Answer:
4 is the coefficient of 4n
Step-by-step explanation:
The equivalence

means that n-5 is a multiple of 12.
that is
n-5=12k, for some integer k
and so
n=12k+5
for k=-1, n=-12+5=-7
for k= 0, n=0+5=5 (the first positive integer n, is for k=0)
we solve 5000=12k+5 to find the last k
12k=5000-5=4995
k=4995/12=416.25
so check k = 415, 416, 417 to be sure we have the right k:
n=12k+5=12*415+5=4985
n=12k+5=12*416+5=4997
n=12k+5=12*417+5=5009
The last k which produces n<5000 is 416
For all k∈{0, 1, 2, 3, ....416}, n is a positive integer from 1 to 5000,
thus there are 417 integers n satisfying the congruence.
Answer: 417
Answer:
4(3x+2), 4(3x)+4(2), 12x+8
Step-by-step explanation:
We have a line passing through 3 points. We can use the first
two points to find the equation of the line.
(6,3), (8,4)
slope m = (4-3)/(8-6) = 1/2
We can use the point slope form y-y1 = m(x-x1) or
the slope intercept form y = mx + b
to find the equation of the line.
Let's take the point (6,3) and use y = mx + b to find b
y = 3, x = 6, m = 1/2
3 = (1/2)(6) + b
3 = 3 + b
0 = b
The equation of our line is y = (1/2)x
We have a line of equation y = (1/2)x going through point (n,-2)
Plugging in we have: -2 = (1/2)n
2(-2) = n
-4 = n
Your answer is n = -4
NOTE: looking at the 3 points as given initially: (6,3), (8,4), (n,-2)
We can see that 3 = (1/2)6 and 4 = (1/2)8 so -2 = (1/2)n makes sense
Hope this helps you :)