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College Algebra 11th Edition Michael Sullivan, Michael Sullivan III - Solutions

Simplify each expression. |-7| +6 -|-10| − (−8+3)
Fill in each blank with the correct response.For the geometric sequence having an = (-2)n, the term a5 = _____.
Write the first five terms of each sequence described.Arithmetic, with a1 = 4 and d = 2
Write the first five terms of each sequence described. an = (-1)" + 1
Find the indicated term and evaluate S10 for each sequence.a40: arithmetic; 1, 7, 13, . . .
Fill in each blank with the correct response.In the sequence 3, 6, 9, 12, the term a3 = _____.
Fill in each blank with the correct response.The complete row of Pascal’s triangle that begins with the terms 1, 4, is _____.
Write the first four terms of each sequence. an 2n - 3
Fill in each blank with the correct response.For the arithmetic sequence having an = 2n + 4, the term a3 = _____.
Fill in each blank with the correct response.In a geometric sequence, if any term after the first is divided by the term that precedes it, the result is the common _____ of the sequence.
Find the indicated term and evaluate S10 for each sequence.a10: geometric; -3, 6, -12, . . .
Fill in each blank with the correct response.The domain of an infinite sequence is _____.
Fill in each blank with the correct response.In each row of Pascal’s triangle, the first and last terms are _____, and each number in the interior of the triangle is the _____ of the two numbers just above it (one to the right and one to the left).
Fill in each blank with the correct response.In an arithmetic sequence, if any term is subtracted from the term that follows it, the result is the common _____ of the sequence.
For f(x) = - 3x2 + 5x - 2, find f(x +h)-f(x) h h = 0
According to a survey by Olsten Staffing Services, the percentage of companies reporting usage of Microsoft Word t years since 1984 is given by (a) What is the growth rate in the percentage of Microsoft Word users? (b) Use a graphing utility to graph P = P(t). (c) What was the percentage of
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. log₂ X x³ - 3 x > 3
Problems 89–96 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Find the midpoint of the line segment connecting the points (3,-8) and (-2,5).
Problems 89–96 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Solve (2x + 3)² + x² = 5x (2 + x) + 1.
Problems 89–96 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Find the area of the region enclosed by the graphs of y = √9x² and y = x + 3.
Problems 89–96 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. The graph of f(x) = Vx² + 25 + (8 - x) has an 1 absolute minimum when √√x² + 25 2 minimum value
Problems 89–96 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. If g(x) = √x - 7+2, find g¯¹(3).
Aircraft such as fighter jets routinely go supersonic (faster than the speed of sound). An aircraft moving faster than the speed of sound produces a cone-shaped shock wave that “booms” as it trails the vehicle. The wave intersects the ground in the shape of one half of a hyperbola and the area
The light from a lamp creates a shadow on a wall with a hyperbolic border. Find the equation of the border if the distance between the vertices is 18 inches and the foci are 4 inches from the vertices. Assume the center of the hyperbola is at the origin.
If 4x = 7, what does 4-2x equal?
Problems 89–96 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.What is the inverse function for f(x) = 3ex-1 + 4?
Problems 89–96 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.Find the horizontal asymptote for the graph of f(x) = 4ex+1 -5
Problems 89–96 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Solve the equation log5x + log5 (x - 4) = 1.
