A = 1/2f(s + z) for s

Solve the following formula for the specified variable

Step-by-step explanation:

It is a little unclear when you state the problem what exactly is going on with that fraction. This is a common issue when you try to type up equations. On the right side, you have a fraction bar and then a bunch of stuff after it. We need to clear up what is supposed to be in the numerator and what is supposed to stay in the denominator. This is important not just for typing up questions on the internet to get help but in using your calculator as well. If what the equation means is that both "f" and "q+z" are in the denominator, but then on your calculator you type something 1 / 2 * f * ( q + z ), most calculators (e.g. TI 83/84 and almost any basic or scientific model) will interpret that as meaning only the 2 is on the bottom and the rest is on top.

If you meant the f and the q+z are on top, then Steve's answer is good.

If you meant the f and the q+z are supposed to be on the bottom, then we have a little bit different process.

First, write down the operations that are happening to q, and in what order they happen from inside out, that is, according to the regular PEMDAS rule:

1. z is added

2. 2f is multiplied

3. The result is divided into 1 (as opposed to being divided by 1).

So, to solve for q, we "invert" the order of operations and do the inverse operation of our 3 steps, and also in reverse order.

1. To get the big thing out of the denominator (Step 3), we will multiply both sides by 2f(q+z). Now we have:

C*2f(q+z) = 1, or as we normally write it,

2Cf(q+z) = 1

2. Now we have to adjust our steps just a little bit because we have the *C part too. So we will change Step 2 above to "2Cf is multiplied." We invert that by dividing, so we have:

q+z = 1/[2Cf]. Notice how I put brackets around the entire denominator so it's clear!

3. Finally to invert Step 1 we subtract z:

q = 1/[2Cf] - z

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

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step-by-step explanation: