1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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}

You might be interested in
The two-way frequency table shows the number of stores in two different cities. What is the percentage of retail stores in City
LuckyWell [14K]

Answer:

Answer: C.

Restaurants: 43%

Retail: 57%

Step-by-step explanation:

3 0
3 years ago
Use properties of equality to Solve 7+3x = 5x+13 for x
mario62 [17]
We basically have to cancel values on both sides until they are both on common ground.

7 + 3x = 5x + 13

-7 from both sides...

3x = 5x + 6

-5x from both sides...

-2x = 6

/-2 from both sides...

x = -3


Hope this helps!
8 0
3 years ago
What is the equation of the line with a slope of –3 and a y-intercept of 4?
arsen [322]

Answer:

y=-3x+4

y=mx+b

m is the slope

b is the yint

5 0
3 years ago
Read 2 more answers
Help asap
ehidna [41]
Angles A and B are exactly the same because
they are congruent angles

Hope This Helps!!!!!
4 0
3 years ago
Read 2 more answers
Please help
Strike441 [17]
My educated guess is A
4 0
2 years ago
Other questions:
  • How often an event occurs based on data from an experiment or survey is its ____________.
    12·1 answer
  • Help me please ???????
    14·1 answer
  • Geometry help! <br> I need help with geometry.
    15·2 answers
  • Find the 7th term in the sequence -1,2,-4,8
    7·2 answers
  • What shapes have only 1 pair of opposite sides parallel?
    14·2 answers
  • Carlos Martin received a statement from his bank showing a balance of $56.75 as of March 15. His checkbook shows a balance of $8
    14·2 answers
  • A bonsai tree is 18 inches wide and stands 2 feet tall. What is the ratio of the width of the bonsai to its height?
    8·1 answer
  • If CDE ~ GDF, find ED
    11·1 answer
  • Fine the area of the trapezoid
    11·1 answer
  • 2.10 Guessing on an exam: In a multiple choice exam, there are 6 questions and 4 choices for each question (a, b, c, d). Nancy h
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!