Is it permissible to combine the intention of Udhiyah (sacrificial offering) with the intention of Aqiqah (sacrifice for a newborn) or with the intention of sacrificing for the purchase of a new car?

It is permissible to slaughter one sheep with the intention of both Uḍḥiyah and ʿAqīqah, according to what some Hanbalis preferred. However, it is better for those who are able not to combine the two intentions. As for slaughtering a sheep with the intention of Uḍḥiyah and thanking Allah for a renewed blessing, it appears that this suffices for the Uḍḥiyah, and he will receive the reward for showing gratitude.