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mathematics
precalculus

Questions and Answers of Precalculus

Write the partial fraction decomposition of each rational expression. х х3 — 4х2 + 5х — 2
Write the partial fraction decomposition of each rational expression. .3 + 1 .4 х
Write the partial fraction decomposition of each rational expression. 7x + 3 .2 x³ – 2r? 3x
Write the partial fraction decomposition of each rational expression. (x² + 16)? .2
Write the partial fraction decomposition of each rational expression. x? + 2x + 3 (x² + 4)²
Write the partial fraction decomposition of each rational expression. х- x? – x - 8 (x + )(x² + 5x + 6)
Write the partial fraction decomposition of each rational expression. x? + 2x – 3
Write the partial fraction decomposition of each rational expression. (2x + 3)(4x – 1)
Write the partial fraction decomposition of each rational expression. х (3x – 2)(2x + 1)
Write the partial fraction decomposition of each rational expression. x - 11x - 18 x(x? + 3x + 3)
Write the partial fraction decomposition of each rational expression. x? + 2x + 3 |(x + 1)(x + 2x + 4)
Write the partial fraction decomposition of each rational expression. 10x? + 2x |(x – )°(x² + 2)
Write the partial fraction decomposition of each rational expression. x + 4 x(x² + 4)
Write the partial fraction decomposition of each rational expression. x? + x |(x + 2)(x – 1)²
Write the partial fraction decomposition of each rational expression. х — 3 х (x + 2)(x + 1)²
Write the partial fraction decomposition of each rational expression. х +1 х x(xх — 2)²
Write the partial fraction decomposition of each rational expression. х (x – 1)(x + 1)2
Write the partial fraction decomposition of each rational expression. 2x + 4 x³ – 1
Write the partial fraction decomposition of each rational expression. 1 x - 8
Write the partial fraction decomposition of each rational expression. х x*(x – 2)
Write the partial fraction decomposition of each rational expression. x? (x – 1)²(x + 1)
Write the partial fraction decomposition of each rational expression. Зх (х + 2)(х — 4)
Write the partial fraction decomposition of each rational expression. х (х — 1)(х — 2)
Write the partial fraction decomposition of each rational expression. (x + 1)(x² + 4)
Write the partial fraction decomposition of each rational expression. x(x + 1)
Write the partial fraction decomposition of each rational expression. Зx (х + 2)(х — 1)
Write the partial fraction decomposition of each rational expression. x(х — 1) 4,
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. 2x(x² + 4) x + 1
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 – 1) (x + 4)(x – 3)
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. Зx4 + x? — 2 х3 +8
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. 5x + 2x – 1 x² – 4
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. 3x - 2 x2 - 1
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 + 5 x - 4
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. 5x + 2 x³ - 1
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. х x? - 1 ,2
True or False.Every polynomial with real numbers as coefficients can be factored into products of linear and/or irreducible quadratic factors.
Factor completely: 3x4 + 6x3 + 3x2.
True or False.The rational expression is proper. 5x – 1 x + 1
True or False. The equation (x – 1)2 -1 = x(x – 2) is an example of an identity?
What is the solution of the system of equations AX = Φ iif, A-1 exists? Discuss the solution of AX = Φ if, A-1 does not exist.
If a, b, and c ≠ 0 are real numbers with ac = bc , then a = b. Does this same property hold for matrices? In other words, if A, B, and C, are matrices and AC = BC must A = B?
Explain why the number of columns in matrix A must equal the number of rows in matrix B when finding the product AB.
Consider the 2 by 2 square matrix If D = ad – bc ≠ 0 show that A is nonsingular and that A = -b D -c
The relative income of a child (low, medium, or high) generally depends on the relative income of the child’s parents. The matrix P, given by is called a left stochastic transition matrix. For
One method of encryption is to use a matrix to encrypt the message and then use the corresponding inverse matrix to decode the message. The encrypted matrix, E, is obtained by multiplying the message
Rizza Ford has two locations, one in the city and the other in the suburbs. In January, the city location sold 400 subcompacts, 250 intermediate-size cars, and 50 SUVs; in February, it sold 350
The Acme Steel Company is a producer of stainless steel and aluminum containers. On a certain day, the following stainless steel containers were manufactured: 500 with 10-gallon (gal) capacity, 350
Jamal and Stephanie each have school loans issued from the same two banks. The amounts borrowed and the monthly interest rates are given next (interest is compounded monthly): (a) Write a matrix
