The functions graphed show the snowfall, in inches, in two cities after x hours. select each correct answer. middletown had a faster rate of snowfall. smithville had a faster rate of snowfall. snow fell in smithville at a rate of 4 inches per hour. middletown already had snow on the ground at the beginning of the storm.

Answers

we know that

the formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

in this problem

the rate of snowfall is equal to the slope of the linear equation

so

Let

x-------> the time in hours

y---------> the snowfall in inches

Step 1

Find the slope of the line of the Smithville city

Let

A(0,0)\\B(5,20)

substitute the values in the formula above

m=\frac{20-0}{5-0}

m=4\frac{inches}{hour}

Step 2

Find the slope of the line of the Middletown city

Let

A(0,0)\\B(5,15)

substitute the values in the formula above

m=\frac{15-0}{5-0}

m=3\frac{inches}{hour}

Step 3

Verify the statements

case A) Middletown had a faster rate of snowfall

The statement is False

Because Smithville had a faster rate of snowfall with 4\frac{inches}{hour}

case B) Smithville had a faster rate of snowfall

The statement is True

case C) Snow fell in Smithville at a rate of 4 inches per hour

The statement is True

case D) Middletown already had snow on the ground at the beginning of the storm

The statement is False

Because at the beginning of the storm the value of the snow is equal to zero

therefore

the answer is

Smithville had a faster rate of snowfall

Snow fell in Smithville at a rate of 4 inches per hour

we know that

the formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

in this problem

the rate of snowfall is equal to the slope of the linear equation

so

Let

x-------> the time in hours

y---------> the snowfall in inches

Step 1

Find the slope of the line of the Smithville city

Let

A(0,0)\\B(5,20)

substitute the values in the formula above

m=\frac{20-0}{5-0}

m=4\frac{inches}{hour}

Step 2

Find the slope of the line of the Middletown city

Let

A(0,0)\\B(5,15)

substitute the values in the formula above

m=\frac{15-0}{5-0}

m=3\frac{inches}{hour}

Step 3

Verify the statements

case A) Middletown had a faster rate of snowfall

The statement is False

Because Smithville had a faster rate of snowfall with 4\frac{inches}{hour}

case B) Smithville had a faster rate of snowfall

The statement is True

case C) Snow fell in Smithville at a rate of 4 inches per hour

The statement is True

case D) Middletown already had snow on the ground at the beginning of the storm

The statement is False

Because at the beginning of the storm the value of the snow is equal to zero

therefore

the answer is

Smithville had a faster rate of snowfall

Snow fell in Smithville at a rate of 4 inches per hour

The answer Fam is Smithville had a faster rate of snowfall., And..Snow fell in Smithville at a rate of 4 inches per hour.


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