I just bombed my first Algebra test. I want to understand the problems I missed... Someone help please!

1. If xy<0, Name all the quadrants in which the point (x,y) can lie.

2. S = 2(pi)rx + 2(pi)r^2 solve for x

3. Solve the inequality... those are supposed to be fractions

2x+3 - 3x-1 < 4x+7
____ ____ _____
5 2 2

4. A company finds that it can produce 10 solar heaters for $7500 while producting 20 heaters costs $13,000. (Assume a linear relationship exists between the two quantities.
a.) express the cost, y, as a linear function of the number of heaters, x.
b.)determine the cost to produce 18 heaters.

I would greatly appreciate it if someone could please help me understand these problems. I dont necessarily want the answers.

1. If x and y are both less than 0, then they are both negative. This puts them in Quadrant III, because Quadrant III is the only one where both x and y are negative.

2. You need to isolate x by removing all the other variables.

S=2(pi)rx + 2(pi)r^2
-2(pi)r^2 from both sides
S-2(pi)r^2=2(pi)rx
Divide both sides by 2(pi)r

(S-2(pi)r^2)/2(pi)r=x
Then you can reduce
S-r=x

I'm not 100% sure on this one, so if I did it wrong, someone please correct me.

3. For this one, you have to find the LCD to remove the fractions. The LCD would be 10. If you need help further than that, email me (in my profile) so I can do it with MathType and you can read it lol Too hard to do fractions like this in a post.

4)let y = cost and x = number of heaters

Make a graph with the points (7500, 10) and (13000, 20). From this you can determine the slope and intercepts and get the function. This is another one that I would need to do in MathType, so please email me if you want me to go further with it.

I hope this helps some

Another observer's point of view...

1. It appears that the product of x and y is negative, therefore one must be negative and the other must be positive. Therefore, you answer is Quadrants II and IV.

2. MTT went about solving this one correctly, but I believe you will find it reduces to:

S/2πr - 2πr = x

(note: 2πr is usually the designation for the circumference of a circle)

3. This didn't seem to work out right when posting.

4. The cost to produce the 10 additional heaters is $5,500 ($13,000 - $7,500). The cost for each of these is $550. It cost $7,500 to produce the first 10! Between these numbers, this may be expressed by the equation, where

y = cost of heaters, and
x = the quantity of heaters

y = $7,500 + (x - 10)*$550.

Solving for x = 18:

y = $7,500 + (18 - 10)*$550
y = $7,500 + 8 * $550
y = $7,500 + $4,400
7 = $11,900

Hope this helps.

I'm pretty sure he's right on the first one. You and I were thinking "where x and y are less than zero", but I believe he's right in thinking it was asking "where x TIMES y is less than zero".