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All Textbook Solutions for Precalculus
For Exercises 49-56, determine the number of possible positive and negative real zeros for the given function. (See Example 7-8) gx=3x7+4x46x3+5x26x+151PEFor Exercises 49-56, determine the number of possible positive and negative real zeros for the given function. (See Example 7-8) hx=4x9+6x85x52x4+3x2x+8For Exercises 49-56, determine the number of possible positive and negative real zeros for the given function. (See Example 7-8) px=0.11x4+0.04x3+0.31x2+0.27x1.1For Exercises 49-56, determine the number of possible positive and negative real zeros for the given function. (See Example 7-8) qx=0.6x4+0.8x30.6x2+0.1x0.4For Exercises 49-56, determine the number of possible positive and negative real zeros for the given function. (See Example 7-8) vx=18x6+16x4+13x2+110For Exercises 49-56, determine the number of possible positive and negative real zeros for the given function. (See Example 7-8) tx=11000x6+1100x4+110x2+1For Exercises 57-58, use Descartes’ rule of signs to determine the total number of real zeros and the number of positive and negative real zeros. fx=x8+5x6+6x4x3For Exercises 57-58, use Descartes’ rule of signs to determine the total number of real zeros and the number of positive and negative real zeros. fx=5x83x64x2+xFor Exercises 59-64, (See Example 9) a. Determine if the upper bound theorem identifies the given number as an upper bound for the real zeros of fx . b. Determine if the lower bound theorem identifies the given number as a lower bound for the real zeros of fx . fx=x5+6x4+5x2+x3a.2b.5For Exercises 59-64, (See Example 9) a. Determine if the upper bound theorem identifies the given number as an upper bound for the real zeros of fx . b. Determine if the lower bound theorem identifies the given number as a lower bound for the real zeros of fx . fx=x4+8x34x2+7x3a.3b.4For Exercises 59-64, (See Example 9) a. Determine if the upper bound theorem identifies the given number as an upper bound for the real zeros of fx . b. Determine if the lower bound theorem identifies the given number as a lower bound for the real zeros of fx . fx=8x342x2+33x+28a.6b.1For Exercises 59-64, (See Example 9) a. Determine if the upper bound theorem identifies the given number as an upper bound for the real zeros of fx . b. Determine if the lower bound theorem identifies the given number as a lower bound for the real zeros of fx . fx=6x3x257x+70a.4b.4For Exercises 59-64, (See Example 9) a. Determine if the upper bound theorem identifies the given number as an upper bound for the real zeros of fx . b. Determine if the lower bound theorem identifies the given number as a lower bound for the real zeros of fx . fx=2x5+11x463x250x+40a.3b.664PEFor Exercises 65-68, determine if the statement is true or false. If a statement is false, explain why. If 5 is an upper bound for the real zeros of fx , then 6 is also an upper bound.For Exercises 65-68, determine if the statement is true or false. If a statement is false, explain why. If 5 is an upper bound for the real zeros of fx , then 4 is also an upper bound.For Exercises 65-68, determine if the statement is true or false. If a statement is false, explain why. If 3 is a lower bound for the real zeros of fx , then 2 is also a lower bound.For Exercises 65-68, determine if the statement is true or false. If a statement is false, explain why. If 3 is a lower bound for the real zeros of fx , then 4 is also a lower bound.For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs and the upper and lower bound theorem to limit your search for rational zeros. (See Example 10) fx=8x342x2+33x+28For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs and the upper and lower bound theorem to limit your search for rational zeros. (See Example 10) fx=6x3x257x+70For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs