1. Dos automóviles Ay B hacen un mismo trayecto de 572 km. El automóvil A lleva recorridos los 5/11 del trayecto cuando el B ha recorrido los 8/13 del mismo. ¿cuál de los dos va primero? ¿cuantos kilómetros lleva recorrido cada uno?

1. El auto B comenzó primero

2. El automóvil A recorrió una distancia de 260 km, mientras que el automóvil B recorrió una distancia de 352 km

Step-by-step explanation:

This question is in Spanish. Let’s have an English translation;

Two cars A and B make the same 572 km journey. Car A has traveled 5/11 of the journey when B has traveled 8/13 of it. Which of the two goes first? How many kilometers has each traveled?

Let’s now proceed to solve the question.

To answer this question properly, we have to assume that both cars are covering the same distance at the same speed but they started at different times. So, let’s now proceed;

The first question is another way of asking which of both is a bigger fraction.

Now Car A travelled 5/11 and Car B had traveled 8/13, to know which of both that started first, the one that subtracts the other without leaving a negative answer started first.

Let’s say Car B - Car A = 8/13 - 5/11 = 34/143

This obviously means that Car B went first.

Second question asks to calculate how many kilometers has each traveled. We calculate this by finding the fraction of the journey multiplied by the distance traveled by both.

For Car A, we have 5/11 * 572 = 260km

For Car B, we have 8/13 * 572 = 352km

hi,

6x times 4 is 24x and 5 times 4 is 20, so the answer is 24x+20.

hope this and for a little humor i am groot.

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24