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
photoshop1234 [79]
3 years ago
11

. Two trains leave a train station traveling different directions. The first train travels 12 miles west, then 6 miles north. Th

e second train travels 20 miles east, then 35 miles north. a. The train station is the origin. What is the coordinate of each train? b. Using the train station and the stop point of the first train, what is the slope of the line? Is it horizontal, vertical or neither? Write the equation of the line in slope-intercept form and standard form. c. The city wants to build a second train station 2 miles directly north of the first train station. They are going to build a train track from the second train station that is parallel to the path the first train would've traveled if it had taken a direct route to its stopping point. What would be the equation of the line in slope intercept form of the new track?
Mathematics
1 answer:
tia_tia [17]3 years ago
6 0

Answer:

a. The coordinates of the first train are (-12,6).  The coordinates of the second train are (20,35).

b. The slope of the line for the first train is -\frac{1}{2}.  The slope is neither horizontal or vertical.  It slopes diagonally downward from left to write since the slope is negative.  In slope-interdept form, it is written as y=-\frac{1}{2} x.  In standard form, it is written as x+2y=0.   The slope of the line for the second train is \frac{7}{4}.  The slope is neither vertical or horizontal.  It slopes diagonally upward from left to right since the slope is positive.  In slope-intercept form, it is written as y=\frac{7}{4}x.  In standard form, it is written as -7x+4y=0.

c. The equarion of a line in slope-intercept form of the new track would be y=-\frac{1}{2} x+2.

Step-by-step explanation:

a.  The way to find the coordinates is either to picture a coordinate grid in your head or to have one out in front of you for a visual.  The first train travels 12 miles west, or 12 units to the left (-12), and 6 miles north, or 6 units up (6).  On a coordinate plane, that would be marked as (-12,6).  The second train travels 20 miles east, or 20 units to the right (20), and 35 miles north, or 35 units up (35).  On a coordinate plane that would be marked as (20,35).  This means that the coordinates of the first train would be (-12,6), and the coordinates of there second train would be (20,35).

b. The way to find slope is to find \frac{delta "x"}{delta  "y"}.  "Delta" means "the change in".  The equation would be m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }.  So, let's find the slope of the first train's travel path.  We'll use the origin, (0,0), and the stopping point, (-12,6), as our coordinates to find the slope.  \frac{0-6}{0-(-12)}=\frac{0-6}{0+12}=\frac{-6}{12}=\frac{-1}{2}=-\frac{1}{2}.  That makes the slope of the first train's travel path to be (-1/2).  Now, let's find the slope of the second train's travel path.  We'll use the origin, (0,0), and the stopping point, (20,35), as our coordinates to find the slope.  \frac{0-35}{0-20}=\frac{-35}{-20}=\frac{35}{20}=\frac{7}{4}.  That makes the slope of the second train's travel path to be (7/4).  They want to know the equation of the travel path line in slope-intercept form and in standard form, and what the line looks like.  To start off, any vertical line would be undefined, and that would be if the slope was a fraction with a denominator of zero, which doesn't occur for either train path.  A horizontal line  would be if the slope was zero itself and the trains were not moving, but the trains are moving, so that's not possible either.  The way to determine theway a slope is diagonally is to look at whether the slope is positive or negative.  The first train's path slopes negatively, so it moves diagonally downward from left to right, or diagonally upward from right to left (both the same thing).  The second train's path slopes positively, so it moves diagonally upward from left to right, or diagonally downward from right to left.  Finally, the equations for this part of the question.  For both trains, the origin is the y-intercept, so the y-intercept does not have to be written in the slope-intercept equation.  The slope-intercept form of an equation of a line is y=mx+b where "m" is the slope and "b" is the y-intercept.  The "b" value is 0, so that will not be written.  The slope for the first train is (-1/2), so the slope-intercept form of the first train's travel path is y=(-1/2)x.  The slope of the second train is (7/4), so the slope-intercept form for this train's path is y=(7/4)x.  As for standard form, subtract the "mx" value from both sides, and set the equation equal to 0. Also, get rid of any fractions. So, for the first train, standard form would be x+2y=0.  And for the second train, standard form would be -7x+4y=0.

c.  Parallel means having the same slope but a different y-intercept.  The second train station would be placed two miles north, or two units up, from the first train station.  The first train station is at (0,0), so the second train station would be placed at (0,2).  That makes 2 the y-intercept for if the first train had taken the second train station's travel route.  The slope for the intitial route was (-1/2), so that will stay the same.  Therefore, the equation of thr route taken if the first train had come out of the second train station, if it was already built, would be y=(-1/2x)+2.

You might be interested in
Need to find the answer to 10 times (-2 ) -8
tekilochka [14]
10 × -2 is -20
-20 -8 = -28
5 0
3 years ago
Read 2 more answers
Which option is true when you expand the binomial expression (x+y)^5
jeka57 [31]

Step-by-step explanation:

(x + y)^5 = 1·x^5·y^0 + 5·x^4·y^1 + 10·x^3·y^2 + 10·x^2·y^3 + 5·x^1·y^4 + 1·x^0·y^5

Correct is only A



3 0
3 years ago
Answer problem below
garri49 [273]

Answer:

  • A = 2, B = 1, C = 28

Step-by-step explanation:

Find the slope of the line AB.

<u>The slope:</u>

  • m = (11 - 9)/(11 - 7) = 2/4 = 1/2

Since the altitude is perpendicular to AB, it has a slope of -2.

The line with the slope of -2 and passes through point C(6, 16).

<u>Use point-slope equation to find the line:</u>

  • y - 16 = -2(x - 6)
  • y - 16 = -2x + 12
  • y + 2x = 16 + 12
  • 2x + y = 28

A = 2, B = 1, C = 28

7 0
3 years ago
Read 2 more answers
42−6×4(12)3 help pls cncencenwevihbviubeuybtcqwctqgvcuqwcbucqwnbnu
Zanzabum

Answer:

42 - 24 * 36

18*36

and rewrite your answer by yourself

7 0
2 years ago
My father's car travel on average 33.4miles on each gallon of petrol. How far will he travel on 55 gallons.
DIA [1.3K]

YOUR FATHER CAN TRAVEL 1837.0 MILES ON 55 GALLONS OF PETROL.  

BRAINLIST PLEASE

6 0
2 years ago
Other questions:
  • Answer the following questions for the expression:
    5·1 answer
  • The diagram shows the position of the ship(S) and the marine base(B) the scale of the diagram is 1cm represents 10km.
    11·1 answer
  • Radhika borrowed Rs.12000 from her friends. Out of which Rs.4000 were borrowed at 18% and the remaining at 15% rate of interest
    15·1 answer
  • 31 workers are working on a construction site. 5 more workers work for company A than for company B. How many workers work for e
    12·1 answer
  • A bag contains 2 red marbles and 4 green marbles. two marbles are drawn at random. one marble is drawn and not replaced. then a
    8·1 answer
  • No Solutions
    10·1 answer
  • Make x the subject of the formula .<br><br> w=x+y
    15·2 answers
  • U 3 4
    12·1 answer
  • I need help asap, taking a test. So please help!!!!
    7·2 answers
  • Please give all the steps, and i will chose brainliest
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!