Answer:
Step-by-step explanation:
Given: △ABC, BC>AC, D∈ AC , CD=CB
To prove: m∠ABD is acute
Proof: In ΔABC, the angle opposite to side BC is ∠BAC and the angle opposite to side AC is ∠ABC.
Now, it is given that BC>AC, then ∠BAC>∠ABC.. (1)
In ΔBDC, using the exterior angle property,
∠ADB=∠DBC+∠BCD
∠ADB=∠DBC+∠BCA
⇒∠ADB>∠BAC (2)
From equation (1) and (2), we get
∠ADB>∠BAC
⇒∠ADB>∠ABC
⇒DB>AB
Hence, m∠ABD is acute
Answer: 370 liters
Step-by-step explanation:
Given : Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 8 liters of natural oil for every 5 liters of synthetic oil.
Then , the amount of Petrolyn oil made by above composition =
Also, the amount of petrolyn oil is proportional to the amount of synthetic oil.
Let x be the amount of synthetic oil need ot make 962 liters of Petrolyn oil, the we have the following equation:-
Hence, In order to make 962 liters of Petrolyn oil, 370 liters of synthetic oil is needed .