and the upper and lower bound theorem to limit your search for rational zeros. (See Example 10) fx=2x5+11x463x250x+40For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs and the upper and lower bound theorem to limit your search for rational zeros. (See Example 10) fx=3x516x4+5x3+90x2138x+36For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs and the upper and lower bound theorem to limit your search for rational zeros. (See Example 10) fx=4x4+20x3+13x230x+9For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs and the upper and lower bound theorem to limit your search for rational zeros. (See Example 10) fx=9x4+30x3+13x220x+4For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs and the upper and lower bound theorem to limit your search for rational zeros. (See Example 10) fx=2x411x3+27x241x+1576PEFor Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs and the upper and lower bound theorem to limit your search for rational zeros. (See Example 10) hx=4x428x3+73x290x+5078PE79PEFor Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs and the upper and lower bound theorem to limit your search for rational zeros. (See Example 10) fx=x6+6x5+12x4+18x3+27x2For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs and the upper and lower bound theorem to limit your search for rational zeros. (See Example 10) fx=x510x4+34x3For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs and the upper and lower bound theorem to limit your search for rational zeros. (See Example 10) fx=x612x5+40x4For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs and the upper and lower bound theorem to limit your search for rational zeros. (See Example 10) fx=x3+3x29x13For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs and the upper and lower bound theorem to limit your search for rational zeros. (See Example 10) fx=x3+5x211x+15For Exercises 85-90, determine if the statement is true or false. If a statement is false, explain why. A polynomial with real coefficients of degree 4 must have at least one real zero.For Exercises 85-90, determine if the statement is true or false. If a statement is false, explain why. Given fx=2ix43+6ix3+5x2+7,ifa+bi is a zero of fx , then abi must also be a zero.For Exercises 85-90, determine if the statement is true or false. If a statement is false, explain why. The graph of a 10th-degree polynomial must cross the x-axis exactly once.88PEFor Exercises 85-90, determine if the statement is true or false. If a statement is false, explain why. If c is a zero of a polynomial fx , with degree n2 then all other zeros of fx are zeros of fxxc.For Exercises 85-90, determine if the statement is true or false. If a statement is false, explain why. If b is an upper bound for the real zeros of a polynomial, then b is a lower bound for the real zeros of the polynomial.Given that xc divides evenly into a polynomial fx , which statements are true? a.xcisafactorfx.b.cisazerooffx.c.Theremainderoffxxcis0.d.cisasolutionrootoftheequationfx=0.a. Use the quadratic formula to solve x27x+5=0. b. Write x27x+5 as a product of linear factors.a. Use the intermediate value theorem to show that fx=2x27x+4 has a real zero on the interval 2,3. b. Find the zeros.Show that xa is a factor of xnan for any positive integer n and constant a.Explain why a polynomial with real coefficients of degree 3 must have at least one real zero.Why is it not necessary to apply the rational zero theorem, Descartes’ rule of signs, or the upper and lower bound theorem to find the zeros of second-degree polynomial?97PEExplain why the fundamental theorem of algebra does not apply to fx=x+3. That is, no complex number c exists such that fc=0.Let n be a positive even integer. Determine the greatest number of possible nonreal zeros of fx=xn1.Let n be a positive odd integer. Determine the greatest