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All Textbook Solutions for Precalculus Enhanced with Graphing Utilities

In Problems 19-26, write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. [ 1 2 3 3 5 6 2 3 4 | 6 4 6 ] R 2 =2 r 1 + r 2 R 3 =3 r 1 + r 3In Problems 19-26, write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. [ 1 6 1 3 5 1 4 6 4 | 6 6 6 ] R 2 =6 r 1 + r 2 R 3 = r 1 + r 3In Problems 19-26, write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. [ 5 2 4 3 5 1 1 6 4 | 2 2 6 ] R 1 =2 r 2 + r 1 R 3 =2 r 2 + r 3In Problems 19-26, write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. [ 4 3 3 3 5 6 1 2 4 | 2 6 6 ] R 1 = r 2 + r 1 R 3 = r 2 + r 3In Problems 27-38, the reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x,y ; or x,y,z ; or x 1 , x 2 , x 3 , x 4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [ 1 0 0 1 | 5 1 ]In Problems 27-38, the reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x,y ; or x,y,z ; or x 1 , x 2 , x 3 , x 4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [ 1 0 0 1 | 4 0 ]In Problems 27-38, the reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x,y ; or x,y,z ; or x 1 , x 2 , x 3 , x 4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [ 1 0 0 0 1 0 0 0 0 | 1 2 3 ]In Problems 27-38, the reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x,y ; or x,y,z ; or x 1 , x 2 , x 3 , x 4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [ 1 0 0 0 1 0 0 0 0 | 0 0 2 ]In Problems 27-38, the reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x,y ; or x,y,z ; or x 1 , x 2 , x 3 , x 4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [ 1 0 0 0 1 0 2 4 0 | 1 2 0 ]In Problems 27-38, the reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x,y ; or x,y,z ; or x 1 , x 2 , x 3 , x 4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [ 1 0 0 0 1 0 4 3 0 | 4 2 0 ]In Problems 27-38, the reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x,y ; or x,y,z ; or x 1 , x 2 , x 3 , x 4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [ 1 0 0 0 1 0 0 0 1 0 1 2 | 1 2 3 ]In Problems 27-38, the reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x,y ; or x,y,z ; or x 1 , x 2 , x 3 , x 4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [ 1 0 0 0 1 0 0 0 1 0 2 3 | 1 2 0 ]In Problems 27-38, the reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x,y ; or x,y,z ; or x 1 , x 2 , x 3 , x 4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [ 1 0 0 0 1 0 0 1 0 4 3 0 | 2 3 0 ]In Problems 27-38, the reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x,y ; or x,y,z ; or x 1 , x 2 , x 3 , x 4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [ 1 0 0 0 1 0 0 0 1 0 0 2 | 1 2 3 ]In Problems 27-38, the reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x,y ; or x,y,z ; or x 1 , x 2 , x 3 , x 4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [ 1 0 0 0 0 1 0 0 0 0 1 0 1 2 1 0 | 2 2 0 0 ]In Problems 27-38, the reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x,y ; or x,y,z ; or x 1 , x 2 , x 3 , x 4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 | 1 2 3 0 ]In problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { x+y=8 xy=4In problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { x+2y=5 x+y=3In problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { 2x4y=2 3x+2y=3In problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { 3x+3y=3 4x+2y= 8 3In problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { x+2y=4 2x+4y=8In problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { 3xy=7 9x3y=21In problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { 2x+3y=6 xy= 1 2In problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { 1 2 x+y=2 x2y=8In problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { 3x5y=3 15x+5y=21In problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { 2xy=1 x+ 1 2 y= 3 2In problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { xy=6 2x3z=16 2y+z=4In problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { 2x+y=4 2y+4z=0 3x2z=11In problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { