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Questions and Answers of College Algebra

List the elements in each set.{x|x is an irrational number that is also rational}
List the elements in each set.{r|r is a number that is both positive and negative}
Write each fraction in lowest terms. 16 64
Perform the indicated operations. 104 3+ 6(-4) .
Write each expression using exponents. (-9)(-9)(-9)
Find each sum or difference. 13 + (-4)
Write each fraction in lowest terms. 144 120
Simplify each expression.5k + 3k
Use set-builder notation to describe each set.{2, 4, 6, 8}
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”. 03
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. 4x + 5y = -3 -2y = -8
In Problems 17–50, find the partial fraction decomposition of each rational expression. x + 1 x²(x - 2)
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”. 03
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 -3 -4 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”. -x + 2y = 5 4x8y = 6
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. 3x - бу = 2 5x +4y = 1 =
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. 5 -3 1 2-5 6 14 -4 -2 -2 6 R₁ =
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
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. 2x + 4y || 2/3 3x-5y = -10 =
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 در 00 |
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”.AC +
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. [2x + y = 1 4x + 2y = 3
In Problems 17–50, find the partial fraction decomposition of each rational expression. 2x + 4 x³ - 1
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.
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 2 14 6 目 1 0 3 1 3 2
In Problems 17–50, find the partial fraction decomposition of each rational expression. x + 1 x²(x - 2)²
In Problems 17–50, find the partial fraction decomposition of each rational expression. x² 2 (x − 1)²(x + 1)²
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. x - y = 5 -3x + 3y = 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 -6 6 1 0 [1][2 2 1 2 5 4 -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”. [3x - 2y = 0 5x+10y = 4
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. [2x - y = 0 4x + 2y = 12
In Problems 27–34, determine whether the product is defined. If it is defined, find the product; if it is not write “not defined.” 1 -1 -3 0 25 2 8 -1 3 6 0 لنا
In Problems 17–50, find the partial fraction decomposition of each rational expression. x - 3 (x + 2) (x + 1)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”. 2 + y = -2 x - 2y = 8
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. 48 x + 2y = 4 (2x + 4y = 8
In Problems 27–34, determine whether the product is defined. If it is defined, find the product; if it is not write “not defined.” 0 23 -1 4 12 10 24 -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”. 2x + 3y = 6 1 x - y = 2
In Problems 17–50, find the partial fraction decomposition of each rational expression. x² + x 2 (x + 2) (x − 1)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-5y = 3 15x + 5y = 21
In Problems 17–50, find the partial fraction decomposition of each rational expression. x + 4 x²(x² + 4)
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 1 3 2 2 x + ||
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. 3x - y = 7 19х - Зу = 21
In Problems 17–50, find the partial fraction decomposition of each rational expression. 10x² + 2x (x - 1)²(x² + 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.” 10 1 1 24 1 6 8 61 3 6 32 2 -1
In Problems 17–50, find the partial fraction decomposition of each rational expression. x² + 2x + 3 (x + 1) (x² + 2x + 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 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 as
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. 2x-3y=-1 Зу 10x + y = 11 У
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 2y + x + 3y - 2z z
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. [3x - 2y = 0 5x + 10y = 4
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 0 −1 -2 3 1 12 01 2 6 1 -1 2 _0
In Problems 17–50, find the partial fraction decomposition of each rational expression. x² - 11x - 18 X x(x² + 3x + 3) 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 as
Which matrix is in reduced row echelon form? (a) (c) 1 2 3-1 12 C 0 0 | 9 28 (b) (d) 10 0 1 12 _01 4 4
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 + y + z z = x = 2x - 3y + 4z 5x +
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. 2x + 3y = 6 1 2 x - y
In Problems 7–14, find the value of each determinant. 64 -1 3
In Problems 7–18, write the augmented matrix of the given system of equations. (2x + 3y - 60 4x - 6y + 2 = 0
In Problems 7–14, find the value of each determinant. 8 4 -3 2
In Problems 5–16, determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression. x³ +
In Problems 7–18, write the augmented matrix of the given system of equations, 9x - y = 0 У (3x-y - 4 = 0
In Problems 7–14, find the value of each determinant. -3 -1 4 2
In Problems 5–16, determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression.
