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mathematics
college algebra graphs and models
Questions and Answers of
College Algebra Graphs And Models
Find the partial fraction decomposition for the rational expression. 3x - 1 x(2x² + 1)²
Evaluate the expression by hand. Check your result with a calculator. (-3)*
Find an exponential model f(x) that describes each situation.A sample of 9500 insects decreases in number by 35% per week.
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. V121
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. -√5
Find an exponential model f(x) that describes each situation.A sample of 5000 insects increases in number by 120% per day.
Find an exponential model f(x) that describes each situation..A sample of 2500 fish increases in number by 5% per month.
Rewrite each summation so that the index starts with n = 1. 32 Σ(34 – 2)
Determine the future value of each annuity. A₁ = $2000, i = 0.08, n = 20
Suppose that the density of female insects during the first year is 500 per acre with r = 0.8. (a) Write a recursive sequence that describes these data, where an, denotes the female insect
Determine the future value of each annuity. Ao = $500, i = 0.15, n = 10
It is possible for some kinds of bacteria to double their size and then divide every 40 minutes.(a) Write a recursive sequence that describes this growth where each value of n represents a 40-minute
Determine the future value of each annuity. Ao = $10,000, i = 0.11, n = 5
Determine the future value of each annuity. 40 = $3000. i = 0.19, n = 45
If bacteria are cultured in a medium with limited nutrients, competition ensues and growth slows. According to Verhulst's model, the number of bacteria at 40-minute intervals is given bywhere K is a
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. x + y = 2z = 2 - [3x - y - 6z y - 6z = -7
In Exercises 9–16, find the following matrices:a. A + Bb. A - Bc. -4Ad. 3A + 2B. A = 6 6 -4 5 0 -2 2 -1 -3 -35 1 -6 4 B 1 2 - 20
For Exercises 11–22, use Cramer’s Rule to solve each system. 3x-4y = 4 2x + 2y = 12
In Exercises 13–18, use the fact that if thento find the inverse of each matrix, if possible. Check that AA-1 = I2 and A-1 A = I2. A = a C b d
In Exercises 13–18, use the fact that if thento find the inverse of each matrix, if possible. Check that AA-1 = I2 and A-1 A = I2. A = a C b d
In Exercises 14–27, perform the indicated matrix operations given that A, B, C, and D are defined as follows. If an operation is not defined, state the reason.-2A + 4D A = [2 -1 5 3 12 C = -1
In Exercises 19–20, a few steps in the process of simplifying the given matrix to row-echelon form, with 1s down the diagonal from upper left to lower right, and 0s below the 1s, are shown. Fill in
In Exercises 17–26, letSolve each matrix equation for X.X - A = B A = -3 -7 2 -9 5 0 and B = -5 -1 0 0 3 -4
In Exercises 9–16, find the following matrices:a. A + Bb. A - Bc. -4Ad. 3A + 2B. A = [ 31 -1 2 5 B = = 2-3 6 1 -4, -3
In Exercises 17–26, letSolve each matrix equation for X.X - B = A A = -3 -7 2 -9 5 0 and B = -5 -1 0 0 3 -4
In Exercises 9–16, find the following matrices:a. A + Bb. A - Bc. -4Ad. 3A + 2B. A = 2 -4 1 B = -5 3 -1
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. 3x + y - 4z = 4 = -2 2 w -2w + x + 2y 3w - 2x 2x + y - 6z -w + 3x +
In Exercises 13–18, perform each matrix row operation and write the new matrix. 0 2 5 1 -2 0 3 12 -1 1 3 0 4 11 4 6 -1 -2R₁ + R₂ -5R₁ + R₁
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. x + 2y + 3z = 5 y - 5z = 0
For Exercises 11–22, use Cramer’s Rule to solve each system. 3x + 2y = 2 2x + 2y = 3 23
In Exercises 14–27, perform the indicated matrix operations given that A, B, C, and D are defined as follows. If an operation is not defined, state the reason.D - A A = [2 -1 5 3 12 C = -1 1 3 2 -1
In Exercises 16–19, graph each equation, function, or inequality in rectangular coordinate system. 3x - 5y < 15
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. √3x + 2y x + 2y = z = 5 z = 1
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. 3w+ 2x - 4w - y + 2z = x + y + 2z w + x x + y + z = -2w + 3x + 2y -
In Exercises 13–18, use the fact that if thento find the inverse of each matrix, if possible. Check that AA-1 = I2 and A-1 A = I2. A = a C b d