In Problems 67–74, analyze each equation.y2 = -12(x + 1)
In Problems 67–74, analyze each equation. (y + 2)² 16 (x - 2)² 4 = 1
In Problems 67–74, analyze each equation. 2 (x-3) ² 4 25 = 1 ||
In Problems 49–62, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation. 2x² - y² + 4x + 4y - 4 = 0
In Problems 67–74, analyze each equation.x2 = 16(y - 3)
In Problems 49–62, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation. y²x² - 4y + 4x − 1 = 0
In Problems 49–62, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation. y²4x² - 4y - 8x - 4 = 0
In Problems 49–62, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation. 2 (x + 4) ²9 (y - 3)2 = 9
In Problems 49–62, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation. (y + 3)² _ (x − 2) ² 4 9 = 1
In Problems 49–62, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation. (x - 2)² 4 (y + 3)² 9 = 1
In Problems 41–48, find an equation for the hyperbola described. Graph the equation. Vertices at (1, -3) and (1,1); asymptote the line y + 1 NIGE (x - 1)
In Problems 41–48, find an equation for the hyperbola described. Graph the equation. Vertices at (-1,-1) and (3,-1); 3 asymptote the line y + 1 = 2 (x - 1)
In Problems 41–48, find an equation for the hyperbola described. Graph the equation. Focus at (-4, 0); vertices at (-4, 4) and (-4,2)
In Problems 41–48, find an equation for the hyperbola described. Graph the equation. Center at (4, -1); focus at (7, -1); vertex at (6, -1)
In Problems 37–40, find an equation for each hyperbola. YA y = -2x VA 5 -5 1 1 -5 y = 2x /1 5 X
In Problems 37–40, find an equation for each hyperbola. у = -2 х -5 у 10 -10 y=2x 5 х
Answer Problems 9–11 using the figure to the right.The equation of the hyperbola is of the form (h, k)- y | Transverse axis F F X
In Problems 37–40, find an equation for each hyperbola. -3 УА 3 -3 - y=x 3 X y = -x
In Problems 37–40, find an equation for each hyperbola. y=-x -3 УА 3 -3 y=x 3 x
In Problems 4–6, find an equation of the conic described; graph the equation. Hyperbola: center (2, 2), vertex (2, 4), contains the point (2+ V10,5)
In Problems 4–6, find an equation of the conic described; graph the equation. Ellipse: center (0, 0), vertex (0, -4), focus (0, 3)
True or False The equation y2 = 9 + x2 is symmetric with respect to the x-axis, the y-axis, and the origin.
In Problems 1–3, identify each equation. If it is a parabola, give its vertex, focus, and directrix; if an ellipse, give its center, vertices, and foci; if a hyperbola, give its center, vertices, foci, and asymptotes. 2х2 2x² + 3у² + 4х - бу = 13 3y
In Problems 1–10, identify each equation. If it is a parabola, give its vertex, focus, and directrix; if it is an ellipse, give its center, vertices, and foci; if it is a hyperbola, give its center, vertices, foci, and asymptotes. y² 25 x² 16 = 1
In Problems 1–10, identify each equation. If it is a parabola, give its vertex, focus, and directrix; if it is an ellipse, give its center, vertices, and foci; if it is a hyperbola, give its center, vertices, foci, and asymptotes. 1² X 25 - y² = 1
In Problems 4–6, find an equation of the conic described; graph the equation. Parabola: focus (-1, 4.5), vertex (-1,3)
The distance d from P1 = (3, - 4) to P2 = (-2, 1) is d =_____ .
Use a graphing utility to find the quadratic function of best fit for the data below. X Y 2 3.08 2.5 3.42 3 3.65 3.5 3.82 4 3.6
Change 52 = z to an equivalent statement involving a logarithm.
In Problems 73–88, use the given function f.f(x) = -ln(-x) (a) Find the domain of f (d) Find f¹, the inverse of f (b) Graph f (c) From the graph, determine the range and any asymptotes of f (e) Find the domain and the range of f-¹. (f) Graph f-¹.
In Problems 73–88, use the given function f.f(x) = ln (2x) - 3 (a) Find the domain of f (d) Find f¹, the inverse of f (b) Graph f (c) From the graph, determine the range and any asymptotes of f (e) Find the domain and the range of f-¹. (f) Graph f-¹.
In Problems 71–78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. log√5 8
In Problems 65–84, solve each equation. 3x²-7 = 272x
In Problems 65–84, solve each equation. 5x²+8 = 1252x
In Problems 71–78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. log e ㅠ
Problems 83–89 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. In 1978, Congress created a gas guzzler tax on vehicles with a fuel economy of less than 22.5 miles
In Problems 71–78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. log V₂
In Problems 65–84, solve each equation.9-x+15 = 27x
In Problems 1–10, identify each equation. If it is a parabola, give its vertex, focus, and directrix; if it is an ellipse, give its center, vertices, and foci; if it is a hyperbola, give its center, vertices, foci, and asymptotes. x² - 4x = 2y
In Problems 1–10, identify each equation. If it is a parabola, give its vertex, focus, and directrix; if it is an ellipse, give its center, vertices, and foci; if it is a hyperbola, give its center, vertices, foci, and asymptotes.4x2 + 9y2 - 16x - 18y = 11
In Problems 73–88, use the given function f.f(x) = -2 ln (x + 1) (a) Find the domain of f (d) Find f¹, the inverse of f (b) Graph f (c) From the graph, determine the range and any asymptotes of f (e) Find the domain and the range of f-¹. (f) Graph f-¹.
