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College Algebra Graphs and Models 5th edition Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna - Solutions

A 24-in. piece of string is cut into two pieces. One piece is used to form a circle while the other is used to form a square. How should the string be cut so that the sum of the areas is a minimum?
Find the zero of the function. a. f (x) = 15 - 2x b. f (x) = -3x + 9
Drivers who were distracted by such things as text-messaging, talking on a cell phone, conversing with passengers, and eating were involved in 5870 highway fatalities in 2008. This was an increase of about 18% over the number of distracted-driving fatalities in 2004 and is attributed largely to the
Together, the Mall of America in Minnesota and the Disneyland theme park in California occupy 181 acres of land. The Mall of America occupies 11 acres more than Disneyland. (Sources: Mall of America; Disneyland) How much land does each occupy?
Solve and write interval notation for the solution set. Then graph the solution set. a. | x | < 7 b. | x | ≤ 4.5 c. | x | ≤ 2
Find the zeros of f (x) = 4x2 - 8x - 3 by completing the square. Show your work.
In Exercises, (a) find the discriminant b2 - 4ac, and then determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist; and (b) solve the equation, finding exact solutions and approximate solutions rounded to three decimal
One number is 2 more than another. The product of the numbers is 35. Find the numbers.
In Exercise a) Find the vertex. b) Find the axis of symmetry. c) Determine whether there is a maximum or minimum value, and find that value. d) Find the range. e) Find the intervals on which the function is increasing and the intervals on which the function is decreasing. f) Graph the function. f
Express the number in terms of i. a. √-36 b. √-5 c. -√-16 d. √-32
Simplify. Write answers in the form a + bi, where a and b are real numbers. a. (3 - 2i) + (-4 + 3i) b. (-5 + i) - (2 - 4i) c. (2 + 3i)(4 - 5i) d. (3 + i) / (-2 + 5i)
Find the zero(s) of the function. a. f (x) = x2 - 2x + 1 b. f (x) = x2 + 2x - 15 c. f (x) = 2x2 - x - 5
Solve and write interval notation for the solution set. Then graph the solution set. a. | 5x | ≥ 15 b. | 3x + 4 | < 10 c. | 6x - 1 | < 5
Simplify each of the following. Write the answer in the form a + bi, where a and b are real numbers. a. (6 + 2i) + (-4 - 3i) b. (3 - 5i) - (2 - i) c. (6 + 2i) (-4 - 3i) d. (2 - 3i) / (1 - 3i)
Solve by completing the square to obtain exact solutions. Show your work. a. x2 - 3x = 18 b. 3x2 - 12x - 6 = 0
In Exercises, complete the square to: a) Find the vertex; b) Find the axis of symmetry; c) Determine whether there is a maximum or minimum value and find that value; d) Find the range; and e) Graph the function. 1. f (x) = -4x2 + 3x - 1 2. f (x) = 5x2 - 10x + 3
In Exercises, match the equation with one of the figures (a)-(d), which follow.1. y = (x - 2)2 2. y = (x + 3)2 - 4 3. y = -2(x + 3)2 +1 4 4. y = - ½ (x - 2)2 + 5
The hypotenuse of a right triangle is 50 ft. One leg is 10 ft longer than the other. What are the lengths of the legs?
Logan and Cassidy leave a campsite, Logan biking due north and Cassidy biking due east. Logan bikes 7 km/h slower than Cassidy. After 4 hr, they are 68 km apart. Find the speed of each bicyclist.
A 60-ft by 80-ft parking lot is torn up to install a sidewalk of uniform width around its perimeter. The new area of the parking lot is two-thirds of the old area. How wide is the sidewalk?
The Berniers have 24 ft of flexible fencing with which to build a rectangular "toy corral." If the fencing is 2 ft high, what dimensions should the corral have in order to maximize its volume?
An open box is made from a 10-cm by 20-cm piece of aluminum by cutting a square from each corner and folding up the edges. The area of the resulting base is 90 cm2. What is the length of the sides of the squares?
Find the zeros of f (x) = 2x2 - 5x + 1. a. (5 ± √17) / 2 b. (5 ± √17) / 4 c. (5 ± √33) / 4 d. (-5 ± √17) /4
At the beginning of the year, $3500 was deposited in a savings account. One year later, $4000 was deposited in another account. The interest rate was the same for both accounts. At the end of the second year, there was a total of $8518.35 in the accounts. What was the annual interest rate?
Find b such that f (x) = -3x2 + bx - 1 has a maximum value of 2.
Is it possible for a quadratic function to have one real zero and one imaginary zero? Why or why not?
Explain why it is necessary to check the possible solutions of a rational equation.
Explain why it is necessary to check the possible solutions when the principle of powers is used to solve an equation.
Solve and write interval notation for the solution set. Then graph the solution set. a. | x + 3 | ≤ 4 b. | 2x - 1 | < 5 c. | x + 5 | > 2
Solve x2 + 4x = 1 by completing the square. Find the exact solutions. Show your work.
The tallest structure in the United States, at 2063 ft, is the KTHI-TV tower in North Dakota (Source: The Cambridge Fact Finder). How long would it take an object falling freely from the top to reach the ground? (Use the formula s = 16t2.)
Find the zeros of each function. a. f (x) = 4x2 - 11x - 3 b. f (x) = 2x2 - x - 7
For the graph of the function f (x) = -x2 + 2x + 8:a) Find the vertex.b) Find the axis of symmetry.c) State whether there is a maximum or minimum value and find that value.d) Find the range.e) Graph the function.
A homeowner wants to fence a rectangular play yard using 80 ft of fencing. The side of the house will be used as one side of the rectangle. Find the dimensions for which the area is a maximum.
The graph of f (x) = x2 - 2x - 1 is which of the following?
Find a such that f (x) = ax2 - 4x + 3 has a maximum value of 12.
Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic? a) g(x) = 1/23 x3 - 10x + 8 b) f(x) = 15x2 - 10 + 0.11x4 - 7x3 c) h(x) = 0.9 x - 0.13
In Exercises 11-18, select one of the four sketches (a)-(d), which follow, to describe the end behavior of the graph of the function.a) f(x) = - 3x3 - x + 4 b) f(x) = ¼ x4 + ½ x3 - 6x2 + x - 5 c) f(x) = - x6 + ¾ x4
In Exercises 19-22, use the leading-term test to match the function with one of the graphs (a)-(d), which follow:a) f(x) = - x6 + 2x5 - 7x2 b) f(x) = 2x4 - x2 + 1 c) f(x) = x5 + 1/10 x - 3
Use substitution to determine whether 4, 5, and - 2 are zeros of f(x) = x3 - 9x2 + 14x + 24?
Use substitution to determine whether 2, 3, and - 1 are Zeros of f(x) = 2x3 - 3x2 + x + 6?
Use substation to determine wheter 2, 3, and - 1 are zeros of g(x) = x4 - 6x3 + 8x2 + 6x - 9?
Use substitution to determine whether 1, -2, and 3 are zeros of g(x) = x4 - x3 - 3x2 + 5x - 2?
