Do not use concrete for an asphalt patch. As Ron stated, you will have separation at the joints, one is flexible the other is rigid
Do you know the cross section? If you have a multiple lift asphalt section I would repair the areas as follows.
1) Saw cut and remove the failed asphalt (keep it square or rectangle if you can)
2) Evaluate the base (if it is wet, you may have a subsurface condition to deal with)
3) Re-compact or replace the base material if needed.
4) Tack all the edges and replace the base layer asphalt up to the bottom of the surface layer.
5) Mill 1'-2' beyond the edge previously saw cut 1.5"-2" depth (to remove the surface layer only)
6) Tack all surfaces
7) Replace the surface asphalt.
One key to asphalt patches it to prevent a continuous joint from the surface to the base material (unless you only have one lift of asphalt).
By milling the surface area wider than it was saw cut, the joints will be staggered. Also, if you can, patch the entire lane width versus patching only one wheel path, likely the wheel path not patched will fail next and it is easier to pave back with an asphalt paver and rollers (typical pavers are 8'wide)
The scale approaches should be concrete, most companies that certify scales for states will not certify a scale if the approaches are asphalt we had to change ours out a few years ago because of this requirement). The typical transition bump created by the failing asphalt affects the scale. There must be a smooth transition from the riding surface to the scale and from the scale back to the riding surface to prevent damage.
For the asphalt to concrete transition, sealing the surface as hokie66 is a must. After the concrete is placed, typically, the joint is sawed to around 3/8" wide to a depth of around 2-3", backer rod installed, and sealant placed. Most manufactures have a detail for this.