Use the number line to compare the numbers -1/2 , -1 9/10, 3/5, 0.4

which choice lists the numbers in increasing order?

a. -1/2, -1 9/10, 3/5 , 0.4

b. -1 9/10, 3/5, - 1/2, 0.4

c. -1 9/10, - 1/2, 0.4, 3/5

d. -1 9/10, - 1/2, 3/5, 0.4

C. -1 9/10, -1/2, 0.4, 3/5

Step-by-step explanation:

Using a number line, we can see that negative numbers are to the left of '0' and positive numbers are to the right of '0'.  To compare numbers for increasing order, we would start with the lowest number to the farthest left on the number line to the greatest number to the farthest right.  Placing the following numbers on the number line, the furthest to the left is -1 9/10, then -1/2, followed by 0.4 and then the greatest, 3/5.  You can also compare by converting them all into decimals:

-1 9/10 = -1.9

-1/2 = -0.5

0.4 = 0.4

3/5 = 0.6

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

2nd one in the first row is correct