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All Textbook Solutions for College Algebra
Repeat Example 1 for the set ,14,63,122,7.5,1,8,22.Plot the real numbers on the real number line. a.52b.1.6 c.34d.0.7Place the appropriate inequality symbol or between the pair of real numbers. a.1,5b.32,7c.23,34Describe the subset of real numbers that the inequality represents. a.x3b.0x4Give a verbal description of the interval 2,5.6ECPEvaluate each expression. a. 1 b. 34 c. 23 d. 0.7Evaluate x+3x+3 for (a) x3 and (b) x3 .Place the appropriate symbol ,,or= between the pair of real numbers. a. 34 b. 44 c. 33a. Find the distance between 35 and 23 . b. Find the distance between 35 and 23 . c. Find the distance between 35 and 23 .Identify the terms and coefficients of 2x+4 .Evaluate 4x5 when x=0 .Identify the rule of algebra illustrated by the statement. a. x+9=9+x b. 5x32=5x32 c. 2+5x2y2=2y2+5x2y2a. Multiply fractions: 35x6 b. Add fractions: .1E2E3E4E5E6EClassifying Real Numbers In Exercises 7-10, determine which numbers in the set are (a) natural numbers, (b) whole numbers, (c) integers, (d) rational numbers, and (e) irrational numbers. 9,72,5,23,2,0,1,4,2,11 .8E9E10E11EPlotting Points on the Real Number Line In Exercises 11 and 12, plot the real numbers on the real number line. a8.5b43c4.75d83Plotting and Ordering Real Numbers In Exercises 13-16, plot the two real numbers on the real number line. Then place the appropriate inequality symbol or between them. 4,814E15E16E17EInterpreting an Inequality or an Interval In Exercises 17-24, (a) give a verbal description of the subset of real numbers represented by the inequality or the interval, (b) sketch the subset on the real number line, and (c) state whether the subset is bounded or unbounded. x0Interpreting an Inequality or an Interval In Exercises 17-24, (a) give a verbal description of the subset of real numbers represented by the inequality or the interval, (b) sketch the subset on the real number line, and (c) state whether the subset is bounded or unbounded. 2x2Interpreting an Inequality or an Interval In Exercises 17-24, (a) give a verbal description of the subset of real numbers represented by the inequality or the interval, (b) sketch the subset on the real number line, and (c) state whether the subset is bounded or unbounded. 0x6Interpreting an Inequality or an Interval In Exercises 17-24, (a) give a verbal description of the subset of real numbers represented by the inequality or the interval, (b) sketch the subset on the real number line, and (c) state whether the subset is bounded or unbounded. [4,]Interpreting an Inequality or an Interval In Exercises 17-24, (a) give a verbal description of the subset of real numbers represented by the inequality or the interval, (b) sketch the subset on the real number line, and (c) state whether the subset is bounded or unbounded. (,2)Interpreting an Inequality or an Interval In Exercises 17-24, (a) give a verbal description of the subset of real numbers represented by the inequality or the interval, (b) sketch the subset on the real number line, and (c) state whether the subset is bounded or unbounded. [5,2).Interpreting an Inequality or an Interval In Exercises 17-24, (a) give a verbal description of the subset of real numbers represented by the inequality or the interval, (b) sketch the subset on the real number line, and (c) state whether the subset is bounded or unbounded. (1,2]Using Inequality and Interval Notation In Exercises 25-28, use inequality notation and interval notation to describe the set. y is nonnegative.26EUsing Inequality and Interval Notation In Exercises 25-28, use inequality notation and interval notation to describe the set. t is at least 10 and at most 22 .Using Inequality and Interval Notation In Exercises 25-28, use inequality notation and interval notation to describe the set. k is less than 5 but no less than 3 .29EEvaluating an Absolute Value Expression In Exercises 29-38, evaluate the expression. 031E32EEvaluating an Absolute Value Expression In Exercises 29-38, evaluate the expression. 