Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus
9AYU10AYU11AYU12AYUIn problems 7-18, write the augmented matrix of the given system of equations. { x+yz=2 3x2y=2 5x+3yz=114AYU15AYU16AYUIn 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 5 | 2 5 ] R 2 =2 r 1 + r 2In 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 5 | 3 4 ] R 2 =2 r 1 + r 2In 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 3 5 3 5 3 4 6 4 | 3 6 6 ] R 2 =3 r 1 + r 2 R 3 =5 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 4 3 3 5 2 3 3 4 | 5 5 6 ] R 2 =4 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 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 3974, solve each system of equations using matrices ( row operations). If the system has no solution, say that it is inconsistent. {3x6y=45x+4y=5In 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 , solve each system of equations using matrices ( row operations). If the system has no solution, say that it is inconsistent.
50AYU51AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYU61AYU62AYUIn 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=164AYU65AYU66AYU67AYU68AYUIn problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. { 2x+3yz=3 xyz=0 x+y+z=0 x+v+3z=570AYUIn 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=372AYU73AYU74AYU75AYUCurve Fitting Find the function f( x )=a x 3 +b x 2 +cx+d for which f( 2 )=10 , f( 1 )=3 , f( 1 )=5 and f( 3 )=15 .Nutrition 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?Nutrition A dietitian at General Hospital wants a patient to have a meal that has 47 grams (g) of protein, 58 g of carbohydrates, and 630 milligrams (mg) of calcium. The hospital food service tells the dietitian that the dinner for today is pork chops, corn on the cob, and 2 milk. Each serving of pork chops has 23g of protein, 0g of carbohydrates, and 10 mg of calcium. Each serving of corn on the cob contains 3 g of protein, 16 g of carbohydrates, and 10 mg of calcium. Each glass of 2 milk contains 9 g of protein. 13 g of carbohydrates, and 300 mg of calcium. How many servings of each food should the dietitian provide for the patient?Financial Planning Carletta has 10,000 to invest. As her financial consultant, you recommend that she invest in Treasury bills that yield 6 . Treasury bonds that yield 7 , and corporate bonds that yield 8 . Carletta wants to have an annual income of 680 . and the amount invested in corporate bonds must be half that invested in Treasury bills. Find the amount in each investment.Landscaping A landscape company is hired to plant trees in three new subdivisions. The company charges the developer for each tree planted, an hourly rate to plant the trees, and a fixed delivery charge. In one subdivision it took 166 labor hours to plant 250 trees for a cost of 7520 . In a second subdivision it took 124 labor hours to plant 200 trees for a cost of 5945 . In the final subdivision it took 200 labor hours to plant 300 trees for a cost of 8985 . Determine the cost for each tree, the hourly labor charge, and the fixed delivery charge.Production 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?82AYU83AYU84AYU85AYU86AYU87AYU88AYU89AYU90AYU91AYU1AYU2AYU3AYU4AYU5AYU6AYU[ 6 4 1 3 ][ 8 3 4 2 ]9AYU10AYU[ 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=4In Problem 15-42, solve each system of equations using Cramers Rule if it is applicable. If Cramers Rule is not applicable, write, Not applicable. {4x6y=427x+4y=1{ 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=429AYU{ 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=12In Problem 15-42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, write, “Not applicable”.
{ 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 ]=0Geometry: Area of a Triangle A triangle has vertices ( x 1 , x 2 ),( x 2 , y 2 ),and( x 3 , y 3 ) . The area of the triangle is given by the absolute value of D , where D= 1 2 | x 1 x 2 x 3 y 1 y 2 y 3 1 1 1 | . Use this formula to find the area o9f a triangle with vertices ( 2, 3 2 ),( 5,2 ),and( 6,5 ) .60AYU61AYU62AYU63AYU64AYU65AYU1AYU2AYU3AYU4AYU5AYU6AYU7AYU8AYUIn Problems 9-26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, say "not defined.� A=[ 0 3 5 1 2 6 ] B=[ 4 1 0 2 3 2 ] C=[ 4 6 2 1 2 3 ] A+BIn Problems 9-26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, say "not defined.� A=[ 0 3 5 1 2 6 ] B=[ 4 1 0 2 3 2 ] C=[ 4 6 2 1 2 3 ] ABIn Problems 9-26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, say "not defined.� A=[ 0 3 5 1 2 6 ] B=[ 4 1 0 2 3 2 ] C=[ 4 6 2 1 2 3 ] 4AIn Problems 9-26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, say "not defined.� A=[ 0 3 5 1 2 6 ] B=[ 4 1 0 2 3 2 ] C=[ 4 6 2 1 2 3 ] 3BIn Problems 9-26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, say "not defined.� A=[ 0 3 5 1 2 6 ] B=[ 4 1 0 2 3 2 ] C=[ 4 6 2 1 2 3 ] 3A2BIn Problems 9-26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, say "not defined.� A=[ 0 3 5 1 2 6 ] B=[ 4 1 0 2 3 2 ] C=[ 4 6 2 1 2 3 ] 2A+4BIn Problems 9-26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, say "not defined.� A=[ 0 3 5 1 2 6 ] B=[ 4 1 0 2 3 2 ] C=[ 4 6 2 1 2 3 ] ACIn Problems 9-26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, say "not defined.