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College Algebra 7th Edition Robert F Blitzer - Solutions

The figure shows the healthy weight region for various heights for people ages 35 and older.If x represents height, in inches, and y represents weight, in pounds, the healthy weight region can be modeled by the following system of linear inequalities:Use this information to solve Exercises
Find a and b in this figure. a b 10 17 9-
Use a system of linear equations to solve Exercises 73–84.How many ounces of a 15% alcohol solution must be mixed with 4 ounces of a 20% alcohol solution to make a 17% alcohol solution?
In Exercises 73–76, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.A system of two equations in two variables whose graphs are a circle and a line can have four real ordered-pair solutions.
Use a system of linear equations to solve Exercises 73–84.How many ounces of a 50% alcohol solution must be mixed with 80 ounces of a 20% alcohol solution to make a 40% alcohol solution?
In Exercises 73–76, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.A system of two equations in two variables whose graphs are a parabola and a circle can have four real ordered-pair solutions.
Solve the systems in Exercises 79–80. flog x² = y + 3 log x = y 1 -
Use a system of linear equations to solve Exercises 73–84.When a crew rows with the current, it travels 16 miles in 2 hours. Against the current, the crew rows 8 miles in 2 hours. Let x = the crew’s rowing rate in still water and let y = the rate of the current. The following chart summarizes
Use a system of linear equations to solve Exercises 73–84.At the north campus of a performing arts school, 10% of the students are music majors. At the south campus, 90% of the students are music majors. The campuses are merged into one east campus. If 42% of the 1000 students at the east campus
The graph of an inequality in two variables is a region in the rectangular coordinate system. Regions in coordinate systems have numerous applications. For example, the regions in the following two graphs indicate whether a person is obese, overweight, borderline overweight, normal weight, or
In Exercises 73–76, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.A system of two equations in two variables whose graphs are two circles must have at least two real ordered-pair solutions.
Use a system of linear equations to solve Exercises 73–84.At the north campus of a small liberal arts college, 10% of the students are women. At the south campus, 50% of the students are women. The campuses are merged into one east campus. If 40% of the 1200 students at the east campus are women,
The graph of an inequality in two variables is a region in the rectangular coordinate system. Regions in coordinate systems have numerous applications. For example, the regions in the following two graphs indicate whether a person is obese, overweight, borderline overweight, normal weight, or
In Exercises 73–76, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.A system of two equations in two variables whose graphs are a parabola and a circle cannot have only one real ordered-pair solution.
Use a system of linear equations to solve Exercises 73–84.In Exercises 83–84, an isosceles triangle containing two angles with equal measure is shown. The degree measure of each triangle’s three interior angles and an exterior angle is represented with variables. Find the measure of the three
Use a system of linear equations to solve Exercises 73–84.A hotel has 200 rooms. Those with kitchen facilities rent for $100 per night and those without kitchen facilities rent for $80 per night. On a night when the hotel was completely occupied, revenues were $17,000. How many of each type of
Use a system of linear equations to solve Exercises 73–84.In Exercises 83–84, an isosceles triangle containing two angles with equal measure is shown. The degree measure of each triangle’s three interior angles and an exterior angle is represented with variables. Find the measure of the three
Many elevators have a capacity of 2000 pounds.a. If a child averages 50 pounds and an adult 150 pounds, write an inequality that describes when x children and y adults will cause the elevator to be overloaded.b. Graph the inequality. Because x and y must be positive, limit the graph to quadrant I
Use a system of linear equations to solve Exercises 73–84.A new restaurant is to contain two-seat tables and four-seat tables. Fire codes limit the restaurant’s maximum occupancy to 56 customers. If the owners have hired enough servers to handle 17 tables of customers, how many of each kind of
Use the exponential growth model, A = A0ekt, to solve this exercise. In 1975, the population of Europe was 679 million. By 2015, the population had grown to 746 million.a. Find an exponential growth function that models the data for 1975 through 2015.b. By which year, to the nearest year, will the
On your next vacation, you will divide lodging between large resorts and small inns. Let x represent the number of nights spent in large resorts. Let y represent the number of nights spent in small inns.a. Write a system of inequalities that models the following conditions: You want to stay at
A person with no more than $15,000 to invest plans to place the money in two investments. One investment is high risk, high yield; the other is low risk, low yield. At least $2000 is to be placed in the high-risk investment. Furthermore, the amount invested at low risk should be at least three
Solve: x4 + 2x3 - x2 - 4x - 2 = 0.
A patient is not allowed to have more than 330 milligrams of cholesterol per day from a diet of eggs and meat. Each egg provides 165 milligrams of cholesterol. Each ounce of meat provides 110 milligrams.a. Write an inequality that describes the patient’s dietary restrictions for x eggs and y
Use a system of linear equations to solve Exercises 73–84.When an airplane flies with the wind, it travels 800 miles in 4 hours. Against the wind, it takes 5 hours to cover the same distance. Find the plane’s rate in still air and the rate of the wind.