1234EEvaluating an Absolute Value Expression In Exercises 29-38, evaluate the expression. 55Evaluating an Absolute Value Expression In Exercises 29-38, evaluate the expression. 4437EEvaluating an Absolute Value Expression In Exercises 29-38, evaluate the expression. x1x1,x139E40E41E42EFinding a Distance In Exercises 43-46, find the distance between a and b. a=126,b=75Finding a Distance In Exercises 43-46, find the distance between a and b. a=20,b=3045E46E47E48EIn Exercises 49-52, use the bar graph, which shows the receipts of the federal government (in billions of dollars) for selected years from 2008 through 2014. In each exercise, you are given the expenditures of the federal government. Find the magnitude of the surplus or deficit for the year. YearReceipts,RExpenditures,ERE2008$2982.5billionIn Exercises 49-52, use the bar graph, which shows the receipts of the federal government (in billions of dollars) for selected years from 2008 through 2014. In each exercise, you are given the expenditures of the federal government. Find the magnitude of the surplus or deficit for the year. YearReceipts,RExpenditures,ERE20103457.1billionIn Exercises 49-52, use the bar graph, which shows the receipts of the federal government (in billions of dollars) for selected years from 2008 through 2014. In each exercise, you are given the expenditures of the federal government. Find the magnitude of the surplus or deficit for the year. YearReceipts,RExpenditures,ERE2012$3537.0billo 20123537.0billionIn Exercises 49-52, use the bar graph, which shows the receipts of the federal government (in billions of dollars) for selected years from 2008 through 2014. In each exercise, you are given the expenditures of the federal government. Find the magnitude of the surplus or deficit for the year. YearReceipts,RExpenditures,ERE20143506.1billoIdentifying Terms and Coefficients In Exercises 53-58, identify the terms. Then identify the coefficients of the variable terms of the expression. 7x+4Identifying Terms and Coefficients In Exercises 53-58, identify the terms. Then identify the coefficients of the variable terms of the expression. 2x355E56E57EIdentifying Terms and Coefficients In Exercises 53-58, identify the terms. Then identify the coefficients of the variable terms of the expression. 22x2359E60E61E62E63EEvaluating an Algebraic Expression In Exercises 59-64, evaluate the expression for each value of x. (If not possible, state the reason.) x2x+2 (a) x=2 (b) x=265E66E67EIdentifying Rules of Algebra In Exercises 65-68, identify the rule(s) of algebra illustrated by the statement. 17712=17712=112=1269EOperations with Fractions In Exercises 69-72, perform the operation. (Write fractional answers in simplest form.) 3x4+x571EOperations with Fractions In Exercises 69-72, perform the operation. (Write fractional answers in simplest form.) 2x36773E74ETrue or False? In Exercises 73 -75, determine whether the statement is true or false. Justify your answer. If a0 and b0 , then ab0 .HOW DO YOU SEE IT? Match each description with its graph. Which types of real numbers shown in Figure P.1 on page 2 may be included in a range of prices? a range of lengths? Explain. (a) The price of an item is within 0.03 of 1.90 . (b) The distance between the prongs of an electric plug may not differ from 1.9 centimeters by more than 0.03 centimeter.77EEvaluate each expression. a. 34 b. 34 c. 323 d. 3538Evaluate each algebraic expression when x=4 . a. x2 b. 14x4Use the properties of exponents to simplify each expression. a. 2x2y3x4y b. 4a2b30 c. 5z3z2 d. 3x4x2y224ECPWrite 45,850 in scientific notation.6ECPEvaluate 24,000,000,0000.00000012300,000 .8ECP9ECPSimplify each radical expression. a. 32 b. 2503 c. 24a5 d. 135x3311ECPRationalize the denominator of each expression. a. 532 b. 1253Rationalize the denominator: 862 .Rationalize the numerator: 223Write (a) 273 , (b) x3y5z, and (c) 3x3x2 in exponential form.Write each expression in radical form. a. x271/2 b. 3b13c23 c. a0.75 d. x22517ECPFill in the blanks. In