Alicia is writing the program for a video game. for one part of the game she uses the rule (x, y)-> (x-3,y+4) to move points on the screen. a) what output does the rule give when the input is (-6,0)? show your work b)what output does the rule give when the input is (3,-4)? show your work c) is the rule a function? explain why it is or why it is not

A.-6-3 = -9
0+4 = 4 
(-9,4)
B.3-3 = 0
-4+4 = 0 
(0,0)
Yes. it shifts the graph left (-3) and up (+4) with each x or y value. 

Okay so n is going to represent our first number. since the second number of five times greater than n, the second number will be represented as 5n. for us to figure out the two  numbers we need to have  the value of n first. this is going to be done by adding the two numbers together, n and 5n. it can be simplified as 6n, which the problem states is equal to 72. divide 72 by 6n and you can solve for n.  n+5n=726n=72n=(72/6)n=12  now that we know the value of n, we have to multiply 5 times 12 which equals 60. so our two numbers/integers are 12 and 60

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

(x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81