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

For the function ƒ(x) = -x2 + 4, a student claimed that ƒ(-2) = 8. This is incorrect.Find the correct value of ƒ(-2).
Find each product. 14x²y³(-2x³y)
Perform the indicated operations and then simplify. Assume that all variables represent nonzero real numbers. 7p5 (3p4 +p³ + 2p²)
Determine whether each statement is true or false. If false, correct the righthand side of the statement. I = o(01-)-
Simplify each expression. Assume that all variables represent nonzero real numbers.5-1 - 6-1
Give the numerical coefficient and the degree of each term.7z
The term “Big Data,” originally coined by NASA researchers, includes all data streaming from sources such as cell phones, tablets, satellites, Amazon, Google, Facebook, and Twitter. Write each “Big Data” number in scientific notation.1,000,000,000,000 bytes (a terabyte)
Find each product. (pds)zdt-
Perform the indicated operations and then simplify. Assume that all variables represent nonzero real numbers. (-ج-ج) 5(2-3)-1
Simplify each expression. Assume that all variables represent nonzero real numbers. 5 4 -2
A student incorrectly gave 6 as the degree of the following polynomial.2xy6 + 3xy5 + 4xy4Give the degree of this polynomial.
Determine whether each statement is true or false. If false, correct the righthand side of the statement. (52)3 = 56
Simplify each expression. Assume that all variables represent nonzero real numbers. (-2x4y-³)0(-4x-³y-8) ²
The term “Big Data,” originally coined by NASA researchers, includes all data streaming from sources such as cell phones, tablets, satellites, Amazon, Google, Facebook, and Twitter. Write each “Big Data” number in scientific notation.1,000,000,000 bytes (a gigabyte)
Find each product. -8m3(3m²)
Perform the indicated operations and then simplify. Assume that all variables represent nonzero real numbers. -(-3)²
Simplify each expression. Assume that all variables represent nonzero real numbers. NIM 3 -4
A student incorrectly gave 2 as the leading coefficient of the following polynomial.2x2 - 5x3 - 8x4Give the correct leading coefficient.
Determine whether each statement is true or false. If false, correct the righthand side of the statement. (04) 0 = 0x
The term “Big Data,” originally coined by NASA researchers, includes all data streaming from sources such as cell phones, tablets, satellites, Amazon, Google, Facebook, and Twitter. Write each “Big Data” number in scientific notation.1,000,000 bytes (a megabyte)
Work each problem involving polynomial functions and function notation.If ƒ(x) = 2x, then ƒ(5) = ________ . Here ƒ(5) = 10 is an abbreviation for the statement “If x = _________ in the function ƒ, then y = _________.” The ordered pair ______ belongs to ƒ.
A student incorrectly claimed that the following number is written in scientific notation.Write this number in scientific notation. 0.2 x 10-2
Simplify each expression. Assume that all variables represent nonzero real numbers. 36r-4(1²)-3 6r4
Match each product in Column I with the correct polynomial in Column II. I (2x - 5)(3x - 4) II A. 6x2 + 23x + 20 B. 6x2 + 7x - 20 C. 6x²7x - 20 D. 6x²23x + 20
Perform the indicated operations and then simplify. Assume that all variables represent nonzero real numbers. -9 21- -2 64(-1) 6y
Simplify each expression. Assume that all variables represent nonzero real numbers. (-5)³
Work each problem involving polynomial functions and function notation.For a function ƒ, the notation ƒ(5) means ________ .A. The variable ƒ times 5, or 5f B. ƒ equals 5C. The range value when the domain value is 5D. The domain value when the range value is 5
Give an example of a polynomial of four terms in the variable x that is of degree 5, is written in descending powers, and lacks a fourth-degree term.
Simplify each expression. Assume that all variables represent nonzero real numbers. 2 (-3)-²
Match each product in Column I with the correct polynomial in Column II. I (2x + 5)(3x - 4) II A. 6x2 + 23x + 20 B. 6x2 + 7x - 20 C. 6x²7x - 20 D. 6x223x + 20
Determine whether each statement is true or false. If false, correct the righthand side of the statement.x3 • x4 = x7
Give an example of a trinomial in the variable y that is of degree 3, has leading coefficient -1, and lacks a term with degree 0.
Simplify each expression. Assume that all variables represent nonzero real numbers. #F) (2) qª -2
Perform the indicated operations and then simplify. Assume that all variables represent nonzero real numbers.5-3
Determine whether each statement is true or false. If false, correct the righthand side of the statement. a 3 || 43 | D (a = 0)
When asked to write 9,275,000 in scientific notation, a student incorrectly wroteWhat is the correct answer? 92.75 X 105.
