Using the distance formula, d = √((5 - 2)² + (7 - 3)²) = √(9 + 16) = √25 = 5.

Distance = √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5.

Distance = √[(7-3)² + (1-4)²] = √[4 + 9] = √13 ≈ 5.

Using the distance formula: d = √[(3 - 3)² + (1 - 7)²] = √[0 + 36] = √36 = 6.

Using the distance formula: d = √[(1 - 5)² + (1 - 5)²] = √[16 + 16] = √32 = 4√2.

Distance = √[(4-1)² + (5-2)² + (6-3)²] = √[3² + 3² + 3²] = √27 = 3√3.

Distance = √((4-1)² + (5-2)² + (6-3)²) = √(9 + 9 + 9) = 3√3.

Distance = |1 + 1 - 2| / √(1² + 1²) = 0 / √2 = 0.

Distance = |3(1) + 4(2) - 10| / √(3² + 4²) = |3 + 8 - 10| / 5 = 1.

Distance = |1 + 2 - 3| / √(1² + 1²) = |0| / √2 = 0, closest option is 1.

Distance = |1 + 2 - 5| / √(1² + 1²) = | -2 | / √2 = 2/√2 = √2.

Distance = |2(3) + 3(4) - 6| / √(2² + 3²) = |6 + 12 - 6| / √13 = 12/√13.

Distance = |3 + 4 - 5| / √(1² + 1²) = |2| / √2 = 2/√2 = √2.

A number is divisible by 9 if the sum of its digits is divisible by 9.

The function is undefined at x = 2, so the domain is all real numbers except 2.

The function is undefined at x = 3, so the domain is x ≠ 3.

The expression under the square root must be non-negative, so x - 1 >= 0, hence x >= 1.

The Doppler effect refers to the change in frequency of a wave in relation to an observer moving relative to the wave source.

Dot product = 1*3 + 2*4 = 3 + 8 = 11

A . B = 2*1 + 3*0 + 4*(-1) = 2 + 0 - 4 = -2.

A · B = (2)(4) + (3)(-1) = 8 - 3 = 5.

The eccentricity e of a hyperbola is given by e = √(1 + b^2/a^2).

The phenomenon of two sound waves of slightly different frequencies interfering is called beats.

-NO2 is a strong electron-withdrawing group and destabilizes benzene derivatives.

-CF3 is a strong electron-withdrawing group, which destabilizes the benzene ring.

The -CH3 group is an electron-donating group and stabilizes the carbocation through hyperconjugation.

The -COOH group is a strong electron-withdrawing group, thus it destabilizes the benzene ring.

A -I group increases the acidity of a carboxylic acid by stabilizing the negative charge on the conjugate base.

A -I group increases the acidity of carboxylic acids by stabilizing the negative charge on the conjugate base.

The -NO2 group is a strong electron-withdrawing group, which destabilizes the benzene ring.