� A=[ 0 3 5 1 2 6 ] B=[ 4 1 0 2 3 2 ] C=[ 4 6 2 1 2 3 ] BCIn Problems 9-26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, say "not defined.� A=[ 0 3 5 1 2 6 ] B=[ 4 1 0 2 3 2 ] C=[ 4 6 2 1 2 3 ] ABIn Problems 9-26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, say "not defined.� A=[ 0 3 5 1 2 6 ] B=[ 4 1 0 2 3 2 ] C=[ 4 6 2 1 2 3 ] BA19AYU20AYU21AYU22AYU23AYU24AYUIn Problems 27-34, determine whether the product is defined. If it is defined, find the product; if it is not, say "not defined." [ 2 2 1 0 ][ 2 1 4 6 3 1 3 2 ]In Problems 27-34, determine whether the product is defined. If it is defined, find the product; if it is not, say "not defined." [ 4 1 2 1 ][ 6 6 1 0 2 5 4 1 ]In Problems 27-34, determine whether the product is defined. If it is defined, find the product; if it is not, say "not defined." [ 1 2 3 0 1 4 ][ 1 1 2 2 0 4 ]In Problems 27-34, determine whether the product is defined. If it is defined, find the product; if it is not, say "not defined." [ 1 3 0 1 2 5 ][ 2 8 1 3 6 0 ]29AYU30AYUIn Problems 35-44, each matrix is nonsingular. Find the inverse of each matrix. [ 2 1 1 1 ]In Problems 35-44, each matrix is nonsingular. Find the inverse of each matrix. [ 3 1 2 1 ]In Problems 35-44, each matrix is nonsingular. Find the inverse of each matrix. [ 6 5 2 2 ]In Problems 35-44, each matrix is nonsingular. Find the inverse of each matrix. [ 4 1 6 2 ]In Problems 35-44, each matrix is nonsingular. Find the inverse of each matrix. [ 2 1 a a ]a0In Problems 35-44, each matrix is nonsingular. Find the inverse of each matrix. [ b 3 b 2 ]b0In Problems 35-44, each matrix is nonsingular. Find the inverse of each matrix. [ 1 1 1 0 2 1 2 3 0 ]In Problems 35-44, each matrix is nonsingular. Find the inverse of each matrix. [ 1 0 2 1 2 3 1 1 0 ]In Problems 35-44, each matrix is nonsingular. Find the inverse of each matrix. [ 1 1 1 3 2 1 3 1 2 ]In Problems 35-44, each matrix is nonsingular. Find the inverse of each matrix. [ 3 3 1 1 2 1 2 1 1 ]In Problems 4564, use the inverses found in Problems 3544 to solve each system of equations. {2x+y=1x+y=3 Problems 3544, each matrix is nonsingular. Find the inverse of each matrix. [2111]In Problems 45-64, use the inverses found in Problems 35-44 to solve each system of equations. { 3xy=8 2x+y=4In Problems 45-64, use the inverses found in Problems 35-44 to solve each system of equations. { 2x+y=0 x+y=5In Problems 45-64, use the inverses found in Problems 35-44 to solve each system of equations. { 3xy=4 2x+y=5In Problems 45-64, use the inverses found in Problems 35-44 to solve each system of equations. { 6x+5y=7 2x+2y=2In Problems 45-64, use the inverses found in Problems 35-44 to solve each system of equations. { 4x+y=0 6x2y=14In Problems 45-64, use the inverses found in Problems 35-44 to solve each system of equations. { 6x+5y=13 2x+2y=5In Problems 45-64, use the inverses found in Problems 35-44 to solve each system of equations. { 4x+y=5 6x2y=9In Problems 45-64, use the inverses found in Problems 35-44 to solve each system of equations. { 2x+y=3 ax+ay=a a0In Problems 45-64, use the inverses found in Problems 35-44 to solve each system of equations. { bx+3y=2b+3 bx+2y=2b+2 b0In Problems 45-64, use the inverses found in Problems 35-44 to solve each system of equations. { 2x+y= 7 a ax+ay=5 a0In Problems 45-64, use the inverses found in Problems 35-44 to solve each system of equations. { bx+3y=14 bx+2y=10 b0In Problems 4564, use the inverses found in Problems 3544 to solve each system of equations. {xy+z=42y+z=12x3y=4 Problems 3544, each matrix is nonsingular. Find the inverse of each matrix. [111021230]In Problems 45-64, use the inverses found in Problems 35-44 to solve each system of equations. { x+2z=6 x+2y+3z=5 xy=6In Problems 45-64, use the inverses found in Problems 35-44 to solve each system of equations. { xy+z=2 2y+z=2 2x3y= 1 2In Problems 45-64, use the inverses found in Problems 35-44 to solve each system of equations. { x+2z=2 x+2y+3z= 3 2 xy=257AYU58AYU59AYU60AYU61AYU62AYU63AYU64AYU65AYU66AYU67AYU68AYU69AYU70AYU71AYU72AYU73AYU74AYU75AYUIn Problems 79-86, algebraically solve each system of equations using any method you wish. { 2x+8y=8 x+7y=1377AYU78AYU79AYU80AYU81AYU82AYU83AYU84AYU85AYU86AYU87AYU88AYU89AYU90AYU91AYU92AYU93AYUTrue or False The equation ( x1 ) 2 1=x( x2 ) is an example of an identity. (p. A43)2AYU3AYU4AYUIn 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 16AYUIn 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 19AYU10AYU11AYU12AYUIn 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 )15AYUIn 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 )19AYU20AYU21AYU22AYU23AYU24AYU25AYU26AYU27AYU28AYUIn problems 13-46, find the partial fraction decomposition of each rational expression. x 2 +2x+3 ( x+1 )( x 2 +2x+4 )30AYU31AYUIn 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 )35AYU36AYU37AYU38AYU39AYU40AYUIn problems 13-46, find the partial fraction decomposition of each rational expression. x 3 ( x 2 +16 ) 342AYU43AYU44AYUIn 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 8Graph the equation: y=3x+2 (pp.35-37)2AYU3AYU4AYUIn 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 =0