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Questions and Answers of College Algebra

Solve the problem.A sum of $5000 is invested in three accounts that pay 2%, 3%, and 4% interest rates. The amount of money invested in the account paying 4% equals the total amount of money invested
Solve each problem.In 2013, the amount spent by a typical American household on food was about $6602. For every $10 spent on food away from home, about $15 was spent on food at home. Find the amount
Solve each system, using the method indicated, if possible.(Cramer’s rule)7x + y - z = 42x - 3y + z = 2-6x + 9y - 3z = -6
Solve each system, using the method indicated, if possible.(Gauss-Jordan)2x + 4y + 4z = 4x + 3y + z = 4-x + 3y + 2z = -1
Solve each system, using the method indicated, if possible.(Elimination)x + y + z = 1-x + y + z = 5y + 2z = 5
Solve each system, using the method indicated, if possible.(Cramer’s rule)5x + 2y = -34x - 3y = -30
Solve each system, using the method indicated, if possible.(Gauss-Jordan)3x + 5y = -5-2x + 3y = 16
Solve each system, using the method indicated, if possible.(Elimination)2x - 3y = 185x + 2y = 7
Solve each system, using the method indicated, if possible.(Elimination)x - y = 6x - y = 4
Solve each system, using the method indicated, if possible.(Substitution)5x + 10y = 10x + 2y = 2
Solve each system, using the method indicated, if possible.(Substitution)2x + y = -4-x + 2y = 2
Find the partial fraction decomposition for the rational expression. 2x + 4 x3 – 2x2
Find the partial fraction decomposition for the rational expression. 4x2 - — Зх — 4 х3 + x2 — 2х
Find the partial fraction decomposition for the rational expression. — 2х2 — 24 х4 — 16
Find the partial fraction decomposition for the rational expression. .2 х4 — 1
Find the partial fraction decomposition for the rational expression. 3x6 + 3x4 + 3x x4 + x2
Find the partial fraction decomposition for the rational expression. 5x + 10x4 – 15x3 + 4x2 + 13x – 9 x3 + 2x2 – 3x
Find the partial fraction decomposition for the rational expression. 3x* + x3 + 5x² – x + 4 (x – 1)(x² + 1)²
Find the partial fraction decomposition for the rational expression. -x4 — 8х2 + Зх — 10 (x + 2)(x² + 4)²
Find the partial fraction decomposition for the rational expression. x4 + 1 x(x² + 1)2
Find the partial fraction decomposition for the rational expression. Зх — 1 x(2x² + 1)²
Find the partial fraction decomposition for the rational expression. 6x5 + 7x4 — х? + 2x Зx2 + 2х 1
Find the partial fraction decomposition for the rational expression. 2x5 + 3x* – 3x³ – 2x2 + x 2x2 + 5x + 2
Find the partial fraction decomposition for the rational expression. 3 x(х + 1)(х? + 1)
Find the partial fraction decomposition for the rational expression. x(2x + 1)(3x² + 4)
Find the partial fraction decomposition for the rational expression. 2x + 1 (x + 1)(x² + 2)
Find the partial fraction decomposition for the rational expression. Зх — 2 (x + 4)(3x² + 1)
Find the partial fraction decomposition for the rational expression. x²(x? – 2)
Find the partial fraction decomposition for the rational expression. -3 x²(x² + 5)
Find the partial fraction decomposition for the rational expression. х3 + 2 х3 — Зх2 + 2х
Find the partial fraction decomposition for the rational expression. x3 + 4 9х3 — 4х
Find the partial fraction decomposition for the rational expression. x²(x + 3)
Find the partial fraction decomposition for the rational expression. x2 x2 + 2x + 1
Find the partial fraction decomposition for the rational expression. 2x (x + 1)(x + 2)²
Find the partial fraction decomposition for the rational expression. 2х + 1 (х + 2)3
Find the partial fraction decomposition for the rational expression. 3 (x+ 1)(x+ 3)
Find the partial fraction decomposition for the rational expression. 4x? — х — 15 x(x + 1) (х — 1)
Find the partial fraction decomposition for the rational expression. x(х — 3)
Find the partial fraction decomposition for each rational expression. 4 x(1 – x)
Find the partial fraction decomposition for each rational expression. 5х — 3 х2 — 2х — 3
Find the partial fraction decomposition for each rational expression. х х2 + 4х — 5
Find the partial fraction decomposition for each rational expression. (x + 1)(x - 1)
Find the partial fraction decomposition for the rational expression. 4х + 2 (x + 2)(2x – 1)
Find the partial fraction decomposition for each rational expression. Зх — 1 x(х + 1)
Find the partial fraction decomposition for each rational expression. 3x(2x + 1)
Answer the question.In Exercise 5, after clearing fractions to decompose, the equation3x - 1 = A(2x2 + 1)2 + (Bx + C)(x)(2x2 + 1) + (Dx + E)(x)results. If we let x = 0, what is the value of A?
