Question

a pool is being drained at a constant rate. the table below shows how much water remains in the pool after “x” hours have passed. how much water was in the pool when it began to get drained? in addition, how fast is the pool being drained?

peter is walking home from school. on his way home, he stops by a park and stays their for a bit. suddenly, he remembers that he has to get home for his sister’s birthday party. peter then leaves the park and sprints the rest of the way. sketch a graph of this.

triangle abc is a reflection of the scalene triangle xyz. select all statements that must be true.

a) ( mangle z=mangle c ) c) ( overline{yz}=overline{ac} ) e) ( overline{xz}=overline{ac} )
b) ( mangle x=mangle c ) d) ( mangle b=mangle x )

which series of transformations demonstrates that the figures are congruent?

a) a rotation of ( 180^circ ) about the origin followed by a translation of 2 units up.
b) a rotation of ( 90^circ ) clockwise about the origin followed by a reflection over the y axis.
c) a reflection over the y axis followed by a translation of 4 units down.
d) a reflection over the x axis followed by a translation of 5 units to the left.

Explanation:

Step1: Find the initial amount of water

When \(x = 0\), the value of \(y\) (gallons in pool) is \(3200\). This is the amount of water in the pool at the start (when \(x = 0\) hours passed).

Step2: Calculate the rate of draining

The rate of change (slope \(m\)) of a linear function \(y=mx + b\) (where \(b\) is the \(y\) - intercept) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Take two points \((x_1,y_1)=(0,3200)\) and \((x_2,y_2)=(1,2900)\).
\(m=\frac{2900 - 3200}{1-0}=\frac{- 300}{1}=-300\) gallons per hour. The negative sign indicates that the amount of water is decreasing.

Answer:

The pool had \(3200\) gallons of water when it began to get drained and it is being drained at a rate of \(300\) gallons per hour.