number of possible nonreal zeros of fx=xn1.The front face of a tent is triangular and the height of the triangle is two-thirds of the base. The length of the tent is 3 ft more than the base of the triangular face. If the tent holds a volume of 108ft3, determine its dimensions.An underground storage tank for gasoline is in the shape of a right circular cylinder with hemispheres on each end. If the total volume of the tank is 1043ft3, find the radius of the tank.A food company originally sells cereal in boxes with dimensions 10 in. by 7 in. by 2.5 in. To make more profit, the company decreases each dimension of the box by x inches but keeps the price the same. If the new volume is 81in.3 by how much was each dimension decreased?104PEA rectangle is bounded by the x-axis and a parabola defined by y=4x2 . What are the dimensions of the rectangle if the area is 6cm2 ? Assume that all units of length are in centimeters.A rectangle is bounded by the parabola defined by y=x2 the x-axis, and the line x=5 as shown in the figure. If the area of the rectangle is 12in.2 determine the dimensions of the rectangle.For Exercises 107-110, a. Factor the polynomial over the set real numbers. b. Factor the polynomial over the set of complex numbers. fx=x4+2x3+x2+8x12For Exercises 107-110, a. Factor the polynomial over the set real numbers. b. Factor the polynomial over the set of complex numbers. fx=x46x3+9x26x+8109PEFor Exercises 107-110, a. Factor the polynomial over the set real numbers. b. Factor the polynomial over the set of complex numbers. fx=x4+8x233Find all fourth roots of 1, by solving the equation x4=1.Find all sixth roots of 1, by solving the equation x6=1.113PE114PEFor Exercises 115-116, use the formula x=n22+m33+n23n22+m33n23 To find a solution to the equation x3+mx=n. x33x=2For Exercises 115-116, use the formula x=n22+m33+n23n22+m33n23 To find a solution to the equation x3+mx=n. x3+9x=26The graph of is given. fx=1x2 Complete the statements. a.Asx,fx.b.Asx2,fx.c.Asx2+,fx.d.AsAsx,fx.Identify the vertical asymptotes. a.fx=3x+1b.hx=x+72x2x10c.mx=5xx4+13SPGiven gx=3x2+4x3x2+3 , determine the horizontal asymptote and the point where the graph crosses the horizontal asymptote.5SPUse transformations to graph gx=1x32.Graph fx=x1x+4.Graph gx=5xx29.9SP10SPRepeat Example 11 under the assumption that the company cuts its fixed costs $200 per month and pays its employees more, leading to a variable cost per house call of $50 .The domain of a rational function defined by fx=pxqx is all real numbers excluding the zeros of .The notation x is read as .The notation x5 is read as .4PE5PE6PE7PE8PE9PE10PE11PE12PEFor Exercises 13-16, refer to the graph of the function and complete the statement. (See Example 1) a.Asx,fx.b.Asx4,fx.c.Asx4+,fx.d.Asx,fx.e.Thegraphisincreasingovertheintervals.f.Thegraphisdecreasingovertheintervals.g.Thedomainis.h.Therangeis.i.Thevaerticalasymptoteistheline.j.Thehorizontalasymptoteistheline.For Exercises 13-16, refer to the graph of the function and complete the statement. (See Example 1) a.Asx,fx.b.Asx3,fx.c.Asx3+,fx.d.Asx,fx.e.Thegraphisincreasingovertheintervals.f.Thegraphisdecreasingovertheintervals.g.Thedomainis.h.Therangeis.i.Thevaerticalasymptoteistheline.j.Thehorizontalasymptoteistheline.15PE16PEFor Exercises 17-24, determine the vertical asymptotes of the graph of the function. (See Example 2) fx=8x4For Exercises 17-24, determine the vertical asymptotes of the graph of the function. (See Example 2) gx=2x+7For Exercises 17-24, determine the vertical asymptotes of the graph of the function. (See Example 2) hx=x32x29x5For Exercises 17-24, determine the vertical asymptotes of the graph of the function. (See Example 2) kx=x+23x2+8x3For Exercises 17-24, determine the vertical asymptotes of the graph of the function. (See Example 2) mx=xx2+5For Exercises 17-24, determine the vertical asymptotes