Madame Pickney has a rather extensive art collection and the overall value of her collection has been increasing each year. Three years ago, her collection was worth $400,000. Two years ago, the value of the collection was $440,000 and last year, the collection was valued at $484,000. Assume that the rate at which Madame Pickney’s art collection’s value increase remains the same as it has been for the last three years. The value of the art collection can be represented by a geometric sequence. The value of the collection three years ago is considered the first term in the sequence. What explicit rule can be used to determine the value of her art collection n years after that?

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general 4 months ago 3816

ΔABC is a right triangle. Prove: a2 + b2 = c2 Right triangle BCA with sides of length a, b, and c. Perpendicular CD forms right triangles BDC and CDA. CD measures h units, BD measures y units, DA measures x units. The following two-column proof with missing justifications proves the Pythagorean Theorem using similar triangles: Statement Justification Draw an altitude from point C to Line segment AB Let segment BC = a segment CA = b segment AB = c segment CD = h segment DB = y segment AD = x y + x = c c over a equals a over y and c over b equals b over x a2 = cy; b2 = cx a2 + b2 = cy + b2 a2 + b2 = cy + cx a2 + b2 = c(y + x) a2 + b2 = c(c) a2 + b2 = c2 Which is not a justification for the proof? Addition Property of Equality Pythagorean Theorem Pieces of Right Triangles Similarity Theorem Cross Product Property

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general 4 months ago 3471

Which table correctly shows all the sample spaces for tossing a coin and rolling an odd number on a six-sided number cube? Coin Number cube Outcome Heads 1 Heads, 1 Heads 3 Heads, 3 Heads 5 Heads, 5 Tails 1 Tails, 1 Tails 3 Tails, 3 Tails 5 Tails, 5 Coin Number cube Outcome Heads 1 Heads, 1 Heads 2 Heads, 2 Heads 3 Heads, 3 Tails 4 Tails, 4 Tails 5 Tails, 5 Tails 6 Tails, 6 Coin Number cube Outcome Heads 2 Heads, 2 Heads 4 Heads, 4 Heads 6 Heads, 6 Tails 2 Tails, 2 Tails 4 Tails, 4 Tails 6 Tails, 6 Coin Number cube Outcome Heads 2 Heads, 1 Heads 4 Heads, 3 Heads 6 Heads, 5 Tails 2 Tails, 2 Tails 4 Tails, 4 Tails 6 Tails, 6

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general 4 months ago 8453

PLEASE HELP8.08, part 211. Find an equation in standard form for the hyperbola with vertices at (0, ±6) and foci at (0, ±9). A) y squared over 45 minus x squared over 36 = 1 B) y squared over 81 minus x squared over 36 = 1 C) y squared over 36 minus x squared over 81 = 1 D) y squared over 36 minus x squared over 45 = 112. Find an equation in standard form for the hyperbola with vertices at (0, ±4) and asymptotes at y = ± 1 divided by 4. x. A) y squared over 16 minus x squared over 64 = 1 B) y squared over 16 minus x squared over 256 = 1 C) y squared over 256 minus x squared over 16 = 1 D) y squared over 64 minus x squared over 4 = 113. Eliminate the parameter.x = t - 3, y = t2 + 5 A) y = x2 + 6x + 14 B) y = x2 - 14 C) y = x2 - 6x - 14 D) y = x2 + 1414. Find the rectangular coordinates of the point with the polar coordinates. ordered pair 3 comma 2 pi divided by 3 A) ordered pair negative 3 divided by 2 comma 3 square root 3 divided by 2 B) ordered pair 3 square root 3 divided by 2 comma negative 3 divided by 2 C) ordered pair negative 3 divided by 2 comma 3 divided by 2 D) ordered pair 3 divided by 2 comma negative 3 divided by 215. Find all polar coordinates of point P where P = negative pi divided by 6 . A) (1, negative pi divided by 6 + (2n + 1)π) or (-1, negative pi divided by 6 + 2nπ) B) (1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + 2nπ) C) (1, negative pi divided by 6 + 2nπ) or (1, pi divided by 6 + (2n + 1)π) D) (1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + (2n + 1)π)16. Determine two pairs of polar coordinates for the point (4, 4) with 0° ≤ θ < 360°. A) (4 square root 2 , 135°), (-4 square root 2 , 315°) B) (4 square root 2 , 45°), (-4 square root 2 , 225°) C) (4 square root 2 , 315°), (-4 square root 2 , 135°) D) (4 square root 2 , 225°), (-4 square root 2 , 45°)17. The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph.a circular graph with an inner loop on the left[-5, 5] by [-5, 5] (5 points) A) r = 3 + 2 cos θ B) r = 2 + 3 cos θ C) r = 2 + 2 cos θ D) r = 4 + cos θ18. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.r = -2 + 3 cos θ A) No symmetry B) y-axis only C) x-axis only D) Origin only19. A railroad tunnel is shaped like a semiellipse, as shown below.A semiellipse is shown on the coordinate plane with vertices on the x axis and one point of intersection with the positive y axis.The height of the tunnel at the center is 54 ft, and the vertical clearance must be 18 ft at a point 8 ft from the center. Find an equation for the ellipse. 20. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.r = 2 cos 3θ

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general 4 months ago 7768