The cost of taking a cab is $4 plus $0.75 per mile. This can be represented using the linear function c=0.75m+4

Question

, where c is the cost per trip and m is the distance in miles. Graph the equation on a coordinate plane. Based on your line, what would the corresponding dependent variable be if you were to travel 4.5 miles? Round your answer to the nearest hundredth.(1 poin

Answer 1

To find the corresponding cost \( c \) when \( m = 4.5 \) miles, you can substitute \( m \) into the linear function:

\[ c = 0.75m + 4 \]

Substituting \( m = 4.5 \):

\[ c = 0.75(4.5) + 4 \]

Now calculate \( 0.75 \times 4.5 \):

\[ 0.75 \times 4.5 = 3.375 \]

Now add this to the base fare of $4:

\[ c = 3.375 + 4 = 7.375 \]

So, the corresponding cost \( c \) for traveling 4.5 miles is approximately:

\[ c \approx 7.38 \text{ (rounded to the nearest hundredth)} \]

Thus, the final answer is \( \mathbf{7.38} \).

Answer 2

A graph of the function y=80x+2
models Carli’s road trip, with her speed measured in miles per hour. The graph includes the two hours of stops she’ll make. Using this information, define which quantity describes the x-axis.(1 point)
Responses

miles traveled
miles traveled

speed traveled
speed traveled

direction traveled
direction traveled

time in hours

Answer 3

In the function \( y = 80x + 2 \), where \( y \) represents the total distance traveled (in miles) and \( x \) represents the time (in hours), the quantity that describes the x-axis is:

time in hours

This is because \( x \) corresponds to the time Carli has traveled, factoring in her speed and any stops made during the road trip.

Answer 4

A rental truck company charges $25 to rent a truck, then $1.25 for every mile it is driven. The situation can be expressed as C=1.25m+25
, where C
is the total cost to rent the truck and m is the miles driven. If you plot points on the linear function, which of the following would appear?(1 point)
Responses

(30,4)
and (35,8)
left parenthesis 30 comma 4 right parenthesis and left parenthesis 35 comma 8 right parenthesis

(2,22.5)
and (4,20)
left parenthesis 2,22.5 right parenthesis and left parenthesis 4 comma 20 right parenthesis

(4,30)
and (8,35)
left parenthesis 4 comma 30 right parenthesis and left parenthesis 8 comma 35 right parenthesis

(2,2.5)
and (4,5)

Answer 5

To determine which points lie on the linear function \( C = 1.25m + 25 \), let's evaluate each pair of points by substituting the values of \( m \) (miles driven) into the equation and calculating the corresponding \( C \) (total cost):

1. For \( (30, 4) \) and \( (35, 8) \):

   • For \( (30, 4) \): \[ C = 1.25(30) + 25 = 37.5 + 25 = 62.5 \quad \text{(not 4)} \]
   • For \( (35, 8) \): \[ C = 1.25(35) + 25 = 43.75 + 25 = 68.75 \quad \text{(not 8)} \]

2. For \( (2, 22.5) \) and \( (4, 20) \):

   • For \( (2, 22.5) \): \[ C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \quad \text{(not 22.5)} \]
   • For \( (4, 20) \): \[ C = 1.25(4) + 25 = 5 + 25 = 30 \quad \text{(not 20)} \]

3. For \( (4, 30) \) and \( (8, 35) \):

   • For \( (4, 30) \): \[ C = 1.25(4) + 25 = 5 + 25 = 30 \quad \text{(correct)} \]
   • For \( (8, 35) \): \[ C = 1.25(8) + 25 = 10 + 25 = 35 \quad \text{(correct)} \]

4. For \( (2, 2.5) \) and \( (4, 5) \):

   • For \( (2, 2.5) \): \[ C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \quad \text{(not 2.5)} \]
   • For \( (4, 5) \): \[ C = 1.25(4) + 25 = 5 + 25 = 30 \quad \text{(not 5)} \]

The only points that appear on the graph of the linear function \( C = 1.25m + 25 \) are:

\((4, 30)\) and \((8, 35)\).

So, the correct response is:

(4, 30) and (8, 35).