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All Textbook Solutions for Precalculus

92PE For Exercises 91-98, simplify each expression. (See Example 7) (4u8v)3(7u2v)+2v For Exercises 91-98, simplify each expression. (See Example 7) (10xz)2(8x4z)3x For Exercises 91-98, simplify each expression. (See Example 7) 124[(82v)+5(3w4v)]w For Exercises 91-98, simplify each expression. (See Example 7) 62[(9z6y)+8(yz)]11 For Exercises 91-98, simplify each expression. (See Example 7) 2y21323(6y29)10+9 For Exercises 91-98, simplify each expression. (See Example 7) 65t234(128t2)+5+11t2 Jake is 1yr younger than Charlotte. a. Write a model for Jake's age J in terms of Charlotte's age C. b. Write a model for Charlotte's age C in term s. of Jake's age J. (See Example 8)For a recent NFL season, Aaron Rodgers had 9 more touchdown passes than Joe Flacco. a. Write a model for the number of touchdown passes R thrown by Rodgers in terms of the number thrown by Flacco F. b. Write a model for the number of touchdown passes F thrown by Flacco in terms of the number thrown by Rodgers R.101PE When Ms. Celano has excellent service at a restaurant, the amount she leaves for a tip tis at least 20% of the cost of the meal c. Write a model representing the amount of the tip.Suppose that an object is dropped from a height h. Its velocity v at impact with the ground is give n by the square root of twice the product of the acceleration due to gravity g and the height h. Write a model to represent the velocity of the object at impact.The height of a sunflower plant can be determined by the time t in weeks after the seed has germinated. Write a model to represent the height h if the height is given by the product of 8 and the square root of t.A power company charges one household S.0. 12 per kilo watt-hour (kWh) and $14.89 in monthly taxes. a. Write a formula for the monthly charge C for this household if it uses K kilowatt-hours b. Compute the monthly charge if the house hold uses 1200 kWh.A utility company charges a base rate for water usage of 19.50 per month, plus $4.58 for every additional 1000 gal of water used over a 2000-gal base. a. Write a formula for the monthly charge C for a household that uses n thousand gallons over the 2000-gal base. b. Compute the cost for a family that uses a total of 6000 gal of water for a given month.The cost C(in)$ to rent an apartment is $640 per month, plus a $500 nonrefundable security deposit, plus a $200 nonrefundable deposit for each dog or cat. a. Write a formula for the total cost to rent an apartment form m months with n cats/ dogs. b. Determine the cost to rent the apartment tor 12 months, with 2 cats and 1 dog.For a certain the cost Cin$ for taking class in first semester is $105 per credit-hour, $35 each lab, plus a one-time admission fee of $40 . a. Write a formula for the total cost to take n credit-hours and L labs the first semester. b. Determine the cost for the first semester if a student takes 12 credit-hours with 2 labs.109PE For Exercise 109-114, evaluate each expression for the given values of the variables. b24acfora=2,b=6,c=4 111PE 112PE For Exercise 109-114, evaluate each expression for the given values of the variables. 13r2hfor227,r=7,h=6 114PE 115PE Under selected conditions, a sedan gets 22 mpg in city driving and 32 mpg for highway driving. The model G=122c+132h represents the amount of gasoline used (in gal) for c miles driven in the city and h miles driven on the highway. Determine the amount of gas required to drive 220 mi in the city and 512 mi on the highway.When is a parenthesis used when writing interval notation?118PE Explain the difference between the commutative property of addition and the associative property of addition.Explain why 0 has no multiplicative inverse.Ifn0,thennn=.Ifn0,thennn=.Ifn0,thenn+n=.Ifn0,thenn+n=.Ifn0,thenn=.Ifn0,thenn=.For Exercises 127- 130, determine the sign of the expression. Assume that, a, b and c are real numbers and a0,b0,andc0. ab2c3 For Exercises 127- 130, determine the sign of the expression. Assume that, a, b and c are real numbers and a0,b0,andc0. a2cb4 For Exercises 127- 130, determine the sign of the expression. Assume that, a, b and c are real numbers and a0,b0,andc0. b(a+c)3a2 For Exercises 127- 130, determine the sign of the expression. Assume that, a, b and c are real numbers and a0,b0,andc0. (a+b)2(b+c)4b 131PE 132PE 133PE 134PE 135PE 136PE For Exercise 135-138, use a calculator to approximate the expression to 2 decimal places. 3+527 For Exercise 135-138, use a calculator to approximate the expression to 2 decimal places. 6354 Simplify. a.4z0b.