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College Algebra 7th Edition Robert F Blitzer - Solutions

Fill in each blank so that the resulting statement is true.Using Gaussian elimination on linear systems in three variables, we obtained each of the matrices shown in Exercises. State whether the linear system has one solution, no solution, or infinitely many solutions._______ . 1 0 0 1 2 19 1 2
Solve each equation or inequality in Exercises 1–6. 5x+8
In Exercises 1–2, perform each matrix row operation and write the new matrix. 2 -2 1 2 6 4 1 -1 3 -1 25 R₁
Bottled water and medical supplies are to be shipped to survivors of an earthquake by plane. The bottled water weighs 20 pounds per container and medical kits weigh 10 pounds per kit. Each plane can carry no more than 80,000 pounds. If x represents the number of bottles of water to be shipped per
Fill in each blank so that the resulting statement is true.Consider the matrixWe can obtain 0 in the position shaded by a rectangle if we multiply the top row of numbers by_________ and add these products to the_________ row of numbers. We can obtain 0 in the position shaded by an oval if we
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. 2x x - 3x 4y + 3y + z = 5 7y + 2z = 12 - z = 3 35
Fill in each blank so that the resulting statement is true.A rectangular array of numbers, arranged in rows and columns and placed in brackets, is called a/an________ . The numbers inside the brackets are called________ .
Fill in each blank so that the resulting statement is true.The multiplicative identity matrix of order 2 is I2 =_______ .
Fill in each blank so that the resulting statement is true.The notation a34 refers to the element in the_______ row and________ column of a matrix.
In Exercises 1–5, use matrices to find the complete solution to each system of equations, or show that none exists. 2x + 4y + 5z = 2 x + y + 2z = 1 3x + 5y + 7z = 4
Fill in each blank so that the resulting statement isUsing Cramer’s Rule to solvewe obtain fx + y = 8 (x - y = -2,
Fill in each blank so that the resulting statement is true.The multiplicative identity matrix of order 3 is I3 =_______ .
Fill in each blank so that the resulting statement is true.The order of A = [2 3 7] is___________ .
Evaluate each determinant in Exercises 1–10. 4 5 8 9
In Exercises 1–12, find the products AB and BA to determine whether B is the multiplicative inverse of A. A || -2 -1 B = 1 1 2
In Exercises 1–2, solve each system of equations using matrices. x - 2y + z = 2 y = z = 1 [2x - y
In Exercises 1–4,a. Give the order of each matrix.b. If A = [aij], identify a32 and a23, or explain why identification is not possible. -6 4 -1 -9 0
In Exercises 3–6, letCarry out the indicated operations.2B + 3C A = 3 1 1 0 2 1 B = 1 [2 1. and C= 1 [43] -1 3
Fill in each blank so that the resulting statement is true.Using Gaussian elimination on linear systems in three variables, we obtained each of the matrices shown in Exercises. State whether the linear system has one solution, no solution, or infinitely many solutions._______ .
Fill in each blank so that the resulting statement is true.The augmented matrix for the systemis y + 4z = -4 у + z = 1 8 2x + 3x 4x + 3y + z
Solve each equation or inequality in Exercises 1–6. √2x + 4√x + 3 − 1 = 0
In Exercises 1–4, find the value of the objective function at each corner of the graphed region. What is the maximum value of the objective function? What is the minimum value of the objective function? Objective Function Z = 3x + 2y y TITI (4, 10) (3,2) (5, 12) TH (8,6) (7,4)
Fill in each blank so that the resulting statement is true.Consider the following system:We can eliminate x from Equations 1 and 2 by multiplying Equation 1 by_________ and adding equations. We can eliminate x from Equations 1 and 3 by multiplying Equation 1 by________ and adding equations. x +
In Exercises 1–26, graph each inequality. 3x - бу = 12
Fill in each blank so that the resulting statement is true.When solvingby the substitution method, we obtain x = -4 or x = 0, so the solution set is_________ . x² - 4y = = 4 x + y = -1 lx
In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. 5x+7 (x - 1)(x + 3)
Fill in each blank so that the resulting statement is true.The set of all points that satisfy a linear inequality in two variables is called the________ of the inequality.
Fill in each blank so that the resulting statement is true.An algebraic expression in two or more variables describing a quantity that must be maximized or minimized is called a/an________ function.
