Find counterexamples to each of these statements about congruences.
a) if ac ≡ bc (mod m), where a, b, c, and m are integers with m ≥ 2, then a ≡ b (mod m).
b) if a ≡ b (mod m) and c ≡ d (mod m), where a, b, c, d, and m are integers with c and d positive and m ≥ 2, then ac ≡ bd (mod m).
(c) 10.4 lb
if paul added each weight before adding, as you state, he got:
apples 3.78 ⟶ 3.8
peaches 2.12 ⟶ 2.1
oranges 4.45 ⟶ 4.4
total 10.3 lb
if he did it this way, he did it incorrectly, and his answer isn't in the list of options, anyway. that's because his method introduces round-off errors.
the correct way is to add the numbers as given, and then round off at the end.
total 10.35 ⟶ 10.4 lb
note: when you drop a 5 followed by nothing, you round off to the nearest even number.
we have a parabola and a small line shown in the graph.
the parabola goes upto x = 2 but does not reach that very value. so x = 2 starts on the line above where x = 2 and ends just before x = 4.
therefore, this function can be modeled by:
subtract 1.88 from each side
8-1.88 = 1.88-1.88+a
6.12 = a
8 = 1.88+a
8 = 1.88+6.12
a) if ac ≡ bc (mod m), wh...