A Quora question asks: What is the equation that states that an object’s observed mass increases with its velocity?
It depends on what you mean by “an object’s observed mass”.
Nowadays the term “mass” is used exclusively for what used to be called the “rest mass” and is a property of the object alone that is independent of the relative velocity of the observer. So no physicist working today would say that “an object’s observed mass increases with its velocity”.
But there was a time in the past when some physicists used the term “mass” (usually, but not always, qualified with the adjective “inertial” or “relativistic”) to identify the multiplier needed to make a relativistically correct equation having the same form as Newton’s third law $#F=ma#$ (albeit only for the special case where the force and acceleration are parallel to the direction of relative motion between object and observer). So the equation you may be thinking of is $#m_{rel}=\frac{m_0}{\sqrt{1-v^2/c^2}}#$, but it is not a statement about what we now mean by “an object’s mass”. (And even adding the adjective “observed” or “apparent” doesn’t change that, as our observation of the “rest” mass is pretty much just as direct as that of the old “inertial” version.)
Despite many strident claims in other answers that it was “incorrect”, the alternative choice of using the word “mass” for $#m_{rel}#$ was in fact perfectly valid if applied correctly. It just wasn’t very useful because the resulting number $#m_{rel}#$ is not a property just of the object itself but depends also on the observer and is different (with a slightly more complicated formula) for accelerations and forces in directions other than that of the relative motion.