-40c.23d.1n5e.3a4b9 Simplify. Write the answer with positive exponents only. a.3w35wt52b.26c5d213cd83 3SP A satellite travels 1.72104 mph. How does it travel in 24 hr 2.4101hr ?5SP Simplify the expressions if possible. a.361/2b.11251/3c.91/2d.14/3e.1252/3 Simplify each expression. Assume that all variables represent positive real numbers. a.d74b.45c.54x13y83 Multiply or divide as indicated. Assume that c,d,andy represent positive real numbers. a.15y21yb.625c2d1035c5d3 Add or subtract as indicated. Assume that all variables represent positive real numbers. a.45w3+95w3115w3b.75cd4+6d27cd2 For a nonzero real number b, the value of b0=.For a nonzero real number b, the value of b=1bn.From the properties of exponents, bmbn=b.4PE From the properties of exponents, bmn=b.Give the expression an , the value a is called the and n is called the .The expression am/n can be written in radical notation as provided that an is a real number.The expression a1/n can be written in radical notation as provided that an is a real number.For Exercises 9-14, simplify each expression. (See Example 1) a.80b.80c.8x0d.8x0 For Exercises 9-14, simplify each expression. (See Example 1) a.70b.70c.7y0d.7y0 For Exercises 9-14, simplify each expression. (See Example 1) a.82b.8x2c.8x2d.82 12PE 13PE 14PE For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2) x7x6x2 16PE 17PE For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2) 7m3n83m5n 19PE 20PE For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2) 18k2p927k5p2 22PE 23PE For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2) 4p7q52p2q2 For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2) p27 26PE For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2) 7ab2 28PE For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2) 4x2y32 30PE 31PE 32PE For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2) 4x3z512y23 34PE 35PE For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2) 15z25z4w63 For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2) 123133+163 38PE 39PE For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2) 13a2b433a5b41 For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2) 4vw3x222v2w3x24v3w2x45 For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2) 4v2w3x2321v5w3x217v4w1x44 43PE For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2) 2y7z42y7z13 45PE 46PE 47PE For Exercises 47-52, write the numbers in scientific notation. (See Example 3) a.2710b.0.00271c.2.71 For Exercises 47-52, write the numbers in scientific notation. (See Example 3) The speed of light is approximately 29,980,000,000 cm/sec.For Exercises 47-52, write the numbers in scientific notation. (See Example 3) The mean distance between the Earth and the sun is approximately 149,000,000 km.For Exercises 47-52, write the numbers in scientific notation. (See Example 3) The size of an HIV particle is approximately 0.00001 cm.52PE For Exercises 53-58, Write the number in standard decimal notation. (see Example 3) a.2.61106b.2.61106c.2.61100 54PE For Exercises 53-58, Write the number in standard decimal notation. (see Example 3) A drop of water has approximately 1.671021 molecules of H2O .For Exercises 53-58, Write the number in standard decimal notation. (see Example 3) A computer with a 3-terabyte hard drive can store approximately 3.01012 bytes.57PE For Exercises 53-58, Write the number in standard decimal notation. (see Example 3) The blue light used to read a laser disc has a wavelength of 4.7107m.For Exercises 59-66, perform the indicates operation. Write the answer in scientific notation. (See Example 4) 8.41062.1102 For Exercises 59-66, perform the indicates operation. Write the answer in scientific notation. (See Example 4) 6.810113.4103 For Exercises 59-66, perform the indicates operation. Write the answer in scientific notation. (See Example 4) 6.210113104 62PE For Exercises 59-66, perform the indicates operation. Write the answer in scientific notation. (See Example 4) 3.610145105 For Exercises 59-66, perform the indicates operation. Write the answer in scientific notation. (See Example 4) 3.681084102 65PE 66PE Jonas has a personal music player with 80 gigabytes of memory (80 gigabytes is approximately 81010 bytes). If each song requires an average of 4 megabytes of memory (approximately 4106 bytes), how many songs can Jonas store on the device?68PE 69PE 70PE For Exercises 71-78, simplify the expression. (See Example 5) 814 72PE For Exercises 71-78, simplify the expression. (See Example 5) 449 74PE For Exercises 71-78, simplify the expression. (See Example 5) 814 For Exercises 71-78, simplify the expression. (See Example 5) 6254 77PE For Exercises 71-78, simplify the expression. (See Example 5) 641253 For Exercises 79-88, Simplify each expression. (See Example 6) a.251/2b.251/2c.251/2 80PE 81PE 82PE For Exercises 79-88, Simplify each expression. (See Example 6) a.1211691/2b.1211691/2 84PE For Exercises 79-88, Simplify each expression. (See Example 6) a.163/4b.163/4c.163/4d.163/4e.163/4f.163/4 86PE For Exercises 79-88, Simplify each expression. (See Example 6) a.642/3b.642/3c.642/3d.642/3e.642/3f.642/3 88PE 89PE a. For what value of c will the statement be true? c+844=c+8 b. For what value of c will the statement be true? c+844=c+8 For Exercises 91-100, simplify each expression. Assume that all variable expressions represent positive real numbers. (see