the exponential form an, n is the and a is the .2E3E4EFill in the blanks. Radical expressions can be combined (added or subtracted) when they are .Fill in the blanks. The expressions a+bm and abm are of each other.7E8E9E10EEvaluating Exponential Expressions In Exercises 9-14, evaluate each expression. (a) 23322 (b) 35353212E13E14EEvaluating an Algebraic Expression In Exercises 15-20, evaluate the expression for the given value of x. 3x3,x=2Evaluating an Algebraic Expression In Exercises 15-20, evaluate the expression for the given value of x. 7x2,x=4Evaluating an Algebraic Expression In Exercises 15-20, evaluate the expression for the given value of x. 6x0,x=10Evaluating an Algebraic Expression In Exercises 15-20, evaluate the expression for the given value of x. 2x3,x=3Evaluating an Algebraic Expression In Exercises 15-20, evaluate the expression for the given value of x. 3x4,x=2Evaluating an Algebraic Expression In Exercises 15-20, evaluate the expression for the given value ofx. 12x3,x=13Using Properties of Exponents In Exercises 21-26, simplify each expression. (a) 5z3 (b) 5x4x2Using Properties of Exponents In Exercises 21-26, simplify each expression. (a) 2x2 (b) 4x30Using Properties of Exponents In Exercises 21-26, simplify each expression. (a) 6y22y02 (b) z33z4Using Properties of Exponents In Exercises 21-26, simplify each expression. (a) 7x2x3 (b) 12x+y39x+yUsing Properties of Exponents In Exercises 21-26, simplify each expression. (a) 4y33y4 (b) b2a2ba2Using Properties of Exponents In Exercises 21-26, simplify each expression. (a) x2y211 (b) 5x2z635x2z63Rewriting with Positive Exponents In Exercises 27-30, rewrite each expression with positive exponents. Simplify, if possible. (a) x+50 (b) 2x22Rewriting with Positive Exponents In Exercises 27-30, rewrite each expression with positive exponents. Simplify, if possible. (a) 4y28y4 (b) z+23z+21Rewriting with Positive Exponents In Exercises 27-30, rewrite each expression with positive exponents. Simplify, if possible. (a) x3y453 (b) a2b2ba3Rewriting with Positive Exponents In Exercises 27-30, rewrite each expression with positive exponents. Simplify, if possible. (a) 3n32n33n32 (b) x2xnx3xn31E32E33E34E35E36E37E38E39E40E41E42E43E44E45E46E47E48E49E50ERationalizing a Denominator In Exercises 51-54, rationalize the denominator of the expression. Then simplify your answer. 13Rationalizing a Denominator In Exercises 51-54, rationalize the denominator of the expression. Then simplify your answer. 823Rationalizing a Denominator In Exercises 51-54, rationalize the denominator of the expression. Then simplify your answer. 514254E55E56E57E58E59E60E61ESimplifying Expressions In Exercises 61-68, simplify each expression. (a) 10032 (b) 941263E64E65E66E67E68EMathematical Modeling A funnel is filled with water to a height of h centimeters. The formula t=0.03[125212h52],0h12 represents the amount of time t (in seconds) that it will take for the funnel to empty. Use the table feature of a graphing utility to find the times required for the funnel to empty for water heights of h=0,h=1,h=2,...,h=12centimeters.HOW DO YOU SEE IT? Package A is a cube with a volume of 500 cubic inches. Package B is a cube with a volume of 250 cubic inches. Is the length x of a side of package A greater than, less than, or equal to twice the length of a side of package B? Explain.71E72E73E74EWrite the polynomial 67x3+2x in standard form. Then identify the degree and leading coefficient of the polynomial.Find the difference2x3x+3x22x3 and write the resulting polynomial in standard form.3ECPMultiply x2+2x+3 by x22x+3 using a vertical arrangement.5ECP6ECPFind 4x13.Find the product of x2+3y and x23y.9ECP1E2E3E4E5E6EWriting Polynomials in Standard Form In Exercises 5-10, (a) write the polynomial in standard form, (b) identify the degree and leading coefficient of the polynomial, and (c) state whether the polynomial is a monomial, a binomial, or a trinomial. 