Simplify each expression. Assume that all variables represent nonzero real numbers. (3x-2y³)-2(4x³y-4)
Which of the following are not polynomial functions? A. P(x) = x-² - 2x C. g(x) = 4x + 1.5 1 B. f(x) = x² +. + x - 1 D. p(x) = x³ x² - 5 - Xx
In 2017, the estimated population of New Zealand was 4.510 × 106. The population density was 44.16 people per square mile. What is the area of New Zealand to the nearest square mile?
Match each product in Column I with the correct polynomial in Column II. I (2x + 5) (3x + 4) II A. 6x² + 23x + 20 B. 6x2 + 7x - 20 C. 6x²7x - 20 D. 6x²23x + 20
Simplify each expression. Assume that all variables represent nonzero real numbers. -- 4
Which polynomial is a trinomial in descending powers that has degree 6? A. 5x6 - 4x5 + 12 C. 2x + 4x²x6 B. 6x5x6+4 D. 4x66x4 + 9x² - 8
Match each expression (a) – (j) in Column I with its equivalent expression A–J in Column II. Choices may be used once, more than once, or not at all. (a) 7-2 (c) -7⁰ (e) -7² (g) (7+2)-¹ (i) 7² I (b) 7⁰ (d) (-7)⁰ (f) 7-¹ + 2-¹ 7-1 2-1 (j) (-7)-² (h) A. 1 C. 49 E. -49 2 7 I.
Determine whether each statement is true or false. If false, correct the righthand side of the statement. (5r)3 = 53r3
Match each number written in scientific notation in (a)–(d) in Column I with the equivalent number written in standard notation in A–F in Column II. Not all choices will be used. (a) 1.5 x 104 (c) 1.5 x 10-4 I (b) 1.5 × 105 (d) 1.5 x 10-5 A. 150,000 D. 15,000 II B. 1500 E. 0.0015 C. 0.00015 F.
Match each product in Column I with the correct polynomial in Column II. I (2x - 5)(3x + 4) II A. 6x² + 23x + 20 B. 6x2 + 7x - 20 C. 6x²7x- 20 D. 6x223x + 20
Match each expression (a) – (j) in Column I with its equivalent expression A–J in Column II. Choices may be used once, more than once, or not at all. (a) 4-² (c) 4⁰ (e) (-4)-² (g) -40+40 (i) 4-2 + 4-1 I (b) -4² (d) (-4)⁰ (f) -4⁰ (h) -4° -4° (j) 4² A. 1 16 C. 1 E. -1 G.
Simplify each expression. Assume that all variables represent nonzero real numbers.43
Use the graph shown in FIGURE 1 at the beginning of this section (and repeated here) to work each exercise.Which type of subscription was more popular in 2017? What Are You Watching? Subscribers (in millions) 50 40 30 20 10 Cable TV Netflix 3 4 Years since 2012 Data from Netflix, Leichtman Research
Use the graph shown in FIGURE 1 at the beginning of this section (and repeated here) to work each exercise.If x = 0 represents 2012 and x = 5 represents 2017, the number of subscribers y in millions can be modeled by the linear equations in the following system.Solve this system. Express values as
Use the graph shown in FIGURE 1 at the beginning of this section (and repeated here) to work each exercise.Between which two years were the numbers of Netflix and cable TV subscribers the same? About how many people subscribed to each video content provider at that point? What Are You
Write an equation of the line passing through the given point and satisfying the given condition. 3 (-2,-2); slope 0
Determine whether each relation defines y as a function of x. (Solve for y first if necessary.) Give the domain. y = √4x + 2
Each table of values gives several points that lie on a line.(a) What is the x-intercept of the line? The y-intercept?(b) Which equation in choices A–D corresponds to the given table of values?(c) Graph the equation. X -4 -2 У -3 0 о 3 2 6 A. 3x + 2y = 6 B. 3x - 2y = -6 C. 3x + 2y = −6 D.
Find the x- and y-intercepts. Then graph each equation.y + 2 = 0
Find the slope of each line, and sketch its graph. 5x - 2y = 10
Determine whether each relation defines y as a function of x. (Solve for y first if necessary.) Give the domain.x + y < 4
The linear equation 2x - 5y = 7 defines y as a function of x. If y = ƒ(x), which of the following defines the same function? 2 7 A. f(x) = x) = - 3 x + ² 5 2 c. f(x) = 3x - 17/ 5 5 B. f(x) = D. f(x) 2 --3/x-17 5 5 2 7 f(x) = ² x + ²/ - 5 5
Let ƒ(x) = -2x2 + 3x - 6. Find the following. (-)
The equation 2x2 - y = 0 defines y as a function f of x. Write it using function notation ƒ(x), and find ƒ(3).
Let ƒ(x) = -2x2 + 3x - 6. Find the following.ƒ(k)
Determine whether each relation defines y as a function of x. Give the domain. Identify any linear functions. y = 7 6 9-x
Let ƒ(x) = -2x2 + 3x - 6. Find the following.ƒ(3)
Let ƒ(x) = -2x2 + 3x - 6. Find the following.ƒ(0)
Determine whether each relation defines y as a function of x. Give the domain. Identify any linear functions.x = y2
Determine whether each relation defines y as a function of x. Give the domain. Identify any linear functions. y = √4x + 7
What is the name that is usually given to the graph of ƒ(x) = 0?
