7. Antonio is President of Maths-R-Us and has asked his financial advisor for a report about the company's expected profits. The advisor told him that the profits were expected to follow the equation y= 150,210(0.82)* over the next 12 months. a. Will Antonio's profit increase or decrease in the coming months and by what percentage? (2 pts) b. How much profit can Antonio expect to make 7 months from now? (1 pt) AL

a) The negative sign indicates that progression is decreasing in time and decreases by 18 percent each month.

b) Antonio is expected to make a profit of 37445.17 in 7 months from now.

Step-by-step explanation:

a) The equation described on statement represents a geometrical progression, which is defined as:

(1)

Where:

- Initial amount, measured in monetary units.

- Rate, dimensionless. (The progression is increasing when , and decreasing when )

- Time, measured in months.

- Profit, measured in monetary units.

Given that , we calculated the rate below:

The negative sign indicates that progression is decreasing in time and decreases by 18 percent each month.

b) If we know that , then the expected amount for Antonio in 7 months from now is:

Antonio is expected to make a profit of 37445.17 in 7 months from now.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

answer:

c) the x-coordinate of the center of the circle increases by 3