Final answer:
While Whataburger, barbecue, NASA, The Alamo, The Dallas Cowboys, and the Texas Longhorns all epitomize Texas culture, 'The Alamo and barbecue' might be chosen for their historical and cultural relevance based on context provided.
Step-by-step explanation:
Whataburger is a fast-food institution that is synonymous with Texas culture. Reflecting on this cultural significance, a fitting completion of the sentence 'Whataburger is as quintessentially Texas as ________ and ________.' could be any of the given options as they all represent key aspects of Texan identity. However, considering the information provided about barbecue being a staple due to the climate favoring cattle ranching, and the historical significance of the battle where Texans defeated the army of General Antonio Lopez de Santa Anna at San Jacinto (not the Alamo), a student might choose 'The Alamo and barbecue' to fill in the blanks.
Moreover, the NASA Lyndon B. Johnson Space Center in Houston exemplifies the high-tech aspect of the Texas economy and represents Texas' contribution to space exploration. Considering Texas' well-known love for football and college sports, 'The Dallas Cowboys and the Texas Longhorns' are also icons deeply embedded in Texan culture. Nevertheless, without a specific context indicating which aspects of Texan life the question alludes to, several of the given options could be considered correct.