The Raymond couple wants to find an apartment in Abu Dhabi, UAE but can’t decide which option is better for long term usage. A 1 BHK apartment costs AED 64,000 yearly to rent and all utilities (Water, Electricity, etc…) are included. However, another 1 BHK apartment can be purchased outright without any utilities included for AED 640,000. The utilities for both apartments cost 11400 AED on average per year. How many years will it take until the house bought outright starts to become cheaper? (Reminder: One has utilities included while the other apartment has to still pay for it) Help, please!

2nd one in the first row is correct

25/14 or 1.

step-by-step explanation:

the dots mean that it has infinitely more numbers behind it

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.