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
a corner of a cube connects 3 sides to each other,
then add the side of the cut
so it would have 4 sides
Let's solve your equation step-by-step.
(−
5
/8
)(x)=−160
Step 1: Simplify both sides of the equation.
−5
/8
x=−160
Step 2: Multiply both sides by 8/(-5).
(
8
/−5
)x(
−5
/8
x)=(
8/
−5
)*(−160)
x=256
Answer:
x=256
12)
9/10 / 3/4
= 9/10 * 4/3
= 12/10
= 6/5