x2y+3z=7 2x+y+z=4 3x+2y2z=10In problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { 2x+y3z=0 2x+2y+z=7 3x4y3z=751AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYUIn problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { 3x+yz= 2 3 2xy+z=1 4x+2y= 8 362AYUIn problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { x+y+z+w=4 2xy+z=0 3x+2y+zw=6 x2y2z+2w=164AYU65AYU66AYU67AYUIn problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { 2x+yz=4 x+y+3z=169AYU70AYUIn problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { 4x+y+zw=4 xy+2z+3w=3In problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { 4x+y=5 2xy+zw=5 z+w=4Curve Fitting Find the function y=a x 2 +bx+c whose graph contains the points ( 1,2 ) , ( 2,7 ) and ( 2,3 ) .74AYU75AYU76AYUNutrition A dietitian at Palos Community Hospital wants a patient to have a meal that has 78 grams (g) of protein. 59 g of carbohydrates, and 75 milligrams (mg) of vitamin A. The hospital food service tells the dietitian that the dinner for today is salmon steak, baked eggs, and acorn squash. Each serving of salmon steak has 30 g of protein, 20 g of carbohydrates, and 2 mg of vitamin A. Each serving of baked eggs contains 15 g of protein. 2g of carbohydrates, and 20 mg of vitamin A. Each serving of acorn squash contains 3 g of protein, 25 g of carbohydrates, and 32 mg of vitamin A. How many servings of each food should the dietitian provide for the patient?78AYU79AYU80AYUProduction To manufacture an automobile requires painting, drying, and polishing. Epsilon Motor Company produces three types of cars: the Delta, the Beta, and the Sigma. Each Delta requires 10 hours (hr) for painting, 3 hr for drying, and 2 hr for polishing. A Beta requires 16 hr for painting, 5 hr for drying, and 3 hr for polishing, and a Sigma requires 8 hr for painting, 2 hr for drying, and 1 hr for polishing. If the company has 240 hr for painting, 69 hr for drying, and 41 hr for polishing per month, how many of each type of car are produced?82AYUElectricity: Kirchhoffs Rules An application of Kirchhoffs Rules to the circuit shown results in the following system of equations: { 4+82 I 2 =0 8=5 I 4 + I 1 4=3 I 3 + I 1 I 3 + I 4 = I 1 Find the currents I 1 , I 2 , I 3 ,and I 4 .84AYUFinancial Planning Three retired couples each require an additional annual income of 2000 per year. As their financial consultant, you recommend that they invest some money in Treasury bills that yield 7 , some money in corporate bonds that yield 9 , and some money in junk bonds that yield 11 . Prepare a table for each couple showing the various ways that their goals can be achieved: a. If the first couple has 20,000 to invest. b. If the second couple has 25,000 to invest. c. If the third couple has 30,000 to invest. d. What advice would you give each couple regarding the amount to invest and the choices available? [Hint: Higher yields generally carry more risk.]Financial Planning A young couple has 25,000 to invest. As their financial consultant, you recommend that they invest some money in Treasury bills that yield 7 , some money in corporate bonds that yield 9 , and some money in junk bonds that yield 11 . Prepare a table showing the various ways that this couple can achieve the following goals: a. 1500 per year in income b. 2000 per year in income. c. 2500 per year in income. d. What advice would you give this couple regarding the income that they require and the choices available?Pharmacy A doctors prescription calls for a daily intake of a supplement containing 40 milligrams (mg) of vitamin C and 30 mg of vitamin D. Your pharmacy stocks three supplements that can he used: one contains 20 vitamin C and 30 vitamin D; a second, 40 vitamin C and 20 vitamin D; and a third, 30 vitamin C and 50 vitamin D. Create a table showing the possible combinations that could be used to fill the prescription.Pharmacy A doctors prescription calls for the creation of pills that contain 12 units of vitamin B 12 and 12 units of vitamin E. Your pharmacy stocks three powders that can be used to make these pills: one contains 20 