Find the zeros of the polynomial function and state the multiplicity of each. a) f(x) = (x + 3)2 (x - 1) b) f (x) = (x + 5)3 (x - 4) (x + 1)2 c) f (x) = - 2(x - 4) (x - 4) (x - 4) (x + 6)
Using a graphing calculator, find the real zeros of the function. Approximate the zeros to three decimal places. a) f (x) = x3 - 3x - 1 b) f (x) = x3 + 3x2 - 9x - 13 c) f (x) = x4 - 2x2
Using a graphing calculator, estimate the real zeros, the relative maxima and minima, and the range of the polynomial function. a) g(x) = x3 - 1.2x + 1 b) h(x) = ½ x4 + 3x3 - 5x2 + 3x + 6 c) f(x) = x6 - 3.8
Twin Births. As a result of a greater number of births to older women and the increased use of fertility drugs, the number of twin births in the United States increased approximately 42% from 1990 to 2005 (National Center for Health Statistics, U.S. Department of Health and Human Services). The
Railroad Miles. The greatest combined length of U.S.-owned operating railroad track existed in 1916, when industrial activity increased during World War I. The total length has decreased ever since. The data over the years 1900 to 2008 are modeled by the quartic functionf(x) = - 0.004091x4 +
Dog Years. A dog's life span is typically much shorter than that of a human. The cubic Function d(x) = 0.010255x3 - 0.340119x2 + 7.397499x + 6.618361, Where x is the dog's age, in years, approximates the equivalent human age in years. Estimate the equivalent human age for dogs that are 3, 12, and
Projectile Motion. A stone thrown downward with an initial velocity of 34.3 m/sec will travel a distance of s meters, where s(t) = 4.9t2 + 34.3t and t is in seconds. If a stone is thrown downward at 34.3 m/sec from a height of 294 m, how long will it take the stone to hit the ground?
Games in a Sports League. If there are x teams in a sports league and all the teams play each other twice, a total of N(x) games are played, where N(x) = x2 - x. A softball league has 9 teams, each of which plays the others twice. If the league pays $110 per game for the field and the umpires, how
Median Home Prices. The median price for an existing home in the United States peaked at$221,900 in 2006 (National Association of REALTORS®). The quartic functionh(x) = 56.8328x4 - 1554.7494x3+ 10,451.8211x2 - 5655.7692x+ 140,589.1608,Where x is the number of years since 2000, can be used to
Circulation of Daily Newspapers. In 1985, the circulation of daily newspapers reached itshighest level (Newspaper Association of America). The quartic functionf (x) = -0.006093x4 + 0.849362x3- 51.892087x2 + 1627.3581x+ 41,334.7289,Where x is the number of years since 1940, can be used to estimate
Interest Compounded Annually. When P dollars is invested at interest rate i, compounded annually, for t years, the investment grows to A dollars, where A = P(1 + i)t. Trevor's parents deposit $8000 in a savings account when Trevor is 16 years old. The principal plus interest is to be used for a
Interest Compounded Annually. When P dollars is invested at interest rate i, compounded annually, for t years, the investment grows to A dollars, where A = P(1 + i)t. When Sara enters the 11th grade, her grandparents deposit $10,000 in a college savings account. Find the interest rate i if the
For the scatterplots and graphs in Exercises 71-76, determine which, if any, of the following functions might be used as a model for the data.a) Linear, f(x) = mx + bb) Quadratic, f(x) = ax2 + bx + c, a > 0c) Quadratic, f(x) = ax2 + bx + c, a 6 0d) Polynomial, not linear or quadratic1.2. 3.
Foreign Adoptions. The number of foreign adoptions in the United States has declined in recent years, as shown in the table below.Year, x Number of U.S. Foreign Adoptions from Top 15 Countries, y2000, 0............................. 18,1202001, 1............................. 19,0872002,
U.S. Farm Acreage. As the number of farms has decreased in the United States, the average size of the remaining farms has grown larger, as shown in the table below.Year Average Acreage per Farm1900..................... 1471910.................... 1391920....................
Classified Ad Revenue. The table below lists the newspaper revenue from classified ads for selected years from 1975 to 2009. Year, x Newspaper Revenue from Classified Ads, y (in billions of dollars) 1975, 0 ................. $2.159 1980, 5 ................. 4.222 1985, 10 ...............
Dog Years. A dog's life span is typically much shorter than that of a human. Age equivalents for dogs and humans are listed in the table below. Age of Dog, x (in years) Human Age, h(x) (in years) 0.25 ................................................5 0.5
Find the distance between the pair of points a) (3, - 5) and (0, - 1) b) (4, 2) and (- 2, - 4) c) Find the center and the radius of the circle? (x - 3)2 + (y + 5)2 = 49
The diameter of a circle connects the points 1-6, 52 and 1-2, 12 on the circle. Find the coordinates of the center of the circle and the length of the radius?
a) The diameter of a circle connects the points (- 6, 5) and (- 2, 1) on the circle. Find the coordinates of the center of the circle and length of the radius. Solve. b) 2y - 3 ( 1 - y + 5 c) (x - 2) (x + 5) > x(x - 3).
