars)
To make a profit, Darius should set the price for a record player between $
and $

.

step-by-step explanation:

$15.40 per mile

step-by-step explanation:

you have to round up to 4 because 6 is over 5 so you have to round the 3 up to 4

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.