Expand: logs (4√x/64y3) .
Exercises 84–86 will help you prepare for the material covered in the next section. In each exercise, graph the linear function.2x - 3y = 6
Exercises 84–86 will help you prepare for the material covered in the next section. In each exercise, graph the linear function.f(x) = - 2/3x
Exercises 84–86 will help you prepare for the material covered in the next section. In each exercise, graph the linear function.f(x) = -2
What is a system of linear equations? Provide an example with your description.
What is the solution of a system of linear equations?
Explain how to solve a system of equations using the substitution method. Use y = 3 - 3x and 3x + 4y = 6 to illustrate your explanation.
What is a linear inequality in two variables? Provide an example with your description.
Explain how to solve a system of equations using the addition method. Use 3x + 5y = -2 and 2x + 3y = 0 to illustrate your explanation.
How do you determine if an ordered pair is a solution of an inequality in two variables, x and y?
When is it easier to use the addition method rather than the substitution method to solve a system of equations?
What is a half-plane?
When using the addition or substitution method, how can you tell if a system of linear equations has infinitely many solutions? What is the relationship between the graphs of the two equations?
What does a solid line mean in the graph of an inequality?
In Exercises 3–5, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. x + 2y + 3z = 2x + y + x + y - || z = z || -5 1 8
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. 5x + 8y 6z = 14 3x + 4y = 2z = 8 x + 2y = 2z = 3
In Exercises 1–5, use matrices to find the complete solution to each system of equations, or show that none exists. w + w - x + y + y + x + 3y + z z = 6 z = -14 12 1 w + 2x 2w + 3x + 6y + z = - 3z =
Evaluate each determinant in Exercises 1–10. -4 5 1 6
In Exercises 1–8, write the augmented matrix for each system of linear equations. x = y + z = 8 y 12z = -15 - 1
In Exercises 3–5, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. X - 2y + z = 0 y - 3z = -1 2y + 5z = -2 N
Fill in each blank so that the resulting statement is true.ifthen x =_________ and y =__________ . 3 Ly X -7. 3 [6 -10 -7
In Exercises 1–8, write the augmented matrix for each system of linear equations. x - 2y + 3z = 9 y + 3z = 5 z = 2
When using the addition or substitution method, how can you tell if a system of linear equations has no solution? What is the relationship between the graphs of the two equations?
What does a dashed line mean in the graph of an inequality?
Describe the break-even point for a business.
Compare the graphs of 3x - 2y > 6 and 3x - 2y ≤ 6. Discuss similarities and differences between the graphs.
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. 3x + 4y + 2z = = 3 4x - 2y - 8z = -4 3 x + y z = =
Write a system of equations having {(-2, 7)} as a solution set.
Fill in each blank so that the resulting statement is true.A matrix that has the same number of rows as columns is called a/an_________ matrix.
Fill in each blank so that the resulting statement is true.True or false: Only square matrices have multiplicative inverses.________
Fill in each blank so that the resulting statement isUsing Cramer’s Rule to solvefor y, we obtain 3x + y + 4z 2x + 3y - 2z. x - 3у зу - 2z = || -8 11 4
Evaluate each determinant in Exercises 1–10. 7 9 -2 -5
In Exercises 1–12, find the products AB and BA to determine whether B is the multiplicative inverse of A. A = -2 1 -2 B = 1 -1 2 -2
In Exercises 3–5, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 3x1 + 5x2 - 8x3 + 5x1 = -8 3x3 + X4 = x1 + 2x2 - = -7 2x1 + 3x2 7x3 + 3x4 = -11 4x1 + 8x2 - 10x3 + 7x4 = -10
In Exercises 3–6, letCarry out the indicated operations.C-1 A = 3 1 1 0 2 1 B = 1 [2 1. and C= 1 [43] -1 3
In Exercises 1–5, use matrices to find the complete solution to each system of equations, or show that none exists. 2x - 2y + x = y + 2x + y 2z = 5 z = 2 z = 1
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 1 3 -5 0 2 -1 1 0 TT -e 5.