In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (-3,5) 9x + 7y=8 8x - 9y -69
In Exercises 1–4, determine if the given ordered triple is a solution of the system. (5, -3, -2) x + y + z = x + 2y - 3z 3x + 4y + 2z 0 5 = -1
In Exercises 1–12, solve each system by the method of your choice. fx = 3y - 7 4x + 3y = 2
Determine whether each partial fraction decomposition is set up correctly. If the setup is incorrect, make the necessary changes to produce the correct decomposition.Correct or incorrect:______ . 3x (x + 5)(x - 4)2 - А x +5 + B x - 4 + C x-4
In Exercises 1–5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. Sy y = 4x + 1 [3x + 2y = 13
In Exercises 1–5, solve the system. [x = y + 4 3x + 7y -18
In Exercises 1–18, solve each system by the substitution method. √x + y = 2 y = x² - 4
In Exercises 1–4, find the value of the objective function at each corner of the graphed region. What is the maximum value of the objective function? What is the minimum value of the objective function? Objective Function 5x + 6y y = IITI (2,10) (1,2). (7,5) (8,3) X
The figure shows the graph of y = f(x) and its two vertical asymptotes. Use the graph to solve Exercises 1–10.Find the domain and the range of f. 2 I 8996 y = f(x) 0000 X
In Exercises 1–26, graph each inequality. x + 2y = 8
Determine whether each partial fraction decomposition is set up correctly. If the setup is incorrect, make the necessary changes to produce the correct decomposition.Correct or incorrect:________ . 7x (x + 2)(x - 3) А x + 2 + в x - 3
Use the graphs of the linear functions to solve Exercises 53–54.Write the linear system whose solution set is {(6, 2)}. Express each equation in the system in slope-intercept form. x + 3y = 12 y. 5+ -3-2 x - 3y = 6 CIV -3+ x - 3y = -6 HAX x - y = 4 TO X
In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. √x² + y² ≤ 1 y = x² > 0
In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. 11x 10 (x − 2)(x + 1)
In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (2,3) Jx √x + 3y = 11 x - 5y = -13
In Exercises 1–4, determine if the given ordered triple is a solution of the system. (2, -1, 3) x + y + z = x - 2y - z z = y2z = 2x - 4 1 −1 -1
In Exercises 47–52, solve each system by the method of your choice. 11 || -| + -14 || 1일
Find the partial fraction decomposition for 2/x(x + 2) and use the result to find the following sum: 2 2 1.3 3.5 + 2 5.7 2 99.101
In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution. [x² + y² ≤9 ly < −3x + 1
Fill in each blank so that the resulting statement is true.A solution to a system of linear equations in two variables is an ordered pair that__________ .
In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. [(x + 1)² + (y − 1)² < 16 (x + 1)² + (y - 1)² ≥ 4
Fill in each blank so that the resulting statement is true.A solution of a system of linear equations in three variables is an ordered_______ of real numbers that satisfies all/some of the equations in the system.
In Exercises 47–52, solve each system by the method of your choice. 7 || + -3 ||
In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. [(x - 1)² + (y + 1)² < 25 (x - 1)² + (y + 1)² ≥ 16
Fill in each blank so that the resulting statement is true.The ordered pair (3, 2) is a/an________ of the= inequality x + y > 1 because when 3 is substituted for and 2 is substituted for________ , the true statement________ is obtained.
In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution. fx2 + y = 16 lx + y < 2
Fill in each blank so that the resulting statement is true.A system of two equations in two variables that contains at least one equation that cannot be expressed in the form Ax + By = C is called a system of________ equations.
A modernistic painting consists of triangles, rectangles, and pentagons, all drawn so as to not overlap or share sides. Within each rectangle are drawn 2 red roses and each pentagon contains 5 carnations. How many triangles, rectangles, and pentagons appear in the painting if the painting contains
Fill in each blank so that the resulting statement is true.A method for finding the maximum or minimum value of a quantity that is subject to various limitations is called_________ .
Describe how the systemcould be solved. Is it likely that in the near future a graphing utility will be available to provide a geometric solution (using intersecting graphs) to this system? Explain. z - 2w = -8 18 10 3 x + y - z x - 2y + 3z + w = 2x + 2y + 2z - 2w = 2x + y z + w =
In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. [x² + y² > 1 [x² + y²
Find the partial fraction decomposition for 1/x(x + 1) and use the result to find the following sum: 1 1 1.2 2.3 1 3.4 1 99.100
In Exercises 47–50, write the partial fraction decomposition of each rational expression. 2 - ax 1 - bx + ab (a + b)
In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution. (2x + y < 4 2x + y > 6
For the linear function f(x) = mx + b, f(-3) = 23 and f(2) = -7. Find m and b.