In Exercises 14–27, perform the indicated matrix operations given that A, B, C, and D are defined as follows. If an operation is not defined, state the reason.B + C A = [2 -1 5 3 12 C = -1 1 3 2 -1
In Exercises 16–19, graph each equation, function, or inequality in rectangular coordinate system.(x - 1)2 + (y + 1)2 = 9
In Exercises 13–18, perform each matrix row operation and write the new matrix. 1 3 1 -1 5 -6 3 -1 10 3 2 5 -3R₁ + R₂
In Exercises 1–12, find the products AB and BA to determine whether B is the multiplicative inverse of A. A 1 0 0 0 1 1 -2 0 00 -2 0 1 1 -2 1 B 1 0 0 0 2 3 4 1 2 3 0 1 2 0 0 1
In Exercises 13–18, use the fact that ifthento find the inverse of each matrix, if possible. Check that AA-1 = I2 and A-1 A = I2. A = a C b d
In Exercises 13–18, perform each matrix row operation and write the new matrix. 2-6 1 5 -5 نیا 3 0 4 107 0 7 54 R₁
Find values for x, y, and z so that the following matrices are equal: x + 7] = [ [2x y + 7 [2 -10 6 13 4
In Exercises 13–18, perform each matrix row operation and write the new matrix. 3 -12 -4 1 2 69 40 0 7 4 R₁
For Exercises 11–22, use Cramer’s Rule to solve each system. 12x + 3у = 15 2х - Зу = 13
Find the partial fraction decomposition of 3x² + 17x - 38 (x − 3)(x − 2)(x + 2)*
Use the exponential decay model A = A0ekt to solve this problem. A radioactive substance has a half-life of 40 days. There are initially 900 grams of the substance.a. Find the decay model for this
In Exercises 14–27, perform the indicated matrix operations given that A, B, C, and D are defined as follows. If an operation is not defined, state the reason.A + D A = [2 -1 5 3 12 C = -1 1 3 2 -1
For Exercises 11–22, use Cramer’s Rule to solve each system. [x - 2y = 5x - 5 y = -2
In Exercises 9–16, find the following matrices:a. A + Bb. A - Bc. -4Ad. 3A + 2B.A = [6 2 -3], B = [4 -2 3]
In Exercises 94–97, determine whether each statement makes sense or does not make sense, and explain your reasoning.A linear system has a solution set involving fractions, such asI can use graphs
Solve the system for x and y in terms of a1, b1, c1, a2, b2, and c2 : Jajx + b₁y = C₁ la₂x + b₂y = c₂.
Graphing utilities can be used to shade regions in the rectangular coordinate system, thereby graphing an inequality in two variables. Read the section of the user’s manual for your graphing
Use a graphing utility to verify any five of the graphs that you drew by hand for the systems in Exercises 27–62.Data from exercise 27-6227.28.29.30.31. [3x + 6y≤6 2x + y ≤ 8 y 10 10 x
Graphing utilities can be used to shade regions in the rectangular coordinate system, thereby graphing an inequality in two variables. Read the section of the user’s manual for your graphing
Graphing utilities can be used to shade regions in the rectangular coordinate system, thereby graphing an inequality in two variables. Read the section of the user’s manual for your graphing
A marching band has 52 members, and there are 24 in the pom-pom squad. They wish to form several hexagons and squares like those diagrammed below. Can it be done with no people left over? B B B B P
Graphing utilities can be used to shade regions in the rectangular coordinate system, thereby graphing an inequality in two variables. Read the section of the user’s manual for your graphing
In Exercises 94–97, determine whether each statement makes sense or does not make sense, and explain your reasoning.If I know the perimeter of this rectangle and triangle, each in the same unit of
Verify your solutions to any five exercises in Exercises 5–42 by using a graphing utility to graph the two equations in the system in the same viewing rectangle. Then use the intersection feature
Graphing utilities can be used to shade regions in the rectangular coordinate system, thereby graphing an inequality in two variables. Read the section of the user’s manual for your graphing
Graphing utilities can be used to shade regions in the rectangular coordinate system, thereby graphing an inequality in two variables. Read the section of the user’s manual for your graphing
What is a system of linear inequalities?
What is a solution of a system of linear inequalities?
In Exercises 94–97, determine whether each statement makes sense or does not make sense, and explain your reasoning.Each equation in a system of linear equations has infinitely many ordered-pair
Explain how to graph the solution set of a system of inequalities.
