Math help ASAP??

Question

I'm helping my boyfriend with his math final and we dont remember half of it because it goes in one ear and out the other lol... Any help is good.

1. The speed of a freight train is 19 miles per hour slower than the speed of a passenger train. The freight train travels 390 miles in the same time that it takes the passenger train to travel 480 miles. Find the speed of the freight train.
Give a numeric answer only, rounded to the nearst tenth of a mph.

2. Factor completely or is it prime... 8x^3 + 27y^3

3. Solve x^2 = 6x - 9

4. Simplify
[18x^-4y^7z^-10]/[27x^5y^...

5. Factor or prime? 25x^2 + 9y^2

6. How many liters of a 60% acid solution must be mixed with a 96 liters of a 75% acid solution to get a mixture that is 72% acid?

Thanks 10 points to any help!

DONE WITH TEST Thanks!!

Answer 1

I don't know how to do all of those but i hope that this helps...
3. x^2 = 6x - 9 (you have to make this a quadratic equation)
x^2 -6x + 9 = 0 (factor it)
(x - 3)(x - 3)
Sorry, this is all i can do off the top of my head...
Hope this helps!

Answer 2

1.
distance = speed * time
speed = distance / time
time = distance / speed

let x : freight train's speed
x + 19 : passenger train's speed

390/x = 480/(x + 19)
390 * (x + 19) = 480x
390x + 7410 = 480x
7410 = 90x
82.3 = x ; the freight train was traveling at 82.13 miles per hour

2. 8x^3 + 27y^3 is prime

3. x^2 = 6x - 9
x^2 - 6x + 9 = 0
(x - 3)^2 = 0
x - 3 = 0
x = 3

4. [18x^-4y^7z^-10]/[27x^5y^]
you didn't complete this :(

5. 25x^2 + 9y^2
could be : (5x - 3iy) (5x + 3iy)
where i is an imaginary number (the square root of -1)

6.
60% = 0.6
75% = 0.75
72% = 0.72
let x : amount in liters of 60% solution to be added

(0.75 * 96) + (0.6x) = 0.72 (96 + x)
72 + 0.6x = 69.12 + 0.72x
2.88 + 0.6x = 0.72x
2.88 = 0.12x
24 = x ; 24 liters of 60% acid sol'n must be added

Answer 3

Speed of passenger train = x
Speed of freight train = x-19

(x-19)/390 = x/480
390x=480x-9120
-90x=-9120
x=101 1/3, or 101.3mph

Answer 4

ouch i have a headache now. lol sorry i tried i really did but im to tired to think right now

Answer 5

what does the little up arrow mean

Exponent??