If \( f(x) = 3x – 2 \) and \( g(x) = -2x + 8 \), what is the \( x \)-coordinate of their intersection?

The following input–output pairs describe a sequence:   Data Table \(n\) 1 2 3 \(a_n\) 4 12 36   Which explicit rule represents this sequence?

A company’s yearly profit increases by $4,000 each year.   Which type of sequence models this situation?

A recursive geometric sequence is defined by   \(f(1)=8\), \(f(n)=2f(n-1)\).   Find \(\sum_{n=1}^{7} f(n)\).

Which of the following describes the Fundamental Theorem of Algebra?

What is the equation of the circle with center \((-3,1)\) that passes through \((-6,5)\)?

A sequence is shown below:   Data Table \(n\) 1 2 3 4 \(a_n\) 3 9 27 81   Which type of sequence is represented?

A sequence is defined by \(a_n = 250(0.7)^n\).   What type of sequence does this represent?

Match the following points to the correct description as it applies to the system of inequalities shown. “The x-axis and the y-axis span from below negative 5 to just above 10. Both axes have a scale of 5 in increments of 1. A dashed red parabola opening upward encloses a red-shaded region above it. The vertex of this parabola is at (2, negative 3), while it passes through the coordinates (negative 1, 6) and (5, 6), extending upwards. A solid purple V-shaped function encloses a light, purple-shaded region below it. It has a sharp vertex at (1, 4) and a y-intercept of (0, 5). The parabola and the V-shaped function intersect at (negative 1, 6) and at a coordinate with x value roughly halfway between 5 and 6 and y value roughly halfway between 8 and 9. Their corresponding shaded areas overlap, while the darkest region appears where the two shaded regions intersect inside the parabolic area. The upper region of the graph contains two white unshaded triangular regions where the shaded regions did not overlap.”

The parabola has equation \((y-4)^2=-12(x+3)\). What is its focus?