Martins interested in joining a gym and has researched the cost of two gyms close to his house Gym A has a $50 registration fee and costs $30 per month. Gym B has a $100
station fee and costs $10 per month. The cost of joining ench gym can be modeled by the
expressions below, where represents the number of months.
• MAS0m - 50
• Om : 10m + 100
Martin writes the equation 30m + 50 = 10m + 100. What would the solution to the
equation de Martin
A How many months he could go to the gym for $100
3. How much money he would be spending after m months
C. How much money he would be spending if he joined both gyms
OD How many months until the total spent is the same for both gyms

the answer is 0.5 mpm

step-by-step explanation:

the line goes half way through the square each time (which is 0.5 or half of course) so that would mean its 0.5 mpm.

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.