of the graph of the function. (See Example 2) nx=6x4+1For Exercises 17-24, determine the vertical asymptotes of the graph of the function. (See Example 2) ft=t2+22t2+4t3For Exercises 17-24, determine the vertical asymptotes of the graph of the function. (See Example 2) ka=5+a43a2+4a1The graph of fx=x2+82x23 will behave like which function for larger values of x? a.y=12b.y=x2c.y=83d.y=12x83The graph of fx=2x3+75x3 will behave like which function for larger values of x? a.y=25xb.y=2x5c.y=25d.y=25x3The graph of fx=3x42x+5x5+x22 will behave like which function for larger values of x? a.y=3b.y=3xc.y=52d.y=028PE29PEFor Exercises 29-36, a. Identify the horizontal asymptotes (if any). (See Example 3) b. If the graph of the function has a horizontal asymptote, determine the point (if any) where the graph crosses the horizontal asymptote. (See Example 4) qx=8x2+4x+4For Exercises 29-36, a. Identify the horizontal asymptotes (if any). (See Example 3) b. If the graph of the function has a horizontal asymptote, determine the point (if any) where the graph crosses the horizontal asymptote. (See Example 4) hx=3x2+8x5x2+3For Exercises 29-36, a. Identify the horizontal asymptotes (if any). (See Example 3) b. If the graph of the function has a horizontal asymptote, determine the point (if any) where the graph crosses the horizontal asymptote. (See Example 4) rx=4x2+5x1x2+233PEFor Exercises 29-36, a. Identify the horizontal asymptotes (if any). (See Example 3) b. If the graph of the function has a horizontal asymptote, determine the point (if any) where the graph crosses the horizontal asymptote. (See Example 4) nx=x3x2+12x335PE36PE37PE38PE39PE40PE41PEFor Exercises 39-48, identify the asymptotes. (See Example 5) kx=2x23x+7x+343PE44PE45PE46PE47PE48PE49PE50PEFor Exercises 49-56, graph the functions by using transformations of the graphs of y=1xandy=1x2. (See Example 6) hx=1x2+2For Exercises 49-56, graph the functions by using transformations of the graphs of y=1xandy=1x2. (See Example 6) kx=1x23For Exercises 49-56, graph the functions by using transformations of the graphs of y=1xandy=1x2. (See Example 6) mx=1x+423For Exercises 49-56, graph the functions by using transformations of the graphs of y=1xandy=1x2. (See Example 6) nx=1x12+255PE56PEFor Exercises 57-62, for the graph of y=fx. a. Identify the x-intercepts. b. Identify any vertical asymptotes. c. Identify the horizontal asymptotes or slant asymptote if applicable. d. Identify the y-intercept. fx=x+32x7x+24x+158PEFor Exercises 57-62, for the graph of y=fx. a. Identify the x-intercepts. b. Identify any vertical asymptotes. c. Identify the horizontal asymptotes or slant asymptote if applicable. d. Identify the y-intercept. fx=4x9x2960PEFor Exercises 57-62, for the graph of y=fx. a. Identify the x-intercepts. b. Identify any vertical asymptotes. c. Identify the horizontal asymptotes or slant asymptote if applicable. d. Identify the y-intercept. fx=5x1x+3x+262PEFor Exercises 63-66, sketch a rational function subject to the given conditions. Answers may vary. Horizontalasymptote:y=2 Verticalasymptote:x=3 y-intercept: 0, 8 3 x-intercept: 4,064PEFor Exercises 63-66, sketch a rational function subject to the given conditions. Answers may vary. Horizontalasymptote:y=0 Verticalasymptote:x=2andx=2 y-intercept: 0,1 Nox-intercepts Symmetrictothey-axis Passesthroughthepoint 3, 4 566PEFor Exercises 67-90, graph the function. (See Example 7-10) nx=32x+7For Exercises 67-90, graph the function. (See Example 7-10) mx=42x5For Exercises 67-90, graph the function. (See Example 7-10) fx=x4x2For Exercises 67-90, graph the function. (See Example 7-10) gx=x3x1For Exercises 67-90, graph the function. (See Example 7-10) hx=2x4x+3For Exercises 67-90, graph the function. (See Example 7-10) kx=3x9x+2For Exercises 67-90, graph the function. (See Example 7-10) px=6x29For Exercises 