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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?

Which complex number is the conjugate you would use to simplify \( \frac{4 + 3i}{2 – i} \)?

Which function corresponds to the graph shown? “The x-axis ranges from just below -5 to 10, and the y-axis ranges from just below -5 to just above 5. Both axes have a scale of 5 with increments of 1. The purple V-shaped function consists of two linear segments that meet at a sharp peak at the coordinate (3, 6). The left segment has a positive slope, increasing from the third quadrant towards the vertex at the first quadrant. The right segment has a negative slope, decreasing after the vertex towards the fourth quadrant. The function passes through the x-axis at the coordinates ((negative 3, 0) and (9, 0) while having a y-intercept of (0, 3). “

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 statements about \( P(x) = x^3 + x^2 – 4x – 4 \) are true?

Which recursive rule represents the geometric sequence with first term \(5\) and common ratio \(0.4\)?

What is the equation of the parabola with focus \(F(0,5)\) and directrix \(y=-5\)?

Which is one of the transformations to  represented in the graph? “The x-axis spans from below negative 5 to above 0, and the y-axis spans from below 0 to above 5. Both axes have a scale of 5 in increments of 1. The purple V-shaped function consists of two linear segments meeting at a vertex at the coordinate (negative 2, 3) in the second quadrant. The left segment has a negative slope passing through the point (negative 6, 4), while the right has a positive slope with a y-intercept of (0, 3.5). The function continues to extend out of view in both directions. “

A food delivery company is designing a new pricing model based on two factors: The minimum delivery fee, yyy (in dollars), depends on how far the customer lives from the restaurant, measured by xxx miles from a central delivery hub.This is modeled by: . This ensures prices cover gas and driver compensation, especially for distances far from the average 3-mile zone. To stay competitive, the delivery fee must also stay below what competitors charge, modeled by: These constraints are represented in the graph below: What can we say about the pricing model?  “The x-axis spans from negative 5 to just above 5, and the y-axis spans from below 0 to just above 10. Both the axes have a scale of 5 in increments of 1. A solid blue V-shaped function has a sharp vertex at (3, 2) and a y-intercept of (0, 5), while the region above it is shaded in light blue. A dashed green diagonal line with a negative slope has an x-intercept at (4,0) and a y-intercept at (0,4), while the triangular region below it is shaded in light green. The blue and green shaded regions do not overlap. A white unshaded diagonal strip separates them, extending into a triangular unshaded area on the right side of the first and second quadrants. “

Identify the vertical asymptotes of \[f(x) = \frac{3x}{x^2 – 1}.\] “The x-axis spans from below 0 to just above 5, and the y-axis spans from below negative 10 to just above 10. The x-axis has a scale of 5 in increments of 1, and the y-axis has a scale of 10 in increments of 2. The leftmost branch is a concave curve in the third quadrant, passing through the approximate points (negative 4, negative 1) and (negative 1.5, negative 4). It starts from negative infinity below the vertical asymptote near x = negative 1, increasing steeply, and then approaching the horizontal asymptote near y =0.  The middle branch is between the asymptotes, decreasing from positive infinity near x = negative 1 in the second quadrant, passing through the origin (0,0) and continuing downward past negative infinity near x = 1 in the fourth quadrant.   The rightmost branch is a convex curve in the first quadrant, passing through the approximate points (1.5, 4) and (4, 1). It starts from positive infinity above the vertical asymptote near x= 1 and decreasing steeply before leveling off as it approaches the horizontal asymptote near y = 0.  “