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If \(ax-3\) is a factor of \(6x^3+27x^2-54x\), where \(a\) is a positive constant, what is the value of \(a\)?
\(x^2-10x+14=0\)
One solution to the given equation can be written as \(x=5+\sqrt n\), where n is a constant. What is the value of n?
In the xy-plane shown, the quadrants are labeled I, II, III, and IV. The graph of \(y=-{(x+h)}^2+k\), where h and k are positive constants, is a parabola. In which quadrant is the vertex of this parabola?
\(y=-3\)
\(y=x^2+10x+a\)
In the system of equations shown, a is a positive constant. For which value of a does the system have exactly one distinct real solution?
The table shows several values of x and their corresponding values of y, where k is a nonzero constant. If the relationship between x and y is linear, which of the following defines this relationship?
\(y=\frac32x-\frac12\)
\(y=\frac k3x+\frac13\)
In the system of equations above, k is a constant. If the system has no solutions, what is the value of k?