67-90, graph the function. (See Example 7-10) qx=4x216For Exercises 67-90, graph the function. (See Example 7-10) rx=5xx2x6For Exercises 67-90, graph the function. (See Example 7-10) tx=4xx22x377PE78PE79PEFor Exercises 67-90, graph the function. (See Example 7-10) cx=2x25x3x2+181PE82PE83PEFor Exercises 67-90, graph the function. (See Example 7-10) dx=x2x12x285PE86PE87PEFor Exercises 67-90, graph the function. (See Example 7-10) gx=x3+3x2x3x22x89PE90PE91PEAn on-demand printing company has monthly overhead costs of $1200 in rent, $420 in electricity. $100 for phone service, and $200 for advertising and marketing. The priming cost is $40 per thousand Pages for paper and ink. a. Write a cost function to represent the cost Cx for printing x thousand Pages for a given month. b. Write a function representing the average cost Cx for printing x thousand Pages for a given month. c. Evaluate C20,C50,C100,andC200. d. Interpret the meaning of C200 . e. For a given month, if the printing company could print an unlimited number of Pages, what value would the average cost per thousand Pages approach? What does this mean in the context of the problem?93PE94PE95PEA certain diet pill is designed to delay the administration of the active ingredient for several hours. The concentration Ct (in mg/L) of the active ingredient in the bloodstream t hours after taking the pill is modeled by Ct=3t2t2+20t+51 a. Use a graphics utility to graph the function. b. What are the domain restrictions on the function? c Use the graph to approximate the maximum concentration. Round to the nearest mg/L. d. What is the limiting concentration?A power company burns coal to generate electricity. The cost Cx (in $1000 ) to remove x of the air pollutants is given by Cx=600x100x a Compute the cost to remove 25 of the air pollutants. b. Determine the cost to remove 50,75,and90 of the air pollutants. c If the power Company budgets 1.4 million for pollution control, what percentage of the air pollutants can be removed?The cost Cxin$1000 for a city to remove x of the waste from a polluted river is given by Cx=80x100x a. Determine the cost to remove 20,40,and90 of the waste. Round to the nearest thousand dollars. b. If the city has $320,000 budgeted for river cleanup, what percentage of the waste can be removed?99PEThe Doppler effect is a change in the observed frequency of a wave (such m a sound wave or light wave) when the source of the wave and observer are in motion relative to each other. The Doppler effect explains why an observer hears a change in pitch of an ambulance siren as the ambulance passes by the observer. The frequency Fv of a sound relative to an observer is given by Fv=fas0s0v, where fa is the actual frequency of the sound at the source. s0 is the speed of sound in air (772.4 mph). and v is the speed at which the source of sound is moving toward the observer. Use this relationship for Exercises 99-100. Suppose the frequency of sound emitted by a police car siren is 600 Hz. a. Write F as a function of v if the police car is moving toward an observer. b. Suppose that the frequency of the siren as heard by an observer is 664 Hz. Determine the velocity of the police car. Round to the nearest tenth of a mph. c. Although a police car cannot travel dose to the speed of sound. interpret the meaning of the vertical asymptote101PE102PE103PE104PE105PE106PE107PE108PE109PE110PE111PE112PE113PEThe rational functions studied in this section all have the characteristic that the numerator and denominator do not share a common variable factor. We now investigate rational functions for which this is not the case. For Exercises 111-114, a. Write the domain of f interval notation. b. Simplify the rational expression defining the function. c. Identify any vertical asymptotes. d. Identify any other value of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous. e. Identify