Answer:
Divisible by 3 is the answer
Step-by-step explanation:
First get everything to have the same base of 5
25^11 - 5^19
(5^2)^11 - 5^19
5^(2*11) - 5^19
5^22 - 5^19
Now factor out the GCF 5^19 to get
5^22 - 5^19
5^(19+3) - 5^(19+0)
5^19*5^3 - 5^19*5^0
5^19(5^3 - 5^0)
5^19(125 - 1)
5^19*(124)
At this point, we factor the 124 into 31*4 to end up with this full factorization: 5^19*31*4
Therefore, 25^11 - 5^19 is equivalent to 5^19*31*4
Since 31 is a factor of the original expression, this means the original expression is divisible by 31.
S= 5? that's at the top of my head
Answer:
Beyonce will get the same result.
Step-by-step explanation:
The given system is
2x-3y=-2
and 4
x+y=24
This system contains two lines that are not parallel to each other therefore the solution x=5, y=4 is unique.
It doesn't matter which method he used or which variable he eliminated first.
The solution will still be the same.
If the system of two equations with has no solution, the Beyonce will not get a solution in the first place, but the fact that the system has no solution remains the same even if Beyonce uses a different method.
If there are infinite solutions, Beyonce might get different solutions using a different method, but the fact that the system has infinite solution remains the same.
Let 
. The tangent plane to the surface at (0, 0, 8) is
The gradient is
so the tangent plane's equation is
The normal vector to the plane at (0, 0, 8) is the same as the gradient of the surface at this point, (1, 1, 1). We can get all points along the line containing this vector by scaling the vector by 
, then ensure it passes through (0, 0, 8) by translating the line so that it does. Then the line has parametric equation
or 
, 
, and 
.
(See the attached plot; the given surface is orange, (0, 0, 8) is the black point, the tangent plane is blue, and the red line is the normal at this point)
