Question
If \( x^{2}+y^{2}=6, x y=5 \), then \( (x+y)^{2}= \)
Ask by Griffiths Hamilton.
Dec 18,2024 19:45
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Tutor-Verified Answer
Answer
\( (x + y)^{2} = 16 \)
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Mind Expander
To find \( (x+y)^{2} \), we can use the identity:
\[
(x+y)^{2} = x^{2} + y^{2} + 2xy.
\]
Given \( x^{2} + y^{2} = 6 \) and \( xy = 5 \), we can substitute these values into the equation:
\[
(x+y)^{2} = 6 + 2(5) = 6 + 10 = 16.
\]
Thus, \( (x+y)^{2} = 16 \).
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Allysa spent $35 to purchase 12 chickens. She bought two different types of chickens. American chickens cost $3.75 each and Delaware chickens cost $2.50 each. Write a system of equations that can be used to determine the number of American chickens, A, and the number of Delaware chickens, D, she purchased. Determine algebraically how many of each type of chicken Allysa purchased. Extension: Each American chicken lays 2 eggs per day and sells eggs by the full dozen for $2.50. Determine how much money she expects to take in at the end of the first week with her 12 chickens.
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