Nikki and Joe take classes at a community college, LCCC, and a local university, SIUE. The number of credit hours taken and the cost per credit hour (2009–2010 academic year, tuition only) are as
Algebraically solve each system of equations using any method you wish. — 4х + 3у + 2z %3D 6 Зх + у — z%3D —2 х+9у + z %3D 6
Algebraically solve each system of equations using any method you wish. 2х — Зу + z %3D 4 - 3х + 2у — z %3D —3 -5y + z = 6 -3
Algebraically solve each system of equations using any method you wish. 3x + 2y – z = 2 2x + y + 6z = -7 2x + 2y – 14z = 17
Algebraically solve each system of equations using any method you wish. 5х — y + 4z = 2 —х + 5у — 4z 3 3 7x + 3y – 4z = 17 5x %3D 17
Algebraically solve each system of equations using any method you wish. 2х + 3у — z %3D -2 3z = 6 бу — 2г 3D 2 4х + %3D
Algebraically solve each system of equations using any method you wish. x - 2y + 4z = 2 -3x + 5y – 2z = 17 4x – 3y = -22
Algebraically solve each system of equations using any method you wish. 2.x + 8y = -8 x + 7y = -13 -13
Algebraically solve each system of equations using any method you wish. 11 |2x + 3y | 5x + 7y = 24 24
Use the idea behind Example 15 with a graphing utility to solve the following systems of equations. Round answers to two decimal places. 25x + 61 y – 12z = 25 12y + 7z = 10 z = -4 18x Зх +
Use the idea behind Example 15 with a graphing utility to solve the following systems of equations. Round answers to two decimal places. 25.x + 61 y – 12z = 21 12y 18x – 12y + 7z = 7 Z.
Use the idea behind Example 15 with a graphing utility to solve the following systems of equations. Round answers to two decimal places. 25x + 61y – 12z = 15 18x – 12y + 7z = -3 z = 12 Зх
Use the idea behind Example 15 with a graphing utility to solve the following systems of equations. Round answers to two decimal places. 25х + 61у — 12z - 10 18x – 12y + 7y = -9 Зх + 4y
Use a graphing utility to find the inverse, if it exists, of the matrix. Round answers to two decimal places. 16 22 -3 5 21 4 -17 8 27 -10 2 20 15 -3
Use a graphing utility to find the inverse, if it exists, of the matrix. Round answers to two decimal places. 44 21 18 6 -2 10 15 5 21 12 -12 4 4 9 -8 -16
Use a graphing utility to find the inverse, if it exists, of the matrix. Round answers to two decimal places. 4 18 -3 6 -20 14 10 25 -15
Use a graphing utility to find the inverse, if it exists, of the matrix. Round answers to two decimal places. 25 61 -12 -2 18 35 21
Show that the matrix has no inverse. 1 1 -3 2 -4 -5
Show that the matrix has no inverse. 1 -1 1 -4 -3 -7 5 2.
Show that the matrix has no inverse. -3 0 4 0
Show that the matrix has no inverse. 15 3 10 2
Show that the matrix has no inverse. -3 2 6 -1
Show that the matrix has no inverse. 4 2 2 1
Solve the system of equations. Зх + 3у + z 3 1 х+ 2у +z %3 0 2х — у+z%3D 4
Solve the system of equations. х+ у+ z%3D 2 Зх + 2у — 3 10 y + 2z 3 Зх +
Solve the system of equations. Зх + Зу + 2 3D 8 х +2у + 2 %3 5 2х — у+z3 4
Solve the system of equations. y + Зх + 2у — z %3D 8 y + 2z = 1 Зх +
Solve the system of equations. x + 2z = 2 3 -x + 2y + 3z x - y = 2.
Solve the system of equations. y + z = 2 – 2y х -2y + z = 2 —2х — Зу - 2
Solve the system of equations. 6. х+2z %3 —х + 2у + 3z 3D —5 х — у%3D 6
Solve the system of equations. y + z = -2y + z = -1 -2х — Зу %3D —5 х -1
Solve the system of equations. |bx + 3y = 14 |bx + 2y = 10 14 10
Solve the system of equations. 2х + y ах + ау 3D 5
Solve the system of equations. |bx + 3y = 2b + 3 b + 0 |bx + 2y = 2b + 2
Solve the system of equations. = -3 | 2х + у %3D — 3 Тах + ау %3D —а
Solve the system of equations. 5 —4х + у 3D 6х — 2у 3D —9 2y
Solve the system of equations. 6x + 5y = 13 13 |2x + 2y = 5
Solve the system of equations. — 4х + у%3D 0 бх — 2у 3D 14 2y = 14
Solve the system of equations. бх + 5у %3D 7 2х + 2у %3D 2
Solve the system of equations. = 4 Зх — 2х + у %3D 5
Solve the system of equations. 2x + y = 0 x + y = 5
Solve the system of equations. Зх — у %3D 8 -2х + у %3D 4
Solve the system of equations. [2x 2х + у %3D8 х +у %3D5
Matrix is nonsingular. Find the inverse of the matrix. 3 3 1 2 1 -1 1
Matrix is nonsingular. Find the inverse of the matrix. 2 -1 3 3 1
Matrix is nonsingular. Find the inverse of the matrix. 2 3 -1 1 -1 0
Matrix is nonsingular. Find the inverse of the matrix. -1 1 0 -2 1 -2 -3 0 –1
Matrix is nonsingular. Find the inverse of the matrix. ь з ь 2 3 b + 0
Matrix is nonsingular. Find the inverse of the matrix. 2 1
Matrix is nonsingular. Find the inverse of the matrix. -4 6 -2
Matrix is nonsingular. Find the inverse of each matrix. 6 5 2 2
Matrix is nonsingular. Find the inverse of each matrix. 3 -1 -2 1.

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