Determine the degree and the leading term of the polynomial function. a) f(x) = (x5 - 1)2 (x2 + 2)3 b) f(x) = (10 - 3x5)2 (5 - x4)3 (x + 4)
For each function in Exercises 1-6, state: a) The maximum number of real zeros that the function can have; b) The maximum number of x-intercepts that the graph of the function can have; and c) The maximum number of turning points that the graph of the function can have? 1. f (x) = x5 - x2 + 6s 2. f
Graph the polynomial function. Follow the steps outlined in the procedure on p. 317. a. f (x) = - x3 - 2x2 b. g(x) = x4 - 4x3 + 3x2 c. h(x) = x2 + 2x - 3
Graph the piecewise function.
Using the intermediate value theorem, determine, if possible, whether the function f has a real zero between a and b. a. f (x) = x3 + 3x2 - 9x - 13; a = - 5, b = - 4 b. f (x) = x3 + 3x2 - 9x - 13; a = 1, b = 2 c. f (x) = 3x2 - 2x - 11; a = -3, b = - 2
Match the equation with one of the graphs (a)-(f), which follow.a. y = x b. x = - 4 c. y - 2x = 6
Use the leading-term test and your knowledge of y-intercepts to match the function with one of the graphs (a)-(f), which follow.1. f (x) = 1/4x2 - 5 2. f (x) = - 0.5x6 - x5 + 4x4 - 5x3 - 7x2 + x - 3 3. f (x) = x5 - x4 + x2 + 4
For the function f (x) = x4 - 6x3 + x2 + 24x - 20, Use long division to determine whether each of the following is a factor of f (x). a) x+1 b) x - 2 c) x + 5
Use synthetic division to find the quotient and the remainder. a. (2x4 + 7x3 + x - 12) ( (x + 3) b. (x3 - 7x2 + 13x + 3), (x - 2) c. (x3 - 2x2 - 8), (x + 2).
For the function h(x) = x3 - x2 - 17x - 15, Use long division to determine whether each of the following is a factor of h(x). a. x + 5 b. x + 1 c. x + 3
Use synthetic division to find the function values. Then check your work using a graphing calculator. a. f (x) = x3 - 6x2 + 11x - 6; find f (1), f (- 2), and f (3). b. f (x) = x3 + 7x2 - 12x - 3; find f (- 3), f (- 2), and f (-2). and f(1). c. f(x) = x4 - 3x3 + 2x + 8; find f(-1), f(4), and f(- 5).
For the function g(x) = x3 - 2x2 - 11x + 12, Use long division to determine whether each of the following is a factor of g(x). a) x - 4 b) x - 3 c) x - 1
Using synthetic division, determine whether the numbers are zeros of the polynomial function. a. - 3, 2; f (x) = 3x3 + 5x2 - 6x + 18 b. - 4, 2; f (x) = 3x3 + 11x2 - 2x + 8 c. - 3, 1; h(x) = x4 + 4x3 + 2x2 - 4x - 3
Factor the polynomial function f(x). Then solve the equation f(x) = 0. a) f (x) = x3 + 4x2 + x - 6 b) f (x) = x3 + 5x2 - 2x - 24 c) f (x) = x3 - 6x2 + 3x + 10
For the function f (x) = x4 + 8x3 + 5x2 - 38x + 24, Use long division to determine whether each of the following is a factor of f (x). a. x + 6 b. x + 1 c. x - 4
Sketch the graph of the polynomial function. Follow the procedure outlined on p. 317. Use synthetic division and the remainder theorem to find the zeros. a. f (x) = x4 - x3 - 7x2 + x + 6 b. f (x) = x4 + x3 - 3x2 - 5x - 2 c. f (x) = x3 - 7x + 6
In each of the following, a polynomial P(x) and a divisor d(x) are given. Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x). Express P(x) in the form d(x) ( Q(x) + R(x).