14x12x58E9E10E11E12E13E14E15E16EAdding or Subtracting Polynomials In Exercises 17-24, add or subtract and write the result in standard form. 6x+58x+1518E19EAdding or Subtracting Polynomials In Exercises 17-24, add or subtract and write the result in standard form. 4y23+7y2+921E22E23E24E25E26EMultiplying Polynomials In Exercises 25-38, multiply the polynomials. 5z(3z1)28E29E30EMultiplying Polynomials In Exercises 25-38, multiply the polynomials. 2x(0.1x+17)32E33E34E35E36E37E38E39E40E41E42EFinding Special Products In Exercises 39-62, find the special product. 2x+3244E45E46E47E48E49E50E51E52E53E54E55E56E57E58E59E60E61E62E63E64E65E66E67E68E69E70E71E72EGenetics In deer, the gene N is for normal coloring and the gene a is for albino. Any gene combination with an N results in normal coloring. The Punnett square shows the possible gene combinations of an offspring and the resulting colors when both parents have the gene combination Na. (a) What percent of the possible gene combinations result in albino coloring? (b) Each parent’s gene combination is represented by the polynomial 0.5N+0.5a. The product 0.5N+0.5a2 represents the possible gene combinations of an offspring. Findthis product. (c) The coefficient of each term of the polynomial you wrote in part (b) is the probability (indecimal form) of the offspring having that gene combination. Use this polynomial toconfirm your answer in part (a). Explain.Construction Management A square-shaped foundation for a building with 100foot sides is reduced byx feet on one side and extended by x feet on an adjacent side. (a) The area of the new foundation is represented by 100x100+x. Find this product. (b) Does the area of the foundation increase, decrease, or stay the same? Explain. (c) Use the polynomial in part (a) to find the area of the new foundation when x= 21.Geometry In Exercises 75-78, find the area of the shaded region in terms of x. Write your result as a polynomial in standard form.Geometry In Exercises 75-78, find the area of the shaded region in terms of x. Write your result as a polynomial in standard form.Geometry In Exercises 75-78, find the area of the shaded region in terms of x. Write your result as a polynomial in standard form.Geometry In Exercises 75-78, find the area of the shaded region in terms of x. Write your result as a polynomial in standard form.Volume of a Box A take-out fast-food restaurant is constructing an open box by cutting squares from the corners of the piece of cardboard shown in the figure. The edge of each cut out square is x centimeters. (a) Find the volume of the box in terms of x. (b) Find the volume when x=1,x=2, and x=3.Volume of a Box An overnight shipping company designs a closed box by cutting along the solid lines and folding along the broken lines on the rectangular piece of corrugated cardboard shown in the figure. (a) Find the volume of the shipping box in terms of x. (b) Find the volume when x=3,x=5, and x=7.81EStopping distance, The stopping distance of an automobile is the distance travelled during the driver’s reaction time plus the distance travelled after the driver applies the brakes. In an experiment, researchers measured these distances (in feet) when the automobile was traveling at a speed of x. miles per hour on dry, level pavement, as shown in the bar graph. The distance travelled during the reaction time R was R=1.1x and the braking distance B was B=0.0475x20.001x+0.23. (a) Determine the polynomial that represents the total stopping distance T. (b) Use the result of part (a) to estimate the total stopping distance when x=30,x=40, andx=55 miles per hour. (c) Use the bar graph to make a statement about the total stopping distance required forincreasing speeds.83E84E85E86E87EDegree of a Sum Find the degree of the sum of two polynomials of degrees m and n, where mn.89E90E91E92EFactor each expression. a. 5x315x2 b. 3+6x12x3 c. x+1x2x+122ECP3ECP4ECP5ECPFactor each expression. a. x3+216 b. 5y3+1357ECP8ECP9ECP10ECP1E2E3E4EFactoring Out a Common Factor In Exercises 5-8, factor out the common factor. 2x36xFactoring Out a Common Factor In Exercises 5-8, factor out the common factor. 3z36z2+9z7E