'Sedentary' refers to a lifestyle with little or no physical activity, contrasting with the other options.

Deforestation is detrimental to environmental conservation, while the others promote it.

Photosynthesis is a biological process, while the others are related to environmental issues.

The Renaissance is a cultural movement, while the other three options are significant historical events related to wars and economic crises.

'Bicycle' is a non-motorized mode of transportation, while the others are motorized.

Processed foods are generally considered unhealthy, while the others are staples of a healthy diet.

'Quantum Mechanics' is a branch of physics, while the other three are significant historical events.

'Ecosystem' refers to a biological community, while the others are technological concepts.

Competition is contrary to the collaborative spirit of teamwork, while the others enhance it.

Betrayal is the opposite of friendship, while the others are positive attributes of friendship.

3x ≡ 9 (mod 6) has no solution because 3 and 6 are not coprime, and 9 is not divisible by the gcd(3, 6).

8 ≡ 15 (mod 8) is false; the correct answer is 5 ≡ 10 (mod 5) is true.

The standard equation of a circle with center (0, 0) and radius r is x^2 + y^2 = r^2. Here, r = 5, so r^2 = 25.

The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Parallel lines have the same slope. The equation 2x + 3y = 12 has the same slope as 2x + 3y = 6.

Parallel lines have the same slope. The slope of y = -3x + 4 is -3, so any line with the same slope, like y = -3x + 1, is parallel.

All options are valid, but 5x ≡ 10 (mod 5) simplifies to 0 ≡ 0, which is trivially true.

Using the power of a power property, (a^m)^n = a^(m*n), we get 2^(3*2) = 2^6.

Expanding (x + 2)(x - 3) gives x^2 - 3x + 2x - 6 = x^2 - x - 6.

Using the power of a product rule, (x^3 * y^2)^2 = x^(3*2) * y^(2*2) = x^6 * y^4.

Distributing 2 gives 2x + 6, and then subtracting 4 results in 2x + 2.

Distributing 2 gives 2 * x + 2 * 3 = 2x + 6.

Distributing gives 3x + 12 - 2x + 2 = x + 14.

Distributing 3 gives 3x + 12, which is the equivalent expression.

Using the property of exponents that states a^m * a^n = a^(m+n), we combine the exponents: 2x + (x + 1) = 3x + 1.

log_10(0.01) can be rewritten as log_10(10^-2) = -2.

log_10(1/100) = log_10(10^-2) = -2.

log_10(100) = 2 and log_10(10) = 1, so 2 + 1 = 3.

Since 1000 is 10^3, log_10(1000) = 3.

Using the property of logarithms, log_5(25) = 2 and log_5(5) = 1. Therefore, log_5(25) + log_5(5) = 2 + 1 = 3, which is log_5(125).