In Exercises 103–104, find the domain of each function. g(x) || x-6 x² - 36
In Exercises 94–97, determine whether each statement makes sense or does not make sense, and explain your reasoning.Every linear system has infinitely many ordered-pair solutions.
Two identical twins can only be distinguished by the characteristic that one always tells the truth and the other always lies. One twin tells you of a lucky number pair: “When I multiply my first
What does it mean if a system of linear inequalities has no solution?
Exercises 106–108 will help you prepare for the material covered in the next section.Consider the following equations:Eliminate z by copying Equation 1, multiplying Equation 2 by 2, and then adding
In Exercises 110–113, write a system of inequalities for each graph. y ++++++ X
In Exercises 110–113, write a system of inequalities for each graph. X HHH Fo #H HH #TH
In Exercises 110–113, write a system of inequalities for each graph. H y तु -1-2-1 +4 S II y = x² N 1 2 3 4 X
The group should write four different word problems that can be solved using a system of linear equations in two variables. All of the problems should be on different topics. The group should turn in
Solve: log3 x + log3 (x + 6) = 3
The functionmodels the population of Florida, f(t), in millions, t years after 1970.a. What was Florida’s population in 1970?b. According to this logistic growth model, what was Florida’s
LetFind f(12) - f(-12). f(x) = [x+3_ if x ≥ 5 8 if x < 5.
In Exercises 103–104, find the domain of each function.f(x) = ln (6 - x)
Exercises 119–121 will help you prepare for the material covered in the next section.a. Graph the solution set of the system:b. List the points that form the corners of the graphed region in part
Exercises 119–121 will help you prepare for the material covered in the next section.a. Graph the solution set of the system:b. List the points that form the corners of the graphed region in part
Exercises 106–108 will help you prepare for the material covered in the next section.If x = 3, y = 2, and z = -3, does the ordered triple (x, y, z) satisfy the equation 2x - y + 4z = -8?
Does your graphing utility have any limitations in terms of graphing inequalities? If so, what are they?
Sketch the graph of the solution set for the following system of inequalities: Sy≥nx + b(n < 0, b>0) ly: ≤ mx + b (m > 0, b > 0).
In Exercises 110–113, write a system of inequalities for each graph. y 7- 6+ 5- 4- 3 2 1 + 1 2 3 4 5 6 7 8 X
Exercises 106–108 will help you prepare for the material covered in the next section.Write an equation involving a, b, and c based on the following description: When the value of x in y = ax2 + bx
In Exercises 1–5, use matrices to find the complete solution to each system of equations, or show that none exists. x + 2y3z = -7 3xy + 2z 8 2x - y + z = 5 ||
In Exercises 106–109, determine whether each statement makes sense or does not make sense, and explain your reasoning.When graphing a linear inequality, I should always use (0, 0) as a test point
In Exercises 106–109, determine whether each statement makes sense or does not make sense, and explain your reasoning.When graphing 3x - 4y < 12, it’s not necessary for me to graph the linear
In Exercises 1–2, perform each matrix row operation and write the new matrix. 1 2 0 1 0 5 22 -12 4 1 -5R₂ + R3
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. 5x+12y + z = 10 5y + 2z = -1 5 2y 2y - 3z = = 2x + x +
In Exercises 106–109, determine whether each statement makes sense or does not make sense, and explain your reasoning.The reason that systems of linear inequalities are appropriate for modeling
In Exercises 106–109, determine whether each statement makes sense or does not make sense, and explain your reasoning.I graphed the solution set of y ≥ x + 2 and x ≥ 1 without using test points.
In Exercises 1–8, write the augmented matrix for each system of linear equations. = 2x + y + 2z 3x-5y - z = x - 2y - 3z 2 4 -6
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
In Exercises 1–12, find the products AB and BA to determine whether B is the multiplicative inverse of A. A || 4 -5 -3). 4 B = 5 4
Write a system of inequalities whose solution set includes every point in the rectangular coordinate system.
Evaluate each determinant in Exercises 1–10. 15 7 2 3
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. 4 -6 -7 8 5 -1]
In Exercises 1–2, solve each system of equations using matrices. 2y x + 2x - 4y + z = -2x + 2y - 3z z = -3 −7 -7 4
Solve each equation or inequality in Exercises 1–6.2x2 = 4 - x
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