Example 7) a.c7b.c73c.c74d.c79 For Exercises 91-100, simplify each expression. Assume that all variable expressions represent positive real numbers. (see Example 7) a.d11b.d113c.d114d.d1112 For Exercises 91-100, simplify each expression. Assume that all variable expressions represent positive real numbers. (see Example 7) a.24b.243 For Exercises 91-100, simplify each expression. Assume that all variable expressions represent positive real numbers. (see Example 7) a.54b.543 For Exercises 91-100, simplify each expression. Assume that all variable expressions represent positive real numbers. (see Example 7) 250x2y6z113 For Exercises 91-100, simplify each expression. Assume that all variable expressions represent positive real numbers. (see Example 7) 40ab13c173 97PE For Exercises 91-100, simplify each expression. Assume that all variable expressions represent positive real numbers. (see Example 7) 243m19n104 99PE 100PE 101PE 102PE For Exercises 101-112, multiply or divide as indicated. Assume that all variable expressions repressions represent positive real numbers. (See Example 8) xy23x2y3 104PE 105PE For Exercises 101-112, multiply or divide as indicated. Assume that all variable expressions repressions represent positive real numbers. (See Example 8) 7t562t56 107PE 108PE For Exercises 101-112, multiply or divide as indicated. Assume that all variable expressions repressions represent positive real numbers. (See Example 8) 4w3z583 110PE 111PE 112PE For Exercises 113-120, add or subtract as indicated. Assume that all variables represent positive real numbers. (See Example 9) 32y2392y23+2y23 For Exercises 113-120, add or subtract as indicated. Assume that all variables represent positive real numbers. (See Example 9) 83z343z34+23z34 115PE For Exercises 113-120, add or subtract as indicated. Assume that all variables represent positive real numbers. (See Example 9) 257523271212 For Exercises 113-120, add or subtract as indicated. Assume that all variables represent positive real numbers. (See Example 9) 3x16xy43+xy54xy35250x4y43 For Exercises 113-120, add or subtract as indicated. Assume that all variables represent positive real numbers. (See Example 9) 832a5b645b2a5b24ab162ab24 119PE 120PE For Exercises 121-122, use the Pythagorean theorem to determine the length of the missing side. Write the answer as a simplified radical.For Exercises 121-122, use the Pythagorean theorem to determine the length of the missing side. Write the answer as a simplified radical.123PE 124PE The depreciation rate for a car is given by r=1SC1/, where S is the value of the car after n years, and C is the initial cost. Determine the depreciation rate for a car that originally cost 22,990 and was valued at 11,500 after 4 yr. Round to the nearest tenth of a percent.126PE 127PE Explain why scientific notation is used.129PE Explain why the given expressions cannot be simplified further. a.2x+3yb.2x+3yc.2x3+3x 131PE For Exercises 131-132, refer to the formula F=Gm1m2d2. This gives the gravitational force F (in Newtons, N) between two masses m1andm2 (each measured in kg) that are a distance of d meters apart. In the formula, G=6.67261011N-m2/kg2. Determine the gravitational force between the Earth mass=5.981024kg and an 80-kg human standing at sea level. The mean radius of the Earth is approximately 6.371106m.For Exercises 133-136, without the assistance of a calculator, fill in the blank with the appropriate symbol ,,or=. a.515517b.515517 134PE For Exercises 133-136, without the assistance of a calculator, fill in the blank with the appropriate symbol ,,or=. a.186187b.186187 136PE 137PE For Exercises 137-142, write each expression as a single radical for positive values of the variable. a2b4ab23 For Exercises 137-142, write each expression as a single radical for positive values of the variable. mm236 140PE 141PE 142PE For Exercises 143-144, evaluate the expression without the use of a calculator. 8.010122.0104 For Exercises 143-144, evaluate the expression without the use of a calculator. 1.4410169.01010 145PE For Exercises 145-146, simplify the expression. 11+12534+81+10003+36+25 Add or subtract as indicated, and simplify. a.7t53t22t+2t55t4b.0.08x3y0.02x2y0.1xy0.05x3y0.07x2y+0.02xy 2SP a. Multiply. 5w3+2y5w32y b. Square the binomial. 6p+52 Multiply and simplify. Assume that all variable expressions represent positive real numbers. a.4t+103t8b.37537+5c.4y32 Factor by grouping. 7cdc2+14d2c 6SP Factor. 30m3200m2n70mn2 Factor. a.64y2+16y+1b.9m430m2n+25n2 Factor completely. a.t2121b.625z5z Factor Completely. a.u3+27b.64v325z6 Factor completely. x5x364x2+64 Factor completely. 