the graph of the function. fx=2x2x2+2x3For Exercises 1-8, refer to px=x3+3x26x8andqx=x32x25x+6. Find the zeros of px.For Exercises 1-8, refer to px=x3+3x26x8andqx=x32x25x+6. Find the zeros of qx.For Exercises 1-8, refer to px=x3+3x26x8andqx=x32x25x+6. Find the x-intercept(s) of the graph of y=qx.4PREFor Exercises 1-8, refer to px=x3+3x26x8andqx=x32x25x+6. Find the x-intercepts of the graph of fx=pxqx=x3+3x26x8x32x25x+66PREFor Exercises 1-8, refer to px=x3+3x26x8andqx=x32x25x+6. Find the horizontal asymptote or slant asymptote of the graph of fx=pxqx=x3+3x26x8x32x25x+6 .8PREFor Exercises 9-16, refer to cx=x34x22x+8anddx=x3+3x24. Find the zeros of cx .10PRE11PRE12PREFor Exercises 9-16, refer to cx=x34x22x+8anddx=x3+3x24. Find the x-intercepts of the graph of gx=cxdx=x34x22x+8x3+3x24.For Exercises 9-16, refer to cx=x34x22x+8anddx=x3+3x24. Find the vertical asymptotes of the graph of gx=cxdx=x34x22x+8x3+3x24.15PREFor Exercises 9-16, refer to cx=x34x22x+8anddx=x3+3x24. Determine where the graph of gx=x34x22x+8x3+3x24 crosses its horizontal or slant asymptote.For Exercises 17-18, use the results from Exercises 5-8 and 13-16 to match the function with its graph. fx=x3+3x26x8x32x25x+6For Exercises 17-18, use the results from Exercises 5-8 and 13-16 to match the function with its graph. gx=x34x22x+8x3+3x24Divide 2x34x210x+12x211 by using an appropriate method. a. Identify the quotient qx. b. Identify the remainder rx.Identify the slant asymptote of fx=2x34x210+12x211 .Identify the point where the graph of fx=2x34x210x+12x211 crosses its slant asymptote.Refer to Exercise 19. Solve the equation rx=0. How does the solution to the equation rx=0 relate to the point where the graph of f crosses its slant asymptotes?Solve the inequality. 2xx121xSolve the inequality. x418x3x24x33SPSolve the inequality. 5xx125SPSolve the inequalities. a.x2x4+10b.x2x4+10c.x2x4+10d.x2x4+10Repeat Example 7 under the assumption that the rocket is launched with an initial speed of 80 ft/sec from a height of 5 ft.Let fx be a polynomial. An inequality of the form fx0,fx0,fx0,orfx0 is called a inequality. If the polynomial is of degree then the inequality is also called a quadratic inequality.Let fx be a rational expression. An inequality of the form fx0,fx0,fx0,orfx0 is called a inequality.The solution set for the inequality x+1024 is , whereas the solution set for the inequality x+1024 is .The solutions to an inequality fx0 are the values of x on the intervals where fx is (positive/negative).5PEFor Exercises 5-14, the graph of y=fx is given. Solve the inequalities. a.fx0b.fx0c.fx0d.fx07PE8PEFor Exercises 5-14, the graph of y=fx is given. Solve the inequalities. a.fx0b.fx0c.fx0d.fx010PEFor Exercises 5-14, the graph of y=fx is given. Solve the inequalities. a.fx0b.fx0c.fx0d.fx0For Exercises 5-14, the graph of y=fx is given. Solve the inequalities. a.fx0b.fx0c.fx0d.fx0For Exercises 5-14, the graph of y=fx is given. Solve the inequalities. a.fx0b.fx0c.fx0d.fx014PE15PEFor Exercises 15-20, solve the equations and inequalities. (See Example 3) a.3x+7x2=0b.3x+7x20c.3x+7x20d.3x+7x20e.3x+7x20For Exercises 15-20, solve the equations and inequalities. (See Example 3) a.x2+x+12=0b.x2+x+120c.x2+x+120d.x2+x+120e.x2+x+120For Exercises 15-20, solve the equations and inequalities. (See Example 3) a.x210x9=0b.x210x90c.x210x90d.x210x90e.x210x90For Exercises 15-20, solve the equations and inequalities. (See Example 3) a.a2+12a+36=0b.a2+12a+360c.a2+12a+360d.a2+12a+360e.a2+12a+360For Exercises 15-20, solve the equations and inequalities. (See Example 3) a.t214t+49=0b.t214t+490c.t214t+490d.t214t+490e.t214t+490For Exercises 21-54, solve the inequalities. (See Examples 1-2) 4w290For Exercises 21-54, solve the inequalities. (See Examples 1-2) 16z2250For Exercises 21-54, solve the inequalities. (See Examples 1-2) 3w2+w2w+2For Exercises 