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?

Two inequalities intersect on the graph shown. Which of the following is a solution to \( f(x) = g(x) \)? Area graph. A gray-shaded area and a purple-shaded area intersect on a coordinate plane, forming a grayish purple area. The x-axis spans from negative 5 to just above 5, and the y-axis spans from below 0 to above 5. Both axes show intervals of 5 with grid lines in increments of 1. A solid black diagonal line with a negative slope has an x-intercept roughly halfway between (2, 0) and (3, 0) and a y-intercept at (0, 7), shading the area below in dark gray. A dashed purple diagonal line with a positive slope has an x-intercept at (negative 3, 0) and a y-intercept at (0, 3), shading the area above in light purple. The two shaded areas overlap, forming a grayish purple region. The overlapping area spans most of the second quadrant and some portion of the first and third quadrants.

A sequence increases by 11 each term and has \(a_1 = 5\).   What is the value of \(a_{13}\)?

Match the transformation with the function representation for each transformation applied to the graph of  as shown in the graph. “The x-axis spans from negative 5 to above 5, and the y-axis spans from below negative 10 to above 0. Both axes have a scale of 5 in increments of 1. The purple inverted V-shaped function consists of two linear segments meeting at a sharp peak at (0, negative 4). The left segment is in the third quadrant with a positive slope, passing through the point (negative 4, negative 6). The right segment is in the fourth quadrant, with a negative slope, passing through the point (4, negative 6). The function is symmetric about the y-axis and extends out of view in both directions. “

A parabola has vertex \((1,-2)\) and focus \((1,1)\). What is its equation?

Which is a valid solution to the system shown? The x-axis and the y-axis span from below negative 5 to above 5, with a scale of 5 in increments of 1. A solid blue parabola opens upward with its vertex at (0, negative 4), enclosing a white region inside. The parabola passes through the coordinates (negative 2, 0) and (2, 0), extending upward. The area around the parabola is shaded in light blue. A dashed orange diagonal line with a positive slope passes through the points (0, -1) and (-2, -5). The line intersects the parabola at (negative 1, negative 3) and (3, 5), while the area above the line is shaded orange. This orange-shaded area overlaps the blue area as well as most of the white region inside the parabola. The overlap spans the second quadrant, most of the third quadrant, and a small portion of the first quadrant. The overlap on the blue area appears brown, while over the white parabolic region, it appears orange. The lower-right portion of the parabolic region remains white without any overlap.

The sequence \(6,\;11,\;16,\;21,\;\dots\) is arithmetic.   Which explicit rule generates this sequence?

A sequence has \(a_1 = -12\) and common difference \(6\).   What is the value of \(a_{11}\)?