Question

1. mishaals pool is partially full and he is using water from a garden hose to add water. he adds water to the pool at a rate of 9 gallons per minute. after the hose has been filling the pool for 120 minutes, the pool contains 7580 gallons of water. a. write an equation in point - slope form for the total amount of water in the pool, y, in gallons, after the hose has been filling the pool for x minutes. (1 point) b. how much water was in the pool when mishaal started filling it with the hose? (1 point) c. the pool will contain a total of 15,000 gallons of water after it is filled. how many minutes, x, will it take for the hose to fill the pool? (2 points)

Explanation:

Step1: Identify the slope - intercept form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$. Here, the initial amount of water $y_1 = 7580$ gallons, the rate of change (slope) $m = 9$ gallons per minute.

Step2: Write the equation

The equation for the total amount of water $y$ in the pool after $x$ minutes is $y-7580 = 9(x - 0)$, which simplifies to $y=9x + 7580$.

Step3: Find the initial amount of water

We know that at $x = 0$ (when Mishaal started filling), substituting $x = 0$ into $y=9x + 7580$, we get $y=7580$ gallons.

Step4: Solve for the time to fill the pool

We set $y = 15000$ (the full - capacity of the pool) in the equation $y=9x + 7580$. So, $15000=9x + 7580$.
Subtract 7580 from both sides: $15000-7580=9x$, which gives $7420 = 9x$.
Then $x=\frac{7420}{9}\approx824.44$ minutes.

Answer:

a. $y = 9x+7580$
b. 7580 gallons
c. $\frac{7420}{9}\approx824.44$ minutes