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rosijanka [135]
3 years ago
6

Helppop!!A car and van are driving on a highway. The table shows the amount y (in gallons) of gas in the cars gas tank after dri

ving x miles. The amount of gas in the van’s gas tank after driving x miles is represented by the equation y=- 1/5x + 31. Which vehicle uses less gasoline per mile? How many miles must the vehicles travel for the amount of gas in each tank to be the same?

Mathematics
1 answer:
Korvikt [17]3 years ago
5 0

Answer:

The car uses less gas

They use the same amount of gas after \frac{640}{7} miles

Step-by-step explanation:

Given

The table represents the car mileage

y = -\frac{1}{5}x + 31 --- The van

First, calculate the car's slope (m)

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

From the table, we have:

(x_1,y_1) = (60,13.5);\ \ (x_2,y_2) = (180,10.5)

So, we have:

m = \frac{10.5 - 13.5}{180 - 60}

m = \frac{-3}{120}

m = -\frac{1}{40}

Calculate the equation using:

y = -\frac{1}{40}(x - 60)+13.5

y = -\frac{1}{40}x + 1.5+13.5

y = -\frac{1}{40}x + 15

m = -\frac{1}{40} implies that for every mile traveled, the car uses 1/40 gallon of gas

Also:

y = -\frac{1}{5}x + 31 --- The van

By comparison to: y = mx + b

m = -\frac{1}{5}

This implies that for every mile traveled, the van uses 1/5 gallon of gas.

By comparison:

1/40 < 1/5

This means that the car uses less gas

Solving (b): Distance traveled for them to use the same amount of gas.

We have:

y = -\frac{1}{5}x + 31 --- The van

y = -\frac{1}{40}x + 15 --- The car

Equate both

-\frac{1}{5}x + 31 =-\frac{1}{40}x + 15

Collect like terms

\frac{1}{40}x -\frac{1}{5}x  =-31 + 15

\frac{1}{40}x -\frac{1}{5}x  =-16

Take LCM

\frac{x - 8x}{40} = -16

\frac{- 7x}{40} = -16

Solve for -7x

-7x = -640

Solve for x

x = \frac{640}{7}

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Answer:

  • \boxed{\sf{3x^3+4x^2-25x-30}}

Step-by-step explanation:

\underline{\text{SOLUTION:}}

To isolate the term of x from one side of the equation, you must multiply by a polynomial.

\underline{\text{GIVEN:}}

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<u>Add/subtract the numbers from left to right.</u>

-5x²+9x²=4x²

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<u>Then rewrite the problem.</u>

\Longrightarrow: \boxed{\sf{3x^3+4x^2-25x-30}}

  • <u>Therefore, the correct answer is 3x³+4x²-25x-30.</u>

I hope this helps! Let me know if you have any questions.

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