Mathematics: Phil is boiling water on the stove. the pot he is using contains 4 gallons of water. if the water is evaporating at a rate of 1 cup per minute, how long will it be before all the water is gone? (hint: 1 gallon = 16 cups)

Phil is boiling water on the stove. the pot he is

laylay1734

23.03.2021

1) These linear functions must not describe a pair of parallel lines.

2) Any intersection of two lines determines a point.

Step-by-step explanation:

Hi there!

Well, since no further details were given. Let's call the linear function that represents the number of animals adopted from the shelter s(x) . And

the hours the volunteers work at the shelter each week v(x)

1) These linear functions must not describe a pair of parallel lines.

If these lines intersect, then their slope must be different.

$m_{s}\neq m_{v}\\e.g.\\m_{s}=2\\m_{v}=-2$

Equal slopes, parallel lines. Parallel lines, no intersection.

Different slopes, then there is an intersection at some point.

2) Any intersection of two lines determines a point. Let's find it.

So to find one common point equalize the two functions, then find the value for the x-coordinate. Plug it in one of the functions, e.g.

$2x+2=-2x+2 \rightarrow 4x=0 \therefore x=0\\2(0)+2=2 \Rightarrow (0,2)$

At the common point, both functions after inserted the same value in the Domain (x) return the same result for their respective Range set.

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