Complete each statement. If (4, -3) is a solution of a linear system in two variables, then substituting ________ for x and___________ for y leads to true statements in both equations.
Complete each statement. A solution of a system of independent linear equations in two variables is an ordered_____________.
Complete each statement. If solving a system leads to a false statement such as 0 = 3, the solution set is ____________.
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. y = 1.4x 0.5x + 1.5y = 26.0
Solve each system. 2x - 5y = 8 3x + 4y = 10
Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. 5x - y = 14 4x + 2y = 0
Evaluate for x = -4, y = 3, and z = 6. |2x + 3y - 23
Complete each statement.If solving a system leads to a true statement such as 0 = 0, the system has_________ equations.
Solve each system. If the system is inconsistent or has dependent equations, say so. x + 4y 2 = 3 8y + 2z = -6 - I -2x 3x + 12y3z = 9
In his motorboat, Bill travels upstream at top speed to his favorite fishing spot, a distance of 36 mi, in 2 hr. Returning, he finds that the trip downstream, still at top speed, takes only 1.5 hr. Find the rate of Bill’s boat and the rate of the current. Let x = the rate of the boat and y = the
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. 1 2 1 | -x + 8 1 4 1 y x. = -5 = 0 =
Solve each system. If the system is inconsistent or has dependent equations, say so. x+ x + 5y - 2z = -1 -2x + 8y + z = -4 3x - y + 5z = 19 =
Traveling for 3 hr into a steady headwind, a plane flies 1650 mi. The pilot determines that flying with the same wind for 2 hr, he could make a trip of 1300 mi. Find the rate of the plane and the wind speed. x -y mph into wind x + y mph with wind
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. 1 3 2 x+ 1 -X 2 - Tin 3 2 y || -6 = 12
Solve each system. If the system is inconsistent or has dependent equations, say so. 2x + y 4x + 2y -X 1 29 2 = 6 2z = 12 1 + 2 N -3
Solve each system. If the system is inconsistent or has dependent equations, say so. x + 3y + z = 2 4x + y + 2z = -4 5x + 2y + 32 = -2
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. x = 3y 3x9y = 0
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. y = 2x у 4x-2y = 0
A car and a truck leave towns 230 mi apart, traveling toward each other. The car travels 15 mph faster than the truck. They pass each other 2 hr later. What are their rates?
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. x = 5y 5x - 25y = 5
Solve each system. If the system is inconsistent or has dependent equations, say so. 8y + 2z = -10 2x -x + 4y - z = 5 1 1 8-2y+ 1 8 2 = T 5100 8
A plane flies 560 mi in 1.75 hr traveling with the wind. The return trip later against the same wind takes the plane 2 hr. Find the rate of the plane and the wind speed.
Braving blizzard conditions on the planet Hoth, Luke Skywalker sets out in his snow speeder for a rebel base 4800 mi away. He travels into a steady headwind and makes the trip in 3 hr. Returning, he finds that the trip back, now with a tailwind, takes only 2 hr. Find the rate of Luke’s snow
Problems 76–85 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 domain of h (x) || √x + 7 + 7x.
In Problems 7–9, solve each inequality. Graph the solution set. 2x − 5 < 3
Consider the graph of the function f below. (a) Find the domain and the range of f.(b) List the intercepts.(c) Find f(1).(d) For what value(s) of x does f(x) = -3?(e) Solve f(x) (-2,0) -4 (-5, -3) у 4 (1,3) (0, 2) -2 -4 (2,0) LX 4 (3, -3) (5,-2)
In Problems 6–8, find the following for each function: (a) f(2) (b) f(-2) (c) f(-x) (d) -f(x) (e) f(x - 2) (f) f(2x) f(x) 3x 2 x² - 1
In Problems 6–8, find the following for each function: a) f(2) (b) f(-2) (c) f(-x) (d) -f(x) (e) f(x - 2) (f) f(2x) 2 f(x) = √x² - 4
While shopping online for AA batteries, Masoud found that he could order a pack of 8 batteries for $6.30, a pack of 16 for $13.99, a pack of 20 for $12.32, or a pack of 24 for $13.99. Define a relation using number of batteries as input and price as output. (a) What is the domain and range of
In Problems 2–5, find the domain and range of each relation. Then determine whether the relation represents a function. { (-1,0), (2,3), (4,0)}
Which function has a graph that is the graph of shifted down 3 units? y = √x:
In Problems 2–5, find the domain and range of each relation. Then determine whether the relation represents a function. y = -4x5| 3
In Problems 2–5, find the domain and range of each relation. Then determine whether the relation represents a function. { (4, -1), (2, 1), (4,2)}

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