Answer the question.By what expression should we multiply each side ofso that there are no fractions in the equation? Dx + E (2г2 + 1)2 Зх — 1 Вх + C x(2к? + 1)? 2x2 + 1 х
In Exercise 3, after clearing fractions to decompose, the equation 3x - 2 = A(3x2 + 1) + (Bx + C)(x + 4) results. If we let x = -4, what is the value of A?Exercise 3 3x – 2 A Bx + C (x + 4)(3x2 +
Answer the question.By what expression should we multiply each side ofso that there are no fractions in the equation? Зх — 2 |(х+ 4)(3x2 + 1) Вх + C Зх? + 1 х+4
In Exercise 1, after clearing fractions to decompose, the equation A(2x + 1) + B(3x) = 5 results. If we let x = 0, what is the value of A?Exercise 1 A + 3x B Зx (2х + 1) 2х + 1
Answer each question.By what expression should we multiply each side ofso that there are no fractions in the equation? B A Зх 2х + 1 Зx(2х + 1)
The determinant of a 3 × 3 matrix A is defined as follows.Does the method of evaluating a determinant using “diagonals” extend to 4 × 4 matrices? a12 a13 fA 3 | а21 аzz аз |, then |А
Exercise 112. Evaluate the determinant by expanding about column 1 and using the method of cofactors. Do these methods give the same determinant for 3 × 3 matrices?Exercise 112Evaluate the
The determinant of a 3 × 3 matrix A is defined as follows.Evaluate the determinantusing the method of “diagonals.” a12 a13 fA 3 | а21 аzz аз |, then |А азі аз2 аз. a11 a13 a12 аз
The determinant of a 3 × 3 matrix A is defined as follows.The determinant of a 3 × 3 matrix can also be found using the method of “diagonals.”Step 1 Rewrite columns 1 and 2 of matrix A to the
In the following system, a, b, c, . . . , l are consecutive integers. Express the solution set in terms of z.ax + by + cz = dex + ƒy + gz = hix + jy + kz = l
Use Cramer’s rule to find the solution set if a, b, c, d, e, and ƒ are consecutive integers.ax + by = cdx + ey = ƒ
Solve each system for x and y using Cramer’s rule. Assume a and b are nonzero constants.x + by = bax + y = a
Solve each system for x and y using Cramer’s rule. Assume a and b are nonzero constants.b2x + a2y = b2ax + by = a
Solve each system for x and y using Cramer’s rule. Assume a and b are nonzero constants. ах + by
Solve each system for x and y using Cramer’s rule. Assume a and b are nonzero constants.bx + y = a2ax + y = b2
Write the sign array representing (-1)i+j for each element of a 4 × 4 matrix.
Find the area of a triangular lot whose vertices have the following coordinates in feet. Round the answer to the nearest tenth of a foot. (101.3, 52.7), (117.2, 253.9), and (313.1, 301.6)
A triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), as shown in the figure, has area equal to the absolute value of D, whereFind the area of each triangle having vertices at P, Q, and
A triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), as shown in the figure, has area equal to the absolute value of D, whereFind the area of each triangle having vertices at P, Q, and
A triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), as shown in the figure, has area equal to the absolute value of D, whereFind the area of each triangle having vertices at P, Q, and
A triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), as shown in the figure, has area equal to the absolute value of D, whereFind the area of each triangle having vertices at P, Q, and
(Refer to Exercise 87.) Use the following system of equations to determine the forces or weights W1 and W2 exerted on each rafter for the truss shown in the figure.Exercise 87.The simplest type of
The simplest type of roof truss is a triangle. The truss shown in the figure is used to frame roofs of small buildings. If a 100-pound force is applied at the peak of the truss, then the forces or
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.5x - 2y = 34y + z = 8x + 2z = 4
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.x + 2y = 103x + 4z = 7-y - z = 1
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.3x + 5y = -72x + 7z = 24y + 3z = -8
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.5x - y = -43x + 2z = 44y + 3z = 22
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.2x - 3y + z - 8 = 0-x - 5y + z + 4 = 03x - 5y + 2z - 12 = 0
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.4x - 3y + z + 1 = 05x + 7y + 2z + 2 = 03x - 5y - z - 1 = 0
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.3x - 2y + 4z = 14x + y - 5z = 2-6x + 4y - 8z = -2
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.-2x - 2y + 3z = 45x + 7y - z = 22x + 2y - 3z = -4
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.2x - y + 3z = 1-2x + y - 3z = 25x - y + z = 2
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.x + 2y + 3z = 44x + 3y + 2z = 1-x - 2y - 3z = 0
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.x + y + z = 42x - y + 3z = 44x + 2y - z = -15
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.2x - y + 4z = -23x + 2y - z = -3x + 4y + 2z = 17
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set. 3 2 3 -37 2
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set. = 2 31 3 -12 2
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.4x + 3y = 912x + 9y = 27
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.3x + 2y = 46x + 4y = 8
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.12x + 8y = 31.5x + y = 0.9
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.1.5x + 3y = 52x + 4y = 3
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.3x + 2y = -45x - y = 2
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.5x + 4y = 103x - 7y = 6
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.4x - y = 02x + 3y = 14
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.4x + 3y = -72x + 3y = -11
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.3x + 2y = -42x - y = -5
Use Cramer’s rule to solve each system of equations. If D = 0, then use another method to determine the solution set.x + y = 42x - y = 2
Use the determinant theorems to evaluate each determinant. 5 -1 -1 4 2 -3 1 -5 3 0 -2
Use the determinant theorems to evaluate each determinant. 5 -1 3 -6 2 -1 3 -6 4 -7 3 1 2.
Use the determinant theorems to evaluate each determinant. -2 0 3 6 3 2 -1
Use the determinant theorems to evaluate each determinant. 5 4 2 7 -4 4 -3 8 -3
Use the determinant theorems to evaluate each determinant. |-1 0 5 4 -3 3 8 2 9 -5 4 4 -1 10 2.
Use the determinant theorems to evaluate each determinant. 9 1 12 5 2 11 4 3
Use the determinant theorems to evaluate each determinant. 2 -1 3 4 10 4 5 6.

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