The monthly cost of driving a car depends on the number of miles driven. lynn found that in may it cost her $494 to drive 380 mi and in june it cost her $638 to drive 860 mi. (a) express the monthly cost c as a function of the distance driven, d, assuming that a linear relationship gives a suitable model.

C = 0,3x + 380

Step-by-step explanation: Assuming that a linear relationship is suitable model, C is a function of d, we can say that:

C = d.x + k. where x is what we call a variable cost and k is a fixed cost. We have to assume a fixed cost. If it does not exist, the value will be zero.

This way: for may we have 494 = 380x+k and for June we have 638 = 860x+k.

Let's subtract them

638 = 860x+k

494 = 380x+k (-)

638 = 860x+k

-494 = -380x-k

144 = 480x

x=144/480

x=0,3

For k, we substitute in one of the equations

638 = 860.0,3 + k

638 = 258 + k

k = 380

∴ C = 0,3x+380

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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