petition
mish.a.lah denotes requests presented in relation to the LORD, including the petitions of the heart.
The attested use presents requests in relation to the LORD: Psalm 20:6 places them within the report that he answers his anointed, while Psalm 37:4 speaks of the petitions of the heart given to the one who delights in him.
Senses in use
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Requests addressed in relation to the LORD · dominant
Both occurrences are common feminine plural construct nouns. In Psalm 20:6, the form occurs in the statement that the LORD answers his anointed from holy heaven; in Psalm 37:4, the APB renders the clause "he will give you the petitions of your heart."
In the Anselm Project Bible: The APB explicitly uses "petitions of your heart" in Psalm 37:4. In Psalm 20:6 it renders the surrounding statement about the LORD answering his anointed without an equally explicit English counterpart.