This value of "a" is exactly the y-coordinate of the vertex of the parabola
y = x%5E2+%2B+4x++-+31.
To find it, complete the square:
x%5E2+%2B+4x++-+31 = %28x%2B2%29%5E2+-+4+-+31 = %28x%2B2%29%5E2+-+35.
So, this value of "a" is a = -35.
Figure. Plot y = x%5E2+%2B+4x++-+31.
Answer:
Chicken is $8
Duck is $5
Step-by-step explanation:
Step 1: Let 
represent the cost of chickens and let 
represent the cost ducks. Since we have two unknowns, we need two equations to find them.
Step 2: The total cost of chickens Michael sold last month can be shown as 
, and the total cost of ducks he sold last month can beshown as 
Since these together add up to 550, we get these equations:
We are also given that this month, Michael sold 44 chickens, and 36start text, 36 ducks, $532. This equaion can be expressed as:
Now that we have a system of the two equations, we can now go ahead and solve the two equations.
Step 3: We can now solve the system of equations by using the elimination method. Manipulate the equations so one of the variables has the same coefficients but with opposite signs.
Now eliminate
When we solve the resulting equation, we obtain that 
. Then, we can substitute this into one of the original equations and solve for to obtain 
.
Step 4: Recall that denotes the cost of a chicken and denotes the cost of a duck. Therefore, a chicken costs $8, and a duck costs $5
Answer:
r = 22.9 in.
Step-by-step explanation:
Central angle in radians, ∅ = π/4
Length of arc, S = 18 in.
radius (r) = ?
Length of arc, C = r∅
Plug in the values and find r
18 = r*π/4
18 = (πr)/4
Multiply both sides by 4
4*18 = πr
72 = πr
Divide both sides by π
72/π = r
r = 22.9183118
r = 22.9 in. (Nearest tenth)
Answer: 113
Step-by-step explanation: 113/113=1(113) =113
