Mieliśmy nadzieję, że oni chcieli ugotować obiad.

Questions & Answers about Mieliśmy nadzieję, że oni chcieli ugotować obiad.

Why does the stem of mieliśmy have an e when the he form is miał with an a?
This is the e/a alternation you are learning in this lesson! For certain verbs like mieć (to have), the past tense stem uses an a for most forms, like miał (he had) or miały (they had, for groups without men). But when talking about a group containing at least one male, the stem changes to an e. Since the speaker here is part of a masculine personal group, it becomes mieliśmy.
Does chcieli (they wanted) follow the same e/a alternation rule?
Exactly. The verb chcieć (to want) normally has an a in the past tense, such as chciał (he wanted) or chciała (she wanted). But because the subject is oni (masculine personal they), the stem vowel changes from a to e, making it chcieli.
Why is the Polish sentence literally translating to we had hope instead of using a single verb for hoped?
While Polish does have verbs for hoping, it is much more common in everyday speech to use the phrase mieć nadzieję, which literally means to have hope. Since the sentence is in the past tense, it becomes mieliśmy nadzieję.
Why does nadzieja change to nadzieję in this sentence?
Because it is the direct object of the verb mieliśmy (we had). Direct objects take the Accusative case, and for feminine nouns ending in -a like nadzieja, the ending changes to .
Why is ugotować used here instead of gotować?
Ugotować is the perfective (completed action) form of the verb. We use it here because the focus is on the finished result of getting dinner cooked, rather than the ongoing process of cooking, which would use the imperfective form gotować.

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