Contrapositive and contradiction (4 points) Consider the following claim: For all integers m and n, if (m − n) is odd then m is odd or n is odd. (1) (2 points) Prove the claim using a proof by contrapositive (2) (2 points) Prove the claim using a proof by contradiction 2. Equivalence (4 points) Prove the following for all x ∈ R: x is rational ⇔ x − 5 is rational ⇔ x/3 is rational.

part 1 answer = 8

part 2 answer = 72

step-by-step explanation:

part 1 explanation = add all of the numbers, then divide by how many numbers you have. so, 200/25 = 8.

part 2 explanation = not gonna lie, this is hard to explain, so just google how to do it.

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.

"standard form:

3x2 + 14x − 10 = 0

solutions based on quadratic formula:

x1   = −14 − √ 142 − 4×3×(−10) /   2×3   = −14 − 2 × √ 79 /   6   ≈ −5.296

x2   = −14 + √ 142 − 4×3×(−10) /   2×3   = −14 + 2 × √ 79 /   6   ≈ 0.629