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mathematics
precalculus

Questions and Answers of Precalculus

Problems 94–103. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.
Problems 91 – 100. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
In Problems 17–50, find the partial fraction decomposition of each rational expression. x² + 1 x3 + x2 – 5x+3
In Problems 44 and 45 graph each inequality. 3x + 4y ≤ 12
In Problems 1 – 10, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, state that it is inconsistent. 130 3x - 2y = 0 2x +
In Problems 23 – 34, graph each system of linear inequalities. 3x - у 2 6 x + 2y < 2
Reduce to lowest terms: 3x - 12 x2 - 16
In Problems 17–50, find the partial fraction decomposition of each rational expression. x + 1 x²(x - 2)
In Problems 25 – 54, solve each system. Use any method you wish. 2x² + y² = xy = 18 4
In Problems 45–56, analyze each equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation.x2 + 4x + 4y2 − 8y + 4 = 0
In 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, write “not defined”CA +
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 4x + 5y = -3 -2y = -8
In Problems 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 + 2y = 5 4x - 8y = 6
In 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, write “not defined”CA
Open the “Parabola Up_Down” interactive figure, which is available in the Video & Resource Library of MyLab Math (under Interactive Figures) or at bit.ly/3raFUGB.(a) U se the sliders to set a
In Problems 23 – 34, graph each system of linear inequalities. 2x-y≤ 4 3x+2y≧-6
In Problems 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.” 2x - 4y = - 2 3x + 2y = = 3 دیا
In Problems 17–50, find the partial fraction decomposition of each rational expression. 1 .3 x³ - 8
In Problems 25 – 54, solve each system. Use any method you wish. x² - y² = 21 x + y = 7
Graph the equation: y = 3x + 2
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 3x - бу = 2 5x +4y = 1
In Problems 23 – 34, graph each system of linear inequalities. 4x - 5y ≤0 2x y ≥ 2
In Problems 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.” 3x + 3y = 3 4x + 2y 3813
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 x1, x2, x3, x4
In Problems 17–50, find the partial fraction decomposition of each rational expression. 2x + 4 3 x³ - 1
In Problems 23 – 34, graph each system of linear inequalities. 2x - 3y ≤ 0 3x + 2y ≤ 6
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 2x + y = 1 4x + 2y = 3
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 213 2x +4y = 3x-5y=-10
In Problems 25 – 54, solve each system. Use any method you wish. у y = 3x + 2 4 3x2 + y2 =
In Problems 23 – 34, graph each system of linear inequalities. 4x - y ≥ 2 x + 2y ≥ 2
In Problems 17–50, find the partial fraction decomposition of each rational expression. x + 1 x²(x - 2)²
In Problems 27 – 34, determine whether the product is defined. If it is defined, find the product; if it is not, write “not defined.” 2-2 1 2 14 6 0 3 1 3 2
In Problems 25 – 54, solve each system. Use any method you wish. x² - 4y² = 16 = 2 2y = x
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. x - y = 5 -3x + 3y = 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 x1, x2, x3, x4
In Problems 23 – 34, graph each system of linear inequalities. x - 2y ≤ 6 2x - 4y ≥ 0
In Problems 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.” 3x - 2y = 0 5x + 10y = 4
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 x1, x2, x3, x4
In Problems 25 – 54, solve each system. Use any method you wish. x+y+1= 0 x2 +у2 + бу - x=-5
In Problems 17–50, find the partial fraction decomposition of each rational expression. x - 3 (x + 2)(x + 1)² 2
In Problems 25 – 54, solve each system. Use any method you wish. 2x²xy + y² = 8 xy = 4
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 2x - y = 0 4x + 2y = 12
In Problems 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.” 2x + 3y = 6 x - - y= 2
In Problems 23 – 34, graph each system of linear inequalities. x + 4y ≤ 8 x + 4y > 4
In Problems 17–50, find the partial fraction decomposition of each rational expression. x² + x (x + 2)(x - 1)²
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 3x + 3y=-1 4x +y= 8/3
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 x1, x2, x3, x4
In Problems 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.” + y = -2 x - 2y = 8
In Problems 17–50, find the partial fraction decomposition of each rational expression. x + 4 x²(x² + 4) -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 x1, x2, x3, x4
In Problems 32 and 33, use properties of determinants to find the value of each determinant if it is known that x A a b 8.