In Problems 73–86, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.ex = x3
In Problems 65–84, solve each equation. 4x.2x² = 16²
In Problems 79–84, graph each function using a graphing utility and the Change-of-Base Formula.y = log4 x
In Problems 73–88, use the given function f. (a) Find the domain of f (d) Find f¹, the inverse of f (b) Graph f (c) From the graph, determine the range and any asymptotes of f (e) Find the domain and the range of f-¹. (f) Graph f-¹.
In Problems 65–84, solve each equation. 92x. 27x² = 3-1
In Problems 73–86, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.ln x = -x
In Problems 79–84, graph each function using a graphing utility and the Change-of-Base Formula.y = log5 x
In Problems 73–86, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.In (2x) -x + 2
In Problems 73–88, use the given function f. (a) Find the domain of f (d) Find f¹, the inverse of f (b) Graph f (c) From the graph, determine the range and any asymptotes of f (e) Find the domain and the range of f-¹. (f) Graph f-¹.
In Problems 73–88, use the given function f. (a) Find the domain of f (d) Find f¹, the inverse of f (b) Graph f (c) From the graph, determine the range and any asymptotes of f (e) Find the domain and the range of f-¹. (f) Graph f-¹.
(a) Solve f(x) = 2. What point is on the graph of f? (b) Solve g(x) = 3. What point is on the graph of g? (c) Solve f(x) = g(x). Do the graphs of f and g intersect? If so, where? (d) Solve (f + g) (x) = 3. (e) Solve (f- g) (x) = 2.f(x) = log3 (x + 5) and g(x) = log3 (x - 1).
(a) Solve f(x) = 3. What point is on the graph of f? (b) Solve g(x) = 4. What point is on the graph of g? (c) Solve f(x) = g(x). Do the graphs of f and g intersect? If so, where? (d) Solve (f + g) (x) = 7. (e) Solve (f- g) (x) = 2.f(x) = log2 (x + 3) and g(x) = log2 (3x + 1).
In Problems 73–88, use the given function f. (a) Find the domain of f (d) Find f¹, the inverse of f (b) Graph f (c) From the graph, determine the range and any asymptotes of f (e) Find the domain and the range of f-¹. (f) Graph f-¹.
In Problems 79–84, graph each function using a graphing utility and the Change-of-Base Formula. y = logx+2(x - 2)
If 2x = 3, what does 4-x equal?
In Problems 79–84, graph each function using a graphing utility and the Change-of-Base Formula. y = log₂ (x + 2)
In Problems 65–84, solve each equation.e2x = e5x+12
In Problems 73–88, use the given function f.f(x) = log (-2x) (a) Find the domain of f (d) Find f¹, the inverse of f (b) Graph f (c) From the graph, determine the range and any asymptotes of f (e) Find the domain and the range of f-¹. (f) Graph f-¹.
In Problems 65–84, solve each equation. 3x e³x = e²-x
In Problems 79–84, graph each function using a graphing utility and the Change-of-Base Formula.y = log4 (x - 3)
In Problems 73–88, use the given function f. (a) Find the domain of f (d) Find f¹, the inverse of f (b) Graph f (c) From the graph, determine the range and any asymptotes of f (e) Find the domain and the range of f-¹. (f) Graph f-¹.
In Problems 65–84, solve each equation. et² = 1 ex. 2 e
In Problems 79–84, graph each function using a graphing utility and the Change-of-Base Formula. y logx-1(x + 1)
In Problems 65–84, solve each equation. 12 (e4) *• et² = e1² .
If 3-x = 2, what does 32x equal?
In Problems 87–96, express y as a function of x. The constant C is a positive number. ln y = ln x + ln C
In Problems 87–96, express y as a function of x. The constant C is a positive number. ln y = ln(x + C)
If 5-x = 3, what does 53x equal?
In Problems 89–112, solve each equation.log3 x = 2
In Problems 87–96, express y as a function of x. The constant C is a positive number. In y = ln x + ln (x + 1) + In C
If 9x = 25, what does 3x equal?

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