Fill in each blank so that the resulting statement isThe easiest way to evaluateis to expand about the elements in_______. 3 с со 28 0 0 5 -4 -6 7
In Exercises 1–8, write the augmented matrix for each system of linear equations. 5x - 2y - 3z = 0 x + y = 5 2x - 3z = 4
Fill in each blank so that the resulting statement is true.Ifthe matrix A is invertible if and only if________ . A b Lc d a
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. 2x - y z = 0 z = 3 x + 2y + 3x + 4y + 2z = 8
The table shows the pollutants in the air in a city on a typical summer day.a. Use the function y = ax2 + bx + c to model the data. Use either Gaussian elimination with back-substitution or Gauss-Jordan elimination to find the values for a, b, and c.b. Use the function to find the time of day at
Evaluate each determinant in Exercises 1–10. -7 14 2-4
In Exercises 5–8, find values for the variables so that the matrices in each exercise are equal. X 4-0
In Exercises 1–12, find the products AB and BA to determine whether B is the multiplicative inverse of A. A || 2 3/2 -2 를 HIN B = 3 2 24
In Exercises 1–8, write the augmented matrix for each system of linear equations. X 2y + z = 10 3x + y = 5 7x + 2z = 2
Sociologists Joseph Kahl and Dennis Gilbert developed a six-tier model to portray the class structure of the United States. The bar graph represents the percentage of Americans who are members of each of the six social classes.Combined, members of the capitalist class, the upper middle class, the
In Exercises 3–6, letCarry out the indicated operations.BC - 3B A = 3 1 1 0 2 1 B = 1 [2 1. and C= 1 [43] -1 3
Solve each equation or inequality in Exercises 1–6.e2x - 14ex + 45 = 0
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. 8x + 5y + 11z = 30 -x - 4y + 2z = 3 2x - y + 5z = 12
In Exercises 5–8, find values for the variables so that the matrices in each exercise are equal. 11 []=[] y
In Exercises 6–10, perform the indicated matrix operations or solve the matrix equation for X given that A, B, and C are defined as follows. If an operation is not defined, state the reason.2C - 1/2 B A = 02 -1 3 10 B = [ 4 -6 c=[+] C = 0 1
In Exercises 1–12, find the products AB and BA to determine whether B is the multiplicative inverse of A. A = 4 2 3 5 B miN T 52 2
Fill in each blank so that the resulting statement is true.True or false: Back-substitution is required to solve linear systems using Gaussian elimination._________
Evaluate each determinant in Exercises 1–10. 1 -8 ∞ -3 2
In Exercises 1–8, write the augmented matrix for each system of linear equations. 2w5x3y + z = 2 3x + y = 4 W w x + 5y = 9 5w5x2y = 1
Carry out the indicated operations. 1 2 2 3 1 -1 -2 B is the inverse of A. If A = 2 3 and B = -3 2 7 -4 -5 3 0 1,show that -1
Fill in each blank so that the resulting statement is true.True or false: Matrix addition is commutative._________
In Exercises 6–10, perform the indicated matrix operations or solve the matrix equation for X given that A, B, and C are defined as follows. If an operation is not defined, state the reason.A(B + C) A = 02 -1 3 10 B = [ 4 -6 c=[+] C = 0 1
Consider the systema. Express the system in the form AX = B, where A, X, and B are appropriate matrices.b. Find A-1, the inverse of the coefficient matrix.c. Use A-1 to solve the given system. 3x + 5y = 9 2x-3y=-13.
Solve each equation or inequality in Exercises 1–6.log3 x + log3(x + 2) = 1
Evaluate each determinant in Exercises 1–10. -5 -2 -1 -7
Fill in each blank so that the resulting statement is true.True or false: is invertible. A 3 9 2] 6
In Exercises 5–8, find values for the variables so that the matrices in each exercise are equal. X 2y 2017]. 9] || [4 3 12] 9
Fill in each blank so that the resulting statement is true.True or false: Back-substitution is required to solve linear systems using Gauss-Jordan elimination._________
In Exercises 1–12, find the products AB and BA to determine whether B is the multiplicative inverse of A. A= 1 001 1 0 0 0 B 0 0 1 0 0 1 0 0
Fill in each blank so that the resulting statement is true.True or false: Matrices of different orders can be added._________
Solve for y using Cramer’s Rule: x - 2y + 2x + y 3x + 2y Z = NN z = 2z = 7 0 -2.
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. x + y - 10z у 10z = -4 X 7z = -5 3x + 5y - 36z 36z = -10
Fill in each blank so that the resulting statement is true.If a square matrix does not have a multiplicative inverse, it is called__________ .
In Exercises 1–8, write the augmented matrix for each system of linear equations. 4w7x 8y + z = 3 - 5x + y = 5 W - x - y = 17 2w - 2x + 11y = 4
Fill in each blank so that the resulting statement is true.True or false: The scalar multiple -4A is obtained by multiplying each element of A by -4._________
In Exercises 8–11, use Gaussian elimination to find the complete solution to each system, or show that none exists. 2х 2x-3y + z = 1 = = x - 2y + 3z = 2 3x-4y-z z = 1
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. 1 -5 ㅠ 0 7 -6 -2 11 호 e -ㅠ 15
In Exercises 1–12, find the products AB and BA to determine whether B is the multiplicative inverse of A. A -4 0 1 3 B -2 4 0 1

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