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mathematics
college algebra
College Algebra 11th Edition Michael Sullivan, Michael Sullivan III - Solutions
Use the quadratic formula to solve each equation. 36x2 - 12x + 1 = 0
Solve each equation using the quadratic formula. (t+3)(t-4)= -2
Identify the vertex of each parabola. f(x) = (x - 1)²
Solve each equation by any method. 9x4 + 4 = 37x²
Match each equation in parts (a) – (f) with the figure that most closely resembles its graph in choices A–F. (a) g(x)=x²-5 (d) G(x) = (x + 1)² A. D. ÷ X X (b) h(x) = x² + 4 (e) H(x) = (x - 1)² + 1 B. E. X X (c) F(x) = (x - 1)² (f) K(x) = (x + 1)² + 1 C. F. y 0 Los X X
Solve each quadratic equation by the method of your choice.3x2 = 3 - 8x
Solve each equation. Check the solutions. 1 + 2 3 X || 我
Solve each equation or inequality. x45x² + 4 = 0
Solve each formula for the specified variable. (Leave ± in the answers as needed.) k R= for d d²
Find the vertex of each parabola. f(x)=x²-x+5
Solve each equation using the quadratic formula. 2x² + 3x + 4 = 0
Identify the vertex of each parabola. f(x) = (x + 3)²
Use the quadratic formula to solve each equation. 9x2 - 6x + 1 = 0
Solve each equation by any method. 12 (2n + 1)² + (2n + 1) =
Solve each equation. Check the solutions. 1 X + 2 x + 2 || 17 35
Solve each quadratic equation by the method of your choice.2r2 - 4r + 1 = 0
Solve each inequality, and graph the solution set. 10x² + 9x ≥ 9
Graph ƒ(x) = 4x2 + 4x - 2. Give the vertex, axis of symmetry, domain, and range.
Solve each equation or inequality. -2x + 4 = -x + 3
Solve each formula for the specified variable. (Leave ± in the answers as needed.) F = ΚΑ v2 for v
Solve each equation using the quadratic formula. 3p² = 2(2p-1)
Use the quadratic formula to solve each equation. 2x2 + 4x + 1 = 0
Terry and Callie do word processing. For a certain prospectus, Callie can prepare it 2-hr faster than Terry can. If they work together, they can do the entire prospectus in 5-hr. How long will it take each of them working alone to prepare the prospectus? Round answers to the nearest tenth of an
Find the vertex of each parabola. f(x)=x²+x-7
Solve each inequality, and graph the solution set. (x + 2)(x − 3)(x + 5) ≤ 0
A ball is projected upward from ground level, and its distance in feet from the ground in t seconds is given byAfter how many seconds does the ball reach a height of 400 ft? Describe in words its position at this height. s(t) = 16t² + 160t.
Find the discriminant. Use it to determine whether the solutions for each equation areA. Two rational numbers B. One rational numberC. Two irrational numbers D. Two nonreal complex numbers.Tell whether the equation can be solved using the zero-factor property, or if the quadratic formula
In one area the demand for Blu-ray discs is 1900/P per day, where P is the price in dollars per disc. The supply is 5P - 1 per day. At what price, to the nearest cent, does supply equal demand?
What is the base in the expression ln x?A. x B. 1 C. 10 D. e
Which point lies on the graph of ƒ(x) = 3x? A. (1,0) B. (3, 1) C. (0, 1) . (V3. 1) D.
The domain of ƒ(x) = ax is (-∞, ∞), while the range is (0, ∞). Therefore because g(x) = loga x is the inverse of f, the domain of g is ________, while the range of g is ________.
Write in logarithmic form. 6 -3 = 216
Graph each function. f(x) = 6*
Graph each function. g(x) = log6x
Solve each equation. Give exact solutions. log5 (12x 8) = 3 -
Which statement is false? A. The domain of the function f(x) = () is (-∞, ∞). B. The graph of the function f(x) = ()* has one x-intercept. C. The range of the function f(x) = (-)* is (0, ∞). D. The point (-2, 16) lies on the graph of f(x) = (1)*.
