Determine the locus of points. All points in a triangle shaped grassy area where a goat could be staked and feed on all the grass while requiring the shortest possible rope.
(a) one point, the incenter of the triangle
(b) one point, the centroid of the triangle
(c) one point, the orthocenter of the triangle
(d) one point, the circumcenter of the triangle
(d) one point, the circumcenter of the triangle
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Find the constant of proportionality k, and write the linear function relating the two variables.Suppose that y varies jointly with x and z. When y = 54, x = 27 and z = 18.
A. k = 
; y = 
B. k = 
; y = 
xz
C. k = 
; y = 
xz
D. k = 
; y = 
Find the equation of a line with the given slope and y-intercept.Slope 0, y-intercept (0, 2)
A. y = 0 B. y = 2x C. y = 2 D. x = 2
Find all zeros of the function and write the polynomial as a product of linear factors.f(x) = x4 + 5x3 + 15x2 + 45x + 54
A. f(x) = (x - i
)(x + i
)(x - 3)(x +3)
B. f(x) = (x - 3)(x + 2)(x - 3)(x + 3)
C. f(x) = (x + 3)(x + 2)(x - 3i)(x + 3i)
D. f(x) = (x - 1)(x - 6)(x - 3i)(x + 3i)
The augmented matrix of a system of equations has been transformed to an equivalent matrix in row-echelon form. If the system is consistent, then give the solution. If it is not, then state that it is inconsistent.
A. (33, -23, 7) B. (50, -24, 7) C. (48, -23, 7) D. Inconsistent