36m26mn9n2 13SP Factor completely and write the answer with no negative exponents. a.11a53a4+2a3b.x4x+33/4+4x+31/4 The term of a polynomial is the term of highest degree.The leading of a polynomial is the numerical factor of the leading term.A is a polynomial that has two terms, and a is a polynomial with three terms.The conjugate of 3x is .The binomial a3+b3 is called a sum of and factors as .The binomial a3b3 is called a of cubes and factors as .The trinomial a2+2ab+b2 is a square trinomial its factored form is .The binomial a2b2 is called a difference of and factors as .For Exercises 9-10, determine if the expression is a polynomial. a.4a2+7b3b.34x2yc.6x+7x+5d.p2+2p5 For Exercises 9-10, determine if the expression is a polynomial. a.3x29x2+2x3b.2ab4c.3y+2d.7x34x2+2x5 For Exercises 11-14, add or subtract as indicated and simplify. (See Example 1) 8p74p4+2p5+2p7+6p4+p2 12PE For Exercises 11-14, add or subtract as indicated and simplify. (See Example 1) 0.05c3b+0.02c2b20.09cb30.03c3b+0.08c2b20.1cb3 For Exercises 11-14, add or subtract as indicated and simplify. (See Example 1) 0.004mn50.001mn4+0.05mn30.003mn5+0.007mn40.07mn3 For Exercises 15-22, multiply and simplify. (See Example 2) 7m22m43m+4 16PE For Exercises 15-22, multiply and simplify. (See Example 2) 2x5x+4 18PE 19PE For Exercises 15-22, multiply and simplify. (See Example 2) 2z3+5u27z3u2 21PE For Exercises 15-22, multiply and simplify. (See Example 2) 10v515v23v+1 Write the expanded from for a+b2.Write the expanded from for a+bab.For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) 4x54x+5 26PE For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) 3w27z3w2+7z For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) 9v3+2u9v32u 29PE For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) 16n45p416n+45p4 For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) 5m32 For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) 7v22 For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) 4t2+3p32 For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) 2a2+11b32 35PE For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) p23 37PE 38PE Suppose that x represents the smaller of two consecutive integers. a. Write a polynomial that represents the larger integer. b. Write a polynomial that represents the sum of the two integers. Then simplify. c. Write a polynomial that represents the product of the two integers. Then simplify. d. Write a polynomial that represents the sum of the squares of the two integers. Then simplify.Suppose that x represents the larger of two consecutive odd integers. a. Write a polynomial that represents the smaller integer. b. Write a polynomial that represents the sum of the two integers. Then simplify. c. Write a polynomial that represents the product of the two integers. Then simplify. d. Write a polynomial that represents the difference of the squares of the two integers. Then simplify.For Exercises 41-48, simplify each expression. y+722y32 For Exercises 41-48, simplify each expression. x426x+12 For Exercises 41-48, simplify each expression. xn+3xn7 For Exercises 41-48, simplify each expression. yn+4yn5 45PE For Exercises 41-48, simplify each expression. wnym2 For Exercises 41-48, simplify each expression. 6x+56x56x+52 For Exercises 41-48, simplify each expression. 2y72y+72y72 For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive real numbers. (See Example 4) 5222+634 50PE For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive real numbers. (See Example 4) 2y34y+5 52PE 53PE For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive real numbers. (See Example 4) 521152+11 For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive real numbers. (See Example 4) 4xy2yx4xy+2yx 56PE 57PE For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive real numbers. (See Example 4) 2v172 For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive real numbers. (See Example 4) x+15x+1+5 60PE 61PE For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive real numbers. (See Example 4) y+242 For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive real numbers. (See Example 4) 5+2x52x 64PE For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive real numbers. (See Example 4) x+yxy2 66PE For Exercises 67-72, factor out the greatest common factor. 15c530c4+5c3 68PE For Exercises 67-72, factor out the greatest common factor. 21a2b514a3b4+35a4b For Exercises 67-72, factor out the greatest common factor. 36p4q7+18p3q527p2q6 71PE 72PE For Exercises 73-76, factor out the indicated common factor. a.Factorout3.6x2+12x+9b.Factorout3.6x2+12x+9 For Exercises 73-76, factor out the indicated common factor. a.Factorout5.15y210y+25b.Factorout5.15y210y+25 75PE For Exercises 73-76, factor out the indicated common factor. Factorout7a3b.14a4b3+21a3b27a3b For Exercises 77-82, factor by grouping. (See Example 5) 8ax+18a+20x+45 For Exercises 77-82, factor by grouping. (See Example 5) 6ty+9y+14t+21 For Exercises 77-82, factor by grouping. (See Example 5) 12x39x240x+30 For Exercises 77-82, factor by grouping. (See Example 5) 30z335z224z+28 For Exercises 77-82, factor by grouping. (See Example 5) cd8d+4c2d2 82PE For Exercises 83-94, factor the trinomials. (See Examples 6-8) p2+2p63 For Exercises 83-94, factor the trinomials. (See Examples 6-8) w2+5w66

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