Mathematics, 13.02.2021 01:00 keke6361

Compare the speed of the train to the speed of the card. How much less time would it be for Lisa to travel 231 miles using the faster mode of tranportation? Show your work or explain how you determined your answer

Answers: 2

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Answer from: jjjoooorrrrddddaannn

Faster mode: Car

Less time: 0.93 hour

Step-by-step explanation:

Given

y = 55x --- The equation of travelling by car

See attachment for missing details

Required

Determine by how much less time Lisa will travel 231 miles using the faster mode

First, we calculate the equation of travelling by train.

Start by calculating the slope (m)

$m=\frac{y_2 - y_1}{x_2 - x_1}$

Where

(x_1,y_1) = (2,90)

(x_2,y_2) = (4,180)

$m = \frac{180 - 90}{4-2}$

$m = \frac{90}{2}$

m = 45

The equation is then calculated using:

y = m(x - x_3) + y_3

Where

(x_3,y_3) = (6,270)

y = 45(x - 6) + 270

y = 45x - 270 + 270

y = 45x

So, we have:

y = 55x --- The equation of travelling by car

y = 45x --- The equation of travelling by train

Next, we calculate the speed travelled using both means for 231 miles.

For travelling by car: Substitute 231 for y in y = 55x

231 = 55 * x

$x = \frac{231}{55}$

x = 4.20

By car, Lisa travels for 4.20 hours

For travelling by train: Substitute 231 for y in y = 45x

231 = 45 * x

$x = \frac{231}{45}$

x = 5.13

By train, Lisa travels for 5.13 hours

So, the faster mode of transportation is the car:

The less time is:

$5.13 - 4.20 =0.93\ hour$

The less time spent is 0.93 hour

Compare the speed of the train to the speed of the card. How much less time would it be for Lisa to

Answer from: Quest

If it is my birthday, then it is snowing

Answer from: Quest

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

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Compare the speed of the train to the speed of the card. How much less time would it be for Lisa to...