HELP PLZ
Solve each proportion for the variable

x = -1

Step-by-step explanation:

4/12 can be simplified to 1/3

1         x+2

---  =

3          2x+5

Using cross products

1 ( 2x+5) = 3 (x+2)

Distribute

2x+5 = 3x+6

Subtract 2x from each side

2x+5-2x = 3x+6-2x

5 = x+6

Subtract 6 from each side

5-6 = x+6-6

-1 =x

Step-by-step explanation:

Key skills: Proportions, One variable equations, Multiplication, Distribution Property

1) The best approach to this problem is with cross multiplication.

Cross multiplication is where we multiply the numerator of one fraction with the denominator of the other fraction, and the denominator of one fraction with the numerator of the other fraction.

2) Here we would do: 4(2x+5) and 12(x+2)

3) Since this is a proportion --> 4(2x+5) = 12(x+2)

4) Now, we use distribution property to expand both.

4(2x+5) --> 8x+ 20                      12(x+2) --> 12x+24

5) With simplifying we can solve for x:

If you plug in x=-1 back into the equation: 4/12= 1/3

4/12 does equal 1/3 so x= -1 is the right answer.

Hope you have a nice day and understood this problem explanation!! :D

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