Graph each exponential function. f(x) = 3 X
Solve. log (3x - 1) = log 10
Solve. In (x² + 3x + 4) = In 2
Write in logarithmic form. 6 -3 = 216
Graph each exponential function. f(x) = 3 X
Solve. log (3x - 1) = log 10
Solve. In (x² + 3x + 4) = In 2
Solve each equation. Give exact solutions. log5 (12x 8) = 3 -
Simplify. V288
A major scientific periodical published an article in 1990 dealing with the problem of global warming. The article was accompanied by a graph that illustrated two possible scenarios.(a) The warming might be modeled by an exponential function of the form(b) The warming might be modeled by a linear
A major scientific periodical published an article in 1990 dealing with the problem of global warming. The article was accompanied by a graph that illustrated two possible scenarios.(a) The warming might be modeled by an exponential function of the form(b) The warming might be modeled by a linear
Determine whether each function is one-to-one. If it is, find the inverse. f(x) = x³ - 4
Use the properties of logarithms to rewrite each expression as a single logarithm. Assume that all variables represent positive real numbers, and that bases are positive numbers not equal to 1. 1 4 - logor + 2log S 2 3 logħt
Solve each equation. log 4 = 1
Use the properties of logarithms to write each expression as a single logarithm. Assume that all variables are defined in such a way that the variable expressions are positive, and bases are positive numbers not equal to 1. 3 loga 5 - 4 loga 3
Simplify. 2√32-5√98
Solve each equation. Give exact solutions. log2 (2x - 1) = 5
Evaluate each logarithm to four decimal places.ln 0.0556
The concentration of a drug injected into the bloodstream decreases with time. The intervals of time T when the drug should be administered are given bywhere k is a constant determined by the drug in use, C2 is the concentration at which the drug is harmful, and C1 is the concentration below which
Determine whether each function is one-to-one. If it is, find the inverse. f(x) = x³ + 5
Evaluate each logarithm to four decimal places.log6 45
Solve each equation or inequality. x45x² + 4 = 0
Determine whether each statement is true or false. log6 60 log6 10 = 1
Suppose that water from a wetland area is sampled and found to have the given hydronium ion concentration. Is the wetland a rich fen, a poor fen, or a bog?2.5 × 10-2
Solve each equation.16x = 64
The estimated number of monthly active Snapchat users (in millions) from 2013 to 2016 can be modeled by the exponential functionwhere x = 0 represents 2013, x = 1 represents 2014, and so on. Use this model to approximate the number of monthly active Snapchat users in each year, to the nearest
Use a calculator to approximate each logarithm to four decimal places.log5 18
Each of the following functions is one-to-one. Graph the function as a solid line (or curve), and then graph its inverse on the same set of axes as a dashed line (or curve). Complete any tables to help graph the functions. f(x) = x³ + 3 f(x) X -2 -1 0 1
Solve each equation.log8 32 = x
How long, to the nearest hundredth of a year, would it take an initial principal P to double if it were invested at 2.5% compounded continuously?
Use the change-of-base rule (with either common or natural logarithms) to approximate each logarithm to four decimal places.log3 12
Solve each equation. Approximate solutions to three decimal places.3x = 9.42
Solve each equation.log81 27 = x
The number of paid music subscriptions (in millions) in the United States from 2010 to 2016 can be modeled by the exponential functionwhere x = 0 represents 2010, x = 1 represents 2011, and so on. Use this model to approximate the number of paid music subscriptions in each year, to the nearest
Solve each equation. log4 V64 = x
Revenues of software publishers in the United States for the years 2004–2016 can be modeled by the functionwhere x = 4 represents 2004, x = 5 represents 2005, and so on, and S(x) is in billions of dollars. Approximate, to the nearest unit, revenue for 2016. S(x) = 91.412e0.05195x
Solve each equation. Give exact solutions. log3 (x + 2) log3x = log3 2
Based on selected figures obtained during the years 1970–2015, the total number of bachelor’s degrees earned in the United States can be modeled by the functionwhere x = 0 corresponds to 1970, x = 5 corresponds to 1975, and so on. Approximate, to the nearest unit, the number of bachelor’s
Solve each equation. log3 (2x + 7) = 4
Solve each equation. log4 (2x + 4) = 3
Solve each equation. Give exact solutions. log (2x + 3) = 1 + log x
How much money must be deposited today to amount to $1000 in 10 yr at 5% compounded continuously?
Use the change-of-base rule (with either common or natural logarithms) to approximate each logarithm to four decimal places.log1/2 5
Use the change-of-base rule (with either common or natural logarithms) to approximate each logarithm to four decimal places.log1/3 7
Determine whether each statement is true or false. log10 7 log10 14 || 1 2
Use the change-of-base rule (with either common or natural logarithms) to approximate each logarithm to four decimal places.log5 3
Solve each equation. log√₂ (√2)² = X
Solve each equation. Approximate solutions to three decimal places.e0.06x = 3
Determine whether each statement is true or false. log10 10 log10 100 || 1 10
Find the amount of money in an account after 8 yr if $4500 is deposited at 6% annual interest compounded as follows.(a) Annually (b) Semiannually (c) Quarterly(d) Daily (Use n = 365.) (e) Continuously
Use the change-of-base rule (with either common or natural logarithms) to approximate each logarithm to four decimal places.log7 4
Use the change-of-base rule (with either common or natural logarithms) to approximate each logarithm to four decimal places.log21 0.7496
Solve each equation. Give exact solutions. log3 (9x + 8) = 2
How much money must be deposited today to amount to $1850 in 40 yr at 6.5% compounded continuously?
Use the change-of-base rule (with either common or natural logarithms) to approximate each logarithm to four decimal places.log19 0.8325
Solve each equation. Give exact solutions. logs (x + 6)³ = 2
In Problems 13–22, for the given functions f and g, find: f(x) 3 x + 1' g(x) = √x
In Problems 13–22, for the given functions f and g, find: f(x) = x³/²; g(x) = 2 x + 1
In Problems 23–38, for the given functions f and g, find: State the domain of each composite function. (a) fog (b) gof (c) fof (d) gᵒg
Which exponential function is increasing? (a) f(x) = 0.5* (c) f(x) = (²)* 3 5 - ()* (d) f(x) = 0.9⁰ (b) f(x)
In Problems 23–38, for the given functions f and g, find: State the domain of each composite function. f(x) = 2x + 3; g(x) = 4x (a) fog (b) gof (c) fof (d) gᵒg
In Problems 13–28, use properties of logarithms to find the exact value of each expression. Do not use a calculator. log69 + log6 4
In Problems 13–28, use properties of logarithms to find the exact value of each expression. Do not use a calculator. log5 35 - log5 7
In Problems 13–28, use properties of logarithms to find the exact value of each expression. Do not use a calculator. log8 16 - logg 2
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