In Exercises 47–52, solve each system by the method of your choice. -9x + y = 45 = x3 + 5x2
Explain what is meant by the partial fraction decomposition of a rational expression.
In Exercises 49–50, solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0 and b ≠ 0. 4ax + by = 3 6ax + 5by = 8
In Exercises 49–50, solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0 and b ≠ 0. [5ax + 4y = 17 ax + 7y = 22
In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution. 으 ≤x≤ 3 VI A 2 VI
In Exercises 47–48, solve each system by the method of your choice. x - y 3 x + 2 2 x + y 2 4 = 1 2 y + 4 3
In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. [x² + y² > 1 [x² + y² < 16 R
For the linear function f(x) = mx + b, f(-2) = 11 and f(3) = -9. Find m and b.
In Exercises 47–52, solve each system by the method of your choice. - 4x + y = 12 y = x² + 3x²
In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. √x² + y² ≤ 4 [x+y> 1
In Exercises 47–50, write the partial fraction decomposition of each rational expression. ax + b (x - c)² (c = 0)
In Exercises 47–48, solve each system by the method of your choice. x + 2 2 x + y 5 y + 4 3 نیا x - y 2 = 3 = 1 5/2
In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution. √x + y ≤ 6 ly ≥ 2x - 3
In Exercises 47–50, write the partial fraction decomposition of each rational expression. ax + b x² 2 - c² 2 (c = 0)
In Exercises 47–52, solve each system by the method of your choice. 4x2 + xy = 30 x² + 3ху = -9
In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution. < x ly≤2
In Exercises 48–51, determine whether each statement makes sense or does not make sense, and explain your reasoning.Because the percentage of the U.S. population that was foreign-born decreased from 1910 through 1970 and then increased after that, a quadratic function of the form f(x) =
In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. [x² + y² ≤ 16 [x+y > 2
In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution. (2x - y = 4 x + 2y < 2
In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. [y=x² - 4 [x - y = 2
In Exercises 47–50, write the partial fraction decomposition of each rational expression. 1 x² - c² 2 (c = 0)
In Exercises 48–51, determine whether each statement makes sense or does not make sense, and explain your reasoning.I’m solving a three-variable system in which one of the given equations has a missing term, so it will not be necessary to use any of the original equations twice when I reduce
In Exercises 47–52, solve each system by the method of your choice. (2x² + xy = 6 [x² + 2xy = 0
In Exercises 43–46, perform each long division and write the partial fraction decomposition of the remainder term. x² + 2x³ 4x² + x - 3 x²-x-2
In Exercises 48–51, determine whether each statement makes sense or does not make sense, and explain your reasoning.A system of linear equations in three variables, x, y, and z, cannot contain an equation in the form y = mx + b.
In Exercises 48–51, determine whether each statement makes sense or does not make sense, and explain your reasoning.Solving a system in three variables, I found that x = 3 and y = -1. Because z represents a third variable, z cannot equal 3 or -1.
In Exercises 43–46, let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers.The sum of three times a first number and twice a second number is 8. If the second number is subtracted from twice
In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution. 3x + 2y ≥ 6 = 2х + у ≥ 6
In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. Jy = x² - 1 lx - y = -1
In Exercises 43–46, perform each long division and write the partial fraction decomposition of the remainder term. x²-x² + 2 x³ = x² 2 - 3
In Exercises 43–46, perform each long division and write the partial fraction decomposition of the remainder term. x5 2 X x² - 4x + 4
AIDS is taking a deadly toll on southern Africa. Describe how to use the techniques that you learned in this section to obtain a model for African life span using projections with AIDS, shown by the red graph in the figure. Let x represent the number of years after 1985 and let y represent African
In Exercises 39–45, graph each inequality. y ≤ 2x
In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. fx + y > 3 x+y> -2
In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. √x +y > 4 lx + y > -1
In Exercises 43–46, let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers.The difference between the squares of two numbers is 5. Twice the square of the second number subtracted
In Exercises 39–45, graph each inequality. 2 y ≤ x² - 1

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