Prove that 25^11 - 5^19 is divisible by 31.

See below  

Step-by-step explanation:

                                        25¹¹ - 5¹⁹

Convert to base 5       = (5²)¹¹ - 5¹⁹

                                    =  5²²   - 5¹⁹

Factor out the GCF     =  5¹⁹(5³ - 1)

                                    =  5¹⁹(125 - 1)

                                    =  5¹⁹ × 124

                                    =  5¹⁹ × 4 × 31

31 is a factor of 25¹¹ - 5¹⁹, so the expression is divisible by 31.

the correct answer is b. negative exponential growth.

step-by-step explanation:

you can tell it's an exponential function because it decreases rapidly then levels out and never touches the x-axis.

it is negative because the y-axis decreases as the x-axis increases.

therefore it is a negative exponential growth graph.

hope i !

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: