Sure! Here are the answers filled in with the infinitive (+ to):

### Use the infinitive (+ to) after adjectives.
1. It is not very polite **to speak** to your teacher like that! (speak)
2. We are happy **to announce** the engagement of our daughter. (announce)
3. This coffee is too hot **to drink** at the moment. (drink)
4. It is very important **to study** before you write exams. (study)

### Use the infinitive (+ to) to express a reason or a purpose.
1. He is working out at the gym **to get** fit. (get)
2. I woke up early **to have** a shower. (have)
3. She went to the supermarket **to buy** bread and milk. (buy)
4. She is going to England **to learn** English. (learn)

### Use the infinitive (+ to) after certain verbs.
1. Please try **to finish** your work on time.
2. I hope **to visit** my grandmother on her birthday. (visit)
3. I must learn **to drive** before I go overseas. (drive)
4. The results seem **to support** your theory. (support)
5. We planned **to meet** after work. (meet)

Feel free to ask if you need further assistance!