Movie Ticket Prices. The average price of a movie ticket has increased linearly over the years, rising from $5.39 in 2000 to $7.89 in 2010 (National Association of Theatre Owners).Using these two data points, find a linear function, f (x) = mx + b, that models the data.Let x represent the number of
The sum of the base and the height of a triangle is 30 in. Find the dimensions for which the area is a maximum?
A graph of a polynomial function is given. On the basis of the graph:a) Find as many factors of the polynomial as you can.b) Construct a polynomial function with the zeros shown in the graph.c) Can you find any other polynomial functions with the given zeros?d) Can you find more than one polynomial
Find k such that x + 2 is a factor of x3 - kx2 + 3x + 7k?
Beam Deflection. A beam rests at two points A and B and has a concentrated load applied to its center. Let y = the deflection, in feet, of the beam at a distance of x feet from A. Under certain conditions, this deflection is given byy = 1/13x3 - 1/14x.Find the zeros of the polynomial is the
Use synthetic division to divide. a. (x4 - y4) ( (x - y) b. (x3 + 3ix2 - 4ix - 2) ( (x + i) c. (x2 - 4x - 2) ( [x - (3 + 2i)]
Find a polynomial function of degree 3 with the given number as zeros? a. - 2, 3, 5 b. - 1, 0, 4 c. - 3, 2i, - 2i.
Complete the square to: a) Find the vertex; b) Find the axis of symmetry; and c) Determine whether there is a maximum or minimum function value and find that value. 1. f(x) = x2 - 8x + 10 2. f(x) = 3x2 - 6x - 1
Find the zeros of the function. a. f(x) =- 4/3x + 8 b. g(x) = x2 - 8x - 33
Determine the leading term, the leading coefficient, and the degree of the polynomial. Then describe the end behavior of the function's graph and classify the polynomial function as constant, linear, quadratic, cubic, or quartic.a) g(x) = - x3 - 2x2b) f(x) = - x2 - 3x + 6c) f(x) = - 4/9?
Consider f(x) = 2x3 - 5x2 - 4x + 3. Find the solutions of each equation.a) f(x) = 0b) f(x - 1) = 0c) f(x + 2) = 0d) f(2x) = 0
Use the rational zeros theorem and the equation x4 - 12 = 0 to show that 4(12 is irrational?
Find the rational zeros of the function. a) P(x) = 2x5 - 33x4 - 84x3 + 2203x2 - 3348x - 10,080 b) P(x) = x6 - 6x5 - 72x4 - 81x2 + 486x + 5832
Find a polynomial function of degree 5 with -1 as a zero of multiplicity 3, 0 as a zero of multiplicity 1, and 1 as a zero of multiplicity 1?
Find a polynomial function of degree 4 with -1 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
Find a polynomial function of degree 5 with - 12 as a zero of multiplicity 2, 0 as a zero of multiplicity 1, and 1 as a zero of multiplicity 2?
Suppose that a polynomial function of degree 4 with rational coefficient has the given numbers as zeros Find the other zero(s)?a. - 1, (3, 11/3b. - (2, - 1, 4/5c. - i, 2 - (5
Suppose that a polynomial function of degree 5 with rational coefficients has the given numbers as zeros. Find the other zero(s).a. - ½, (5, - 4ib. ¾, (3, 2ic. - 5, 0, 2 - i, 4
Find a polynomial function of lowest degree with ration al coefficients that has the given numbers as some of its zeros. a. 1 + i, 2 b. 2 - i, - 1 c. 4i
Given that the polynomial function has the given zero, find the other zeros?a. f (x) = x3 + 5x2 - 2x - 10; -5b. f (x) = x3 - x2 + x - 1; 1c. f(x) = x4 - 5x3 + 7x2 - 5x + 6; - i

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