vitamin B 12 and 30 vitamin E; a second, 40 vitamin B 12 and 20 vitamin E; and a third, 30 vitamin B 12 and 40 vitamin E. Create a table showing the possible combinations of these powders that could be mixed in each pill. Hint: 10 units of the first powder contains 10( 0.2 )=2 units of vitamin B 12 .Write a brief paragraph or two outlining your strategy for solving a system of linear equations using matrices.When solving a system of linear equations using matrices, do you prefer to place the augmented matrix in row echelon form or in reduced row echelon form? Give reasons for your choice.Make up a system of three linear equations containing three variables that has: a. No solution. b. Exactly one solution. c. Infinitely many solutions. Give the three systems to a friend to solve and critique.D=[ a b c d ]= _______.Using Cramer’s Rule, the value of x that satisfies the system of equations. { 2x+3y=5 x4y=3 isx= [ 2 3 1 4 ]True or False A determinant can never equal 0.True or False When using Cramer’s Rule, if D=0 , then the system of linear equations is inconsistent.5AYUTrue or False If any row (or any column) of a determinant is multiplied by a nonzero number k , the value of the determinant remains unchanged.[ 6 4 1 3 ][ 8 3 4 2 ][ 3 1 4 2 ][ 4 2 5 3 ][ 3 4 2 1 1 5 1 2 2 ]12AYU[ 4 1 2 6 1 0 1 3 4 ][ 3 9 4 1 4 0 8 3 1 ]{ x+y=8 xy=4{ x+2y=5 xy=3{ 5xy=13 2x+3y=12{ x+3y=5 2x3y=8{ 3x=24 x+2y=0{ 4x+5y=3 2y=4{ 3x6y=24 5x+4y=12{ 2x+4y=16 3x5y=9{ 3x2y=4 6x4y=0{ x+2y=5 4x8y=6{ 2x4y=2 3x+2y=3{ 3x+3y=3 4x+2y= 8 3{ 2x3y=1 10x+10y=5{ 3x2y=0 5x+10y=4{ 2x+3y=6 xy= 1 2{ 1 2 x+y=2 x2y=8{ 3x5y=3 15x+5y=21{ 2xy=1 x+ 1 2 y= 3 2{ x+yz=6 3x2y+z=5 x+3y2z=14{ xy+z=4 2x3y+4z=15 5x+y2z=12{ x+2yz=3 2x4y+z=7 2x+2y3z=4{ x+4y3z=8 3xy+3z=12 x+y+6z=1{ x2y+3z=1 3x+y2z=0 2x4y+6z=2{ xy+2z=5 3x+2y=4 2x+2y4z=10{ x+2yz=0 2x4y+z=0 2x+2y3z=0{ x+4y3z=0 3xy+3z=0 x+y+6z=0{ x2y+3z=0 3x+y2z=0 2x4y+6z=0{ xy+2z=0 3x+2y=0 2x+2y4z=0In problems 43-50, use properties of determinants to find the value of each determinant if it is known that [ x u 1 y v 2 z w 3 ]=4 [ 1 u x 2 v y 3 w z ]In problems 43-50, use properties of determinants to find the value of each determinant if it is known that [ x u 1 y v 2 z w 3 ]=4 [ x u 2 y v 4 z w 6 ]In problems 43-50, use properties of determinants to find the value of each determinant if it is known that [ x u 1 y v 2 z w 3 ]=4 [ x 3 u y 6 v z 9 w ]In problems 43-50, use properties of determinants to find the value of each determinant if it is known that [ x u 1 y v 2 z w 3 ]=4 [ 1 xu u 2 yv v 3 zw w ]In problems 43-50, use properties of determinants to find the value of each determinant if it is known that [ x u 1 y v 2 z w 3 ]=4 [ 1 x3 2u 2 y6 2v 3 z9 2w ]In problems 43-50, use properties of determinants to find the value of each determinant if it is known that [ x u 1 y v 2 z w 3 ]=4 [ x u 1 y v 2 zx wu 2 ]In problems 43-50, use properties of determinants to find the value of each determinant if it is known that [ x u 1 y v 2 z w 3 ]=4 [ 1 2x u1 2 2y v2 3 2z w3 ]In problems 43-50, use properties of determinants to find the value of each determinant if it is known that [ x u 1 y v 2 z w 3 ]=4 [ x+3 3u1 1 y+6 3v2 2 z+9 3w3 3 ]solve for x. [ x x 4 3 ]=5solve for x. [ x 1 3 x ]=2solve for x. [ x 4 1 1 3 2 1 2 5 ]=2solve for x. [ 3 1 0 2 x 1 4 5 2 ]=0solve for x. [ x 1 6 2 x 1 3 0 2 ]=7solve for x. [ x 1 0 1 x 1 2 3 2 ]=4xGeometry: Equation of a inline An equation of the inline containing the two points ( x 1 , y 1 ) and ( x 2 , y 2 ) may be expressed as the determinant [ x x 1 x 2 y y 1 y 2 1 1 1 ]=0 Prove this result by expanding the determinant and comparing the result to the two-point form of the equation of a inlineGeometry: Collinear Points Using the result obtained in Problem 57, show that three distinct points ( x 1 , y 1 ) , ( x 2 , y 2 ) , and ( x 3 , y 3 ) are collinear (lie on the same line) if and only if [ x 1 x 2 x 3 y 1 y 2 y 3 1 1 1 ]=059AYU60AYU61AYU62AYU63AYU64AYU65AYU1AYU2AYU3AYU4AYU5AYU6AYU7AYU8AYU9AYU10AYU11AYU12AYU13AYU14AYU15AYU16AYU17AYU18AYU19AYU20AYU21AYU22AYU23AYU24AYU25AYU26AYU27AYU28AYU29AYU30AYU31AYU32AYU33AYU34AYU35AYU36AYU37AYU38AYU39AYU40AYU41AYU42AYU43AYU44AYU45AYU46AYU47AYU48AYU49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYU61AYU62AYU63AYU64AYU65AYU66AYU67AYU68AYU69AYU70AYU71AYU72AYU73AYU74AYU75AYU76AYU77AYU78AYU79AYU80AYU81AYU82AYU83AYU84AYU85AYU86AYU87AYU88AYU89AYU90AYU91AYU92AYU93AYUTrue or False The equation ( x1 ) 2 1=x( x2 ) is an example of an identity. (p. A43)True or False The rational expression 5 x 2 1 x 3 +1 is proper. (p. 227)Factor completely: 3 x 4 +6 x 3 +3 x 2 (pp. A27-A28)True or False Every polynomial with real numbers as coefficients can be factored into products of linear and/or irreducible quadratic factors. (p. 219)In Problems 5-12, tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression. x x 2 1In Problems 5-12, tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression. 5x+2 x 3 1In Problems 5-12, tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression. x 2 +5 x 2 4In Problems 5-12, tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression. 3 x 2 2 x 2 1In Problems 5-12, tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression. 5 x 3 +2x1 x 2 4In Problems 5-12, tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression. 3 x 4 + x 2 2 x 3 +8In Problems 5-12, tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression. x( x1 ) ( x+4 )( x3 )In Problems 5-12, tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression. 2x( x 2 +4 ) x 2 +1In problems 13-46, find the partial fraction decomposition of each rational expression. 4 x( x1 )In problems 13-46, find the partial fraction decomposition of each rational expression. 3x ( x+2 )( x1 )In problems 13-46, find the partial fraction decomposition of each rational expression. 1 x( x 2 +1 )In problems 13-46, find the partial fraction decomposition of each rational expression. 1 ( x+1 )( x 2 +4 )In problems 13-46, find the partial fraction decomposition of each rational expression. 1 ( x1 )( x2 )In problems 13-46, find the partial fraction decomposition of each rational expression. 3x ( x+2 )( x4 )In problems 13-46, find the partial fraction decomposition of each rational expression. x 2 ( x1 ) 2 ( x+1 )In problems 13-46, find the partial fraction decomposition of each rational expression. x+1 x 2 ( x2 )In problems 13-46, find the partial fraction decomposition of each rational expression. 1 x 3 8In problems 13-46, find the partial fraction decomposition of each rational expression. 2x+4 x 3 1In problems 13-46, find the partial fraction decomposition of each rational expression. x 2 ( x1 ) 2 ( x+1 ) 2In problems 13-46, find the partial fraction decomposition of each rational expression. x+1 x 2 ( x2 ) 2In problems 13-46, find the partial fraction decomposition of each rational expression. x3 ( x+2 ) ( x+1 ) 2In problems 13-46, find the partial fraction decomposition of each rational expression. x 2 +x ( x+2 ) ( x1 ) 2In problems 13-46, find the partial fraction decomposition of each rational expression. x+4 x 2 ( x 2 +4 )In problems 13-46, find the partial fraction decomposition of each rational expression. 10 x 2 +2x ( x1 ) 2 ( x 2 +2 )In problems 13-46, find the partial fraction decomposition of each rational expression. x 2 +2x+3 ( x+1 )( x 2 +2x+4 )In problems 13-46, find the partial fraction decomposition of each rational expression. x 2 11x18 x( x 2 +3x+3 )In problems 13-46, find the partial fraction decomposition of each rational expression. x ( 3x2 )( 2x+1 )In problems 13-46, find the partial fraction decomposition of each rational expression. 1 ( 2x+3 )( 4x1 )In problems 13-46, find the partial fraction decomposition of each rational expression. x x 2 +2x3In problems 13-46, find the partial fraction decomposition of each rational expression. x 2 x8 ( x+1 )( x 2 +5x+6 )In problems 13-46, find the partial fraction decomposition of each rational expression. x 2 +2x+3 ( x 2 +4 ) 2In problems 13-46, find the partial fraction decomposition of each rational expression. x 3 +1 ( x 2 +16 ) 2In problems 13-46, find the partial fraction decomposition of each rational expression. 