Answer:it has multiple steps because you can work step by step
Step-by-step explanation:
Answer: The min value of Q is Q = 84 and it happens when x = 4 and y = 3
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Explanation:
x+y = 7 turns into y = 7-x after subtracting x from both sides
Replace y with 7-x in the other equation to get
Q = 3x^2 + 4y^2
Q = 3x^2 + 4( y )^2
Q = 3x^2 + 4(7-x)^2
Q = 3x^2 + 4(49 - 14x + x^2)
Q = 3x^2 + 196 - 56x + 4x^2
Q = 7x^2 - 56x + 196
We have a function with one variable. Graphing 7x^2-56x+196 produces a parabola in which the vertex point is what we're after
Anything in the form p(x) = ax^2+bx+c will have a vertex (h,k) such that
h = -b/(2a)
k = p(h)
Let's find the x coordinate of the vertex
h = -(-56)/(2*7)
h = 4
Use this to find the y coordinate of the vertex
k = p(h)
p(x) = 7x^2-56x+196
p(h) = 7h^2-56h+196
p(4) = 7(4)^2-56(4)+196
p(4) = 84
The vertex is the lowest point in this case (since a = 7 is positive) and the vertex is (4,84)
Therefore, the minimum value of Q is Q = 84 and this happens when x = 4 and y = 3. Recall that y = 7-x.
We can see that,
Q = 3x^2 + 4y^2
Q = 3(4)^2 + 4(3)^2
Q = 3(16) + 4(9)
Q = 48 + 36
Q = 84
Which helps us verify we have the right Q value.
Answer:
1. The data show that skipping breakfast is associated with earning lower exam grades.
2. There is an increase in B's for those who do eat breakfast before the exam.
No and 2/5 is the simplest form I hope I helped you
Hello!
To total amount is 78
Jake caught 22 so
78 - 22 = 56
So Andy and Damon caught 56 between the two of them
Andy caught at least 30
56 - 30 = 26
Damon caught at most 26
And caught at most 36
56 - 36 = 20
Damon caught at least 20
The answer is
The answer is A
Hope this helps!