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mathematics
precalculus

Questions and Answers of Precalculus

In Problem 51–58, use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. x = y + z = -2y + z = 1 -2x - 3y = -4 4
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2х Зу 2x-3y - z = 0 3x + 2y + 2z = 2 x +5y +3z = 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. x + 4y - 3z = -8 3x у + 3z
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2x - 2y + 3z = 6 4x - 3y + 2z = 0 -2x + 3y - 7z = 1
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 3x-2y 7x-3y 2x-3y + 2z 6 = + 2z = –1 + 4z = 0 =
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. x + 2z = 6 -x + 2y + 3z = -5 x - y = 6
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x + y z = 6 3x - 2y + z = -5 x + 3y - 2z = 14
The formula from Problem 59 can be used to find the area of a polygon. To do so, divide the polygon into non-overlapping triangular regions and find the sum of the areas. Use this approach to find
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x = y + z = -4 2x - 3y + 4z = -15 5x + y 2z = 12
Another approach for finding the area of a polygon by using determinants is to use the formulawhere (x1, y1), (x2 , y2), . . . , (xn, yn) are the n corner points in counterclockwise order. Use this
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. x + 2z: -x + 2y + 3z 2 y = 2322
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. z = -3 2x - 4y + z = -7 -2x + 2y3z = 4 x + 2y
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. z = 9 3x + 2y z = 8 3x + y + 2z = 1 x + y +
A tetrahedron (triangular pyramid) has vertices (x1, y1, z1), (x2 , y2 , z2), (x3, y3, z3), and (x4 , y4 , z4). The volume of the tetrahedron is given by the absolute value of D, whereUse this
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x +4y - 3z = -8 - 3x - x + x у + 3z = 12 y + 6z =1 у
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. 3x + 3y + z = 8 x + 2y + z = 5 2xy +z = 4
A movie theater charges $15.00 for adults and $13.00 for senior citizens. On a day when 325 people paid for admission, the total receipts were $4445. How many who paid were adults? How many were
Problems 61–70. 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
Problems 61–70. 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.If
Graph the system of inequalities. [[x]+[y] ≤ 4 ||y[ < |x? - 3 |
An equation of the circle containing the distinct points (x1, y1), (x2 , y2), and (x3, y3) can be found using the following equation.Find the standard equation of the circle containing the points (7,
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 3x + y = 2x = y + -y+ 4x + z = 2/31 7 = 1 z 2y 8 00 |
Show that x2 X y2 y 1 = (y z)(x - y)(x − z). 1 N -
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x + y = 1 2xy + z = 1 x + 2y + z = 1813
Problems 61–70. 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
Problems 63–72. 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 61–70. 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 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x + 2y + z = 1 2xy + 2z = 2 3x + y + 3z = 3
In Problems 65–70 show that each matrix has no inverse. -3 6-1
Problems 61–70. 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
Problems 63–72. 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 65–70 show that each matrix has no inverse. 15 3 10 2
Problems 63–72. 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 61–70. 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 63–72. 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 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x = y + y 3x + 2y + z = 5 2z = 0
Problems 63–72. 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.Use
Problems 61–70. 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 71–74, use a graphing utility to find the inverse, if it exists, of each matrix. Round answers to two decimal places. 25 18 -12 3 4 61 - 12 7 -1
In Problems 65–70, graph each equation and find the point(s) of intersection, if any. y 4 and the circle x2 + 4x + y² -4 = 0 x + 2
Problems 61–70. 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 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 4x + y + z w = 4 x = y + 2z + 3w = 3
Problems 63–72. 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 63–72. 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.If
Problems 61–70. 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
Problems 63–72. 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
Problems 70–79. 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.For
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. - 4x 2xy + z + y = 5 w = 5 z + w = 4
In Problems 75–78, use the inverse matrix found in Problem 71 to solve the following systems of equations. Round answers to two decimal places. 25x + 61y - 18x - 12y + 3x + 4y - + 12z = 15 72 =
Problems 61–70. 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
Problems 63–72. 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
Problems 70–79. 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
Problems 70–79. 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
Consider the functions f (x) = x3 − 7x2 − 5x + 4 and f'(x) = 3x2 − 14x − 5. Given that f is increasing where f'(x) > 0 and f is decreasing where f'(x) < 0, find where f is increasing