21-54, solve the inequalities. (See Examples 1-2) 5y2+7y3y+4For Exercises 21-54, solve the inequalities. (See Examples 1-2) a23aFor Exercises 21-54, solve the inequalities. (See Examples 1-2) d26dFor Exercises 21-54, solve the inequalities. (See Examples 1-2) 106x5x2For Exercises 21-54, solve the inequalities. (See Examples 1-2) 64x3x2For Exercises 21-54, solve the inequalities. (See Examples 1-2) m249For Exercises 21-54, solve the inequalities. (See Examples 1-2) y29For Exercises 21-54, solve the inequalities. (See Examples 1-2) 16p22For Exercises 21-54, solve the inequalities. (See Examples 1-2) 54q250For Exercises 21-54, solve the inequalities. (See Examples 1-2) x+4x1x30For Exercises 21-54, solve the inequalities. (See Examples 1-2) x+2x+5x40For Exercises 21-54, solve the inequalities. (See Examples 1-2) 5cc+224c0For Exercises 21-54, solve the inequalities. (See Examples 1-2) 6uu+123u0For Exercises 21-54, solve the inequalities. (See Examples 1-2) t410t2+90For Exercises 21-54, solve the inequalities. (See Examples 1-2) w420w2+640For Exercises 21-54, solve the inequalities. (See Examples 1-2) 2x3+5x28x+20For Exercises 21-54, solve the inequalities. (See Examples 1-2) 3x33x4x24For Exercises 21-54, solve the inequalities. (See Examples 1-2) 2x4+10x36x2180For Exercises 21-54, solve the inequalities. (See Examples 1-2) 4x4+4x3+64x2+800For Exercises 21-54, solve the inequalities. (See Examples 1-2) 5u6+28u5+15u40For Exercises 21-54, solve the inequalities. (See Examples 1-2) 3w6+8w54w40For Exercises 21-54, solve the inequalities. (See Examples 1-2) 6x2x543x+15x40For Exercises 21-54, solve the inequalities. (See Examples 1-2) 5x3x224x+13x340For Exercises 21-54, solve the inequalities. (See Examples 1-2) 5x322For Exercises 21-54, solve the inequalities. (See Examples 1-2) 4x+12649PEFor Exercises 21-54, solve the inequalities. (See Examples 1-2) 1x+22For Exercises 21-54, solve the inequalities. (See Examples 1-2) 16y224y9For Exercises 21-54, solve the inequalities. (See Examples 1-2) 4w220w25For Exercises 21-54, solve the inequalities. (See Examples 1-2) x+3x+11For Exercises 21-54, solve the inequalities. (See Examples 1-2) x+2x+41For Exercises 55-58, the graph of y=fx is given. Solve the inequalities. a.fx0b.fx0c.fx0d.fx0For Exercises 55-58, the graph of y=fx is given. Solve the inequalities. a.fx0b.fx0c.fx0d.fx057PEFor Exercises 55-58, the graph of y=fx is given. Solve the inequalities. a.fx0b.fx0c.fx0d.fx059PEFor Exercises 59-62, solve the inequalities. (See Example 6) a.x+4x10b.x+4x10c.x+4x10d.x+4x10For Exercises 59-62, solve the inequalities. (See Example 6) a.x4x2+90b.x4x2+90c.x4x2+90d.x4x2+90For Exercises 59-62, solve the inequalities. (See Example 6) a.x2x4+160b.x2x4+160c.x2x4+160d.x2x4+160For Exercises 63-84, solve the inequalities. (See Examples 4-5) 5xx+10For Exercises 63-84, solve the inequalities. (See Examples 4-5) 2xx+60For Exercises 63-84, solve the inequalities. (See Examples 4-5) 42xx20For Exercises 63-84, solve the inequalities. (See Examples 4-5) 93xx20For Exercises 63-84, solve the inequalities. (See Examples 4-5) w2w2w+30For Exercises 63-84, solve the inequalities. (See Examples 4-5) p22p8p10For Exercises 63-84, solve the inequalities. (See Examples 4-5) 52t71For Exercises 63-84, solve the inequalities. (See Examples 4-5) 43c81For Exercises 63-84, solve the inequalities. (See Examples 4-5) 2xx22For Exercises 63-84, solve the inequalities. (See Examples 4-5) 3x3x71For Exercises 63-84, solve the inequalities. (See Examples 4-5) 4xx+52For Exercises 63-84, solve the inequalities. (See Examples 4-5) 3xx+2475PEFor Exercises 63-84, solve the inequalities. (See Examples 4-5) d3d2+10For Exercises 63-84, solve the inequalities. (See Examples 4-5) 10x+22x+2For Exercises 63-84, solve the inequalities. (See Examples 4-5) 4x31x3For Exercises 63-84, solve the inequalities. (See Examples 4-5) 4y+32y