In Problems 25 – 54, solve each system. Use any method you wish. 9x²8xy + 4y² = 70 3x + 2y = 10
In Problems 23 – 34, graph each system of linear inequalities. 2x + y 2 -2 2x + y 2 2
In Problems 27 – 34, determine whether the product is defined. If it is defined, find the product; if it is not, write “not defined.” -4 1 0 2 3 -1
In Problems 23 – 34, graph each system of linear inequalities. x - 4y ≤ 4 x - 4y ≥ 0
In Problems 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.” 3x-5y=3 15x + 5y = 21
In Problems 17–50, find the partial fraction decomposition of each rational expression. 10x² + 2x 2 (x - 1)²(x² + 2)
In Problems 25 – 54, solve each system. Use any method you wish. 2у2 - 3xy + бу + 2x + 4 = 0 - 2x-3y + 4 = 0
In Problems 27 – 34, determine whether the product is defined. If it is defined, find the product; if it is not, write “not defined.” 2 -1 8 -6 0 256 5 64 2 -3 51 90 7
In Problems 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.” 2x - y = -1 3 -1/2y = 2 x +
An airline has two classes of service: first class and coach. Management’s experience has been that each aircraft should have at least 8 but no more than 16 first-class seats and at least 80 but no
In Problems 32 and 33, use properties of determinants to find the value of each determinant if it is known that x A a b 8.
In Problems 17–50, find the partial fraction decomposition of each rational expression. x² + 2x + 3 (x + 1)(x² + 2x + 4)
In Problems 25 – 54, solve each system. Use any method you wish. x² - 4y² + 7 = 0 3x² + y² = 31
In Problems 23 – 34, graph each system of linear inequalities. 2x + 3y > 6 2x + 3y ≤ 0
In Problems 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 + y 3x - 2y + z= 6 z = -5 14 x + 3y
Problems 34–43. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
In Problems 25 – 54, solve each system. Use any method you wish. 3x22y² + 5 = 0 2x² - y² + 2 = 0
In Problems 23 – 34, graph each system of linear inequalities. 2x + y 20 2x + y 22
In Problems 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.” y + z = -4 2x - 3y + 4z = -15 5x +
In Problems 17–50, find the partial fraction decomposition of each rational expression. (3x − 2)(2x + 1)
In Problems 35 – 44, each matrix is nonsingular. Find the inverse of each matrix. 21 1 1
In Problems 25 – 54, solve each system. Use any method you wish. 7x²3y² + 5 = 0 3x2 + 5y2 = 12
In Problems 35 – 42, graph each system of inequalities. x² + y² ≤9 x + y 23
In Problems 35 – 42, graph each system of inequalities. 2 x² + y² ≥ 9 x + y ≤ 3
In Problems 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 + 3y - z = -2 3у 2x 2х - бу
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. ·x + y = -2 x - 2y = 8
In Problems 25 – 54, solve each system. Use any method you wish. x² - 3у² + 1 = = 0 2x² - 7y² + 5 = 0
In Problems 35 – 44, each matrix is nonsingular. Find the inverse of each matrix. 3 -2 -1 1
In Problems 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 + 4y - 3z = -8 - 3x - y + x + y +
In Problems 17–50, find the partial fraction decomposition of each rational expression. 1 (2x + 3)(4x - 1)
Problems 34–43. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
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 x1, x2, x3, x4
In Problems 17–50, find the partial fraction decomposition of each rational expression. x x² + 2x - 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 x1, x2, x3, x4
In Problems 25 – 54, solve each system. Use any method you wish. x2 + 2xy = 10 3x² - xу = 2 ху
In Problems 35 – 42, graph each system of inequalities. y≥ x² - 4 y≤ x -2
Problems 34–43. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.The
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. IN 1 X + +3y = 3y = 3 = -1
In Problems 35 – 44, each matrix is nonsingular. Find the inverse of each matrix. 65 22
In Problems 35 – 42, graph each system of inequalities. < x y > x VINI
In Problems 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 - 2y + 3z = 1 3x + y - 2z = 0 2x -
In Problems 17–50, find the partial fraction decomposition of each rational expression. x2 -x-8 (x + 1)(x2 + 5x + 6)
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 3w - x + 3 ZY || -5 y = 11
In Problems 25 – 54, solve each system. Use any method you wish. 5xy + 13y2 + 36 = 0 xy + 7y² = 6
In Problems 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.” xy + 2z = 3x + 2y = -2x + 2y 4z
Problems 34–43. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
In Problems 25 – 54, solve each system. Use any method you wish. 2x² + y² = 2 x22y² + 8 = 0
In Problems 35 – 44, each matrix is nonsingular. Find the inverse of each matrix. -4 1 6-2
In Problems 35 – 42, graph each system of inequalities. x² + y² ≤ 16 y > x² - 4

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