7x+3 x 3 2 x 2 3xIn problems 13-46, find the partial fraction decomposition of each rational expression. x 3 +1 x 5 x 4In problems 13-46, find the partial fraction decomposition of each rational expression. x 2 x 3 4 x 2 +5x2In problems 13-46, find the partial fraction decomposition of each rational expression. x 2 +1 x 3 + x 2 5x+3In problems 13-46, find the partial fraction decomposition of each rational expression. x 3 ( x 2 +16 ) 3In problems 13-46, find the partial fraction decomposition of each rational expression. x 2 ( x 2 +4 ) 3In problems 13-46, find the partial fraction decomposition of each rational expression. 4 2 x 2 5x3In problems 13-46, find the partial fraction decomposition of each rational expression. 4x 2 x 2 +3x2In problems 13-46, find the partial fraction decomposition of each rational expression. 2x+3 x 4 9 x 2In problems 13-46, find the partial fraction decomposition of each rational expression. x 2 +9 x 4 2 x 2 8In Problems 47-54, use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the proper rational expression. Finally, express the improper rational expression as the sum of a polynomial and the partial fraction decomposition. x 3 + x 2 3 x 2 +3x4In Problems 47-54, use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the proper rational expression. Finally, express the improper rational expression as the sum of a polynomial and the partial fraction decomposition. x 3 3 x 2 +1 x 2 +5x+6In Problems 47-54, use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the proper rational expression. Finally, express the improper rational expression as the sum of a polynomial and the partial fraction decomposition. x 3 x 2 +1In Problems 47-54, use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the proper rational expression. Finally, express the improper rational expression as the sum of a polynomial and the partial fraction decomposition. x 3 +x x 2 +4In Problems 47-54, use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the proper rational expression. Finally, express the improper rational expression as the sum of a polynomial and the partial fraction decomposition. x 4 5 x 2 +x4 x 2 +4x+4In Problems 47-54, use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the proper rational expression. Finally, express the improper rational expression as the sum of a polynomial and the partial fraction decomposition. x 4 + x 3 x+2 x 2 2x+1In Problems 47-54, use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the proper rational expression. Finally, express the improper rational expression as the sum of a polynomial and the partial fraction decomposition. x 5 + x 4 x 2 +2 x 4 2 x 2 +1In Problems 47-54, use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the proper rational expression. Finally, express the improper rational expression as the sum of a polynomial and the partial fraction decomposition. x 5 x 3 + x 2 +1 x 4 +6 x 2 +9Graph the equation: y=3x+2 (pp.35-37)Graph the equation: y+4= x 2 (pp.655-659)Graph the equation: y 2 = x 2 1 (pp.676-683)Graph the equation: x 2 +4 y 2 =4 (pp.665-670)In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { y= x 2 +1 y=x+1In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { y= x 2 +1 y=4x+1In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { y= 36 x 2 y=8xIn Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { y= 4 x 2 y=2x+4In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { y= x y=2xIn Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { y= x y=6xIn Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { y= x y=6xIn Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { y=x1 y= x 2 6x+9In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { x 2 + y 2 =4 x 2 +2x+ y 2 =0In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { x 2 + y 2 =8 x 2 + y 2 +4y=0In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { y=3x5 x 2 + y 2 =5In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { x 2 + y 2 =10 y=x+2In Problems 5-24, graph each equation of the system. Then solve the system to find the points of intersection. { x 2 + y 2 =4 y 2 x=4
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