True or False If A and B are square matrices, then AB = BA.
In Problems 7–18, write the augmented matrix of the given system of equations. f0.01x0.03y = 0.06 [0.13x + 0.10y = 0.20
In Problems 7–14, find the value of each determinant. -4 -4 2 -5 3
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”.A - B
In Problems 7–14, find the value of each determinant. 4 -1 2 25
In Problems 5–16, determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression. x³ +
If any two rows of a determinant are interchanged, its value: (a) Changes sign (b) Becomes zero (c) Remains the same (d) No longer relates to the original value.
In Problems 5–16, determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression. 5x²
In Problems 7–14, find the value of each determinant. 13 -2 UN 6 1 -5 8 2 3
In Problems 7–18, write the augmented matrix of the given system of equations. y + z = 10 3x + 3y = 5 x + y + 2z = 2 N 52
If a system of two linear equations in two variables is inconsistent, then the graphs of the lines in the system are_______ .(a) Intersecting (b) Parallel (c) Coincident (d)
In Problems 7–18, write the augmented matrix of the given system of equations. 4 3* 1 x + 4 3 1 3.Y || || 3/4 23 2
In Problems 9–18, verify that the values of the variables listed are solutions of the system of equations. x - y = 3 -3x + y = 1 x = -2, y = -5; (-2,-5)
A matrix that has no inverse is called a(n): (a) Zero matrix (b) Nonsingular matrix (c) Identity matrix (d) Singular matrix
In Problems 7–14, find the value of each determinant. 6 1 -1 -1 -3 2 0 4
In Problems 5–16, determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression. 3x +
In Problems 7–18, write the augmented matrix of the given system of equations. z = 2 3x - 2y = 2 z = 1 x + y 5x + 3y
In Problems 9–18, verify that the values of the variables listed are solutions of the system of equations. 3x + 3y + 2z = = 4 y-z 0 2y3z = -8 x = 1, y = -1, z = 2; (1,-1,2)
In Problems 7–18, write the augmented matrix of the given system of equations. 5x - y - y z=0 x + y = 5 2x - 3z = 2
In Problems 7–14, find the value of each determinant. 3-9 -9 4 4 0 1 1 8 -3
In Problems 5–16, determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression. 2x
In Problems 5–16, determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression. x(x -
In Problems 7–18, write the augmented matrix of the given system of equations. 2x + 3y - 4z 0 x 5z + 2 = 0 x + 2y3z = -2
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”.CB 03
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”.BC 03
In Problems 7–18, write the augmented matrix of the given system of equations. y z = 10 - y + 2z = -1 5 0 x - 2x + -3x + 4y 4x - 5y + Z ||
In Problems 9–18, verify that the values of the variables listed are solutions of the system of equations. 3x + 3y + 2z = 4 x - 3y + 3y + z = 10 5x2y3z = 8 x = 2, y = -2, z = 2; (2, -2, 2)
In Problems 17–50, find the partial fraction decomposition of each rational expression. 1 (x + 1)(x² + 4)
In Problems 7–18, write the augmented matrix of the given system of equations. 5 x = y + 2z -w= x + 3y - 4z + 2w = 2 3x-y5z w = -1
In Problems 9–18, verify that the values of the variables listed are solutions of the system of equations. 4x - 5z = 6 5yz -17 24 = -x 6y + 5z = - x = 4, y = -3, z = 2; (4, -3,2)
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”. 4x + 5y = -3 -2y = -4
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”.AB 03
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”. | 4x - бу = -42 7x + 4y = -1
In Problems 17–50, find the partial fraction decomposition of each rational expression. X (x - 1)(x - 2)
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”.(A +
In Problems 17–50, find the partial fraction decomposition of each rational expression. 3x (x + 2) (x - 4) -
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 - 10x + Зу = 10y -1 5

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