In Problems 75–78, use the inverse matrix found in Problem 71 to solve the following systems of equations. Round answers to two decimal places. 25x + 61y 18x12y + 3x + 4y - 12z = 21 7z = 7 Z=-2
Problems 70–79. 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 75–78, use the inverse matrix found in Problem 71 to solve the following systems of equations. Round answers to two decimal places. 25x + 61y - 18x 12y + 3x + 4y - 12z = 25 7z = 10 z =
Problems 70–79. 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
Find real numbers a, b, and c so that the graph of the function y = ax2 + bx + c contains the points (−1, −2), (1, −4), and (2, 4).
Problems 70–79. 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 79–86, solve each system of equations using any method you wish. 2x + 3y = 11 5x + 7y = 24
Solve for x, y, and z, assuming a ≠ 0, b ≠ 0, and c ≠ 0. ax+by+cz = a + b + c a²x + b²y + c²z = ac + ab + bc abx + bcy = bc + ac
In Problems 90–96, use Descartes’ method from Problem 89 to find an equation of the tangent line to each graph at the given point.y = x2 + 2; at (1, 3)Data from problem 89Descartes’ method for
Problems 70–79. 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
Problems 70–79. 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
Find the function y = ax2 + bx + c whose graph contains the points (1, −1), (3, −1), and (−2, 14).
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 (2021–2022 academic year, tuition and
In Problems 90–96, use Descartes’ method from Problem 89 to find an equation of the tangent line to each graph at the given point.2x2 + 3y2 = 14; at (1, 2)Data from problem 89Descartes’ method
In Problems 79–86, solve each system of equations using any method you wish. 5x - y + 4z = 2 = 3 -x+ 5y4z 7x + 13y4z = 17
Problems 70–79. 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
Three painters (Beth, Solana, and Edie), working together, can paint the exterior of a home in 10 hours (h). Solana and Edie together have painted a similar house in 15 h. One day, all three worked
Find the function f (x) = ax3 + bx2 + cx + d for which f (−3) = −112, f (−1) = −2, f (1) = 4, and f (2) = 13.
In Problems 90–96, use Descartes’ method from Problem 89 to find an equation of the tangent line to each graph at the given point.x2 + y = 5; at (−2, 1)Data from problem 89Descartes’ method
Solve for x and y, assuming a ≠ 0 and b ≠ 0. ax + by + by = a + b abxb²y = b² - ab
Find the function f (x) = ax3 + bx2 + cx + d for which f (−2) = −10, f (−1) = 3, f (1) = 5, and f (3) = 15.
Problems 70–79. 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 90–96, use Descartes’ method from Problem 89 to find an equation of the tangent line to each graph at the given point.3x2 + y2 = 7; at (−1, 2)Data from problem 89Descartes’ method
Solve for matrix X:Use the following discussion for Problems 94 and 95. In graph theory, an adjacency matrix, A, is a way of representing which nodes (or vertices) are connected. For a simple
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
Asako has $20,000 to invest. As her financial planner, you recommend that she diversify into three investments: Treasury bills that yield 5% simple interest, Treasury bonds that yield 7% simple
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
An unofficial, and often contested, guideline for website design is to make all website content available to a user within three clicks. The webpage adjacency matrix for a certain website is given
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
Three retired couples each require an additional annual income of $2000 per year. As their financial consultant, you recommend that they invest some money in Treasury bills that yield 7%, some money
A young couple has $25,000 to invest. As their financial consultant, you recommend that they invest some money in Treasury bills that yield 7%, some money in corporate bonds that yield 9%, and some
Write a brief paragraph outlining your strategy for solving a system of two linear equations containing two variables.
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 90–96, use Descartes’ method from Problem 89 to find an equation of the tangent line to each graph at the given point.x2 − y2 = 3; at (2, 1)Data from problem 89Descartes’ method
In Problems 90–96, use Descartes’ method from Problem 89 to find an equation of the tangent line to each graph at the given point.2y2 − x2 = 14; at (2, 3)Data from problem 89Descartes’ method
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
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.
An important aspect of computer graphics is the ability to transform the coordinates of points within a graphic. For transformation purposes, a point (x, y) is represented as the column matrixTo
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
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
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
Besides translating a point, it is also important in computer graphics to be able to rotate a point. This is achieved by multiplying a point’s column matrix by an appropriate rotation matrix R to
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
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
Iffind a, b, c, d so that AB = BA. a b -=[ @ $ ] ₁ C d A and B = 1 1 -1 1

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