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mathematics
college algebra graphs and models
College Algebra With Modeling And Visualization 6th Edition Gary Rockswold - Solutions
What is a perfect square trinomial and how is it factored?
In Exercises 133–136, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. . 11 72.72 = 49
In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number.Eight decreased by three times the sum of a number and six
Explain how to convert from decimal to scientific notation and give an example.
Explain how to factor x3 + 1.
In Exercises 129–132, determine whether each statement makes sense or does not make sense, and explain your reasoning.There are many exponential expressions that are equal to 36x12, such as (6x6)2, (6x3)(6x9), 36(x3)9, and 62(x2)6.
What does it mean to factor completely?
In Exercises 129–132, determine whether each statement makes sense or does not make sense, and explain your reasoning.Using my calculator, I determined that 67 = 279,936, so 6 must be a seventh root of 279,936.
In Exercises 133–136, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 8 1-3 -2
In Exercises 129–132, determine whether each statement makes sense or does not make sense, and explain your reasoning.If 5-2 is raised to the third power, the result is a number between 0 and 1.
In Exercises 130–133, determine whether each statement makes sense or does not make sense, and explain your reasoning.Although 20x3 appears in both 20x3 + 8x2 and 20x3 + 10x, I’ll need to factor 20x3 in different ways to obtain each polynomial’s factorization.
You had $10,000 to invest. You put x dollars in a safe, government-insured certificate of deposit paying 5% per year. You invested the remainder of the money in noninsured corporate bonds paying 12% per year. Your total interest earned at the end of the year is given by the algebraic expression
It takes you 50 minutes to get to campus. You spend t minutes walking to the bus stop and the rest of the time riding the bus. Your walking rate is 0.06 mile per minute and the bus travels at a rate of 0.5 mile per minute. The total distance walking and traveling by bus is given by the algebraic
Read the Blitzer Bonus beginning on page 15. Use the formulaand replace w with your body weight. Using this formula and a calculator, compute your BAC for integers from n = 1 to n = 10. Round to three decimal places. According to this model, how many drinks can you consume in an hour without
In Exercises 133–140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 4-² 4-³ V
In Exercises 129–132, determine whether each statement makes sense or does not make sense, and explain your reasoning. In Exercises 129–132, determine whether each statement makes sense or does not make sense, and explain your reasoning.I simplified the terms of 2√20 + 4√75, and then I was
In Exercises 129–132, determine whether each statement makes sense or does not make sense, and explain your reasoning.The population of Colorado is approximately 4.6 × 1012.
In Exercises 130–133, determine whether each statement makes sense or does not make sense, and explain your reasoning.You grouped the polynomial’s terms using different groupings than I did, yet we both obtained the same factorization.
In Exercises 133–140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 5-2 V 2-5
In Exercises 129–132, determine whether each statement makes sense or does not make sense, and explain your reasoning.When I use the definition for am/n, I usually prefer to first raise a to the m power because smaller numbers are involved.
In Exercises 129–132, determine whether each statement makes sense or does not make sense, and explain your reasoning.I just finished reading a book that contained approximately 1.04 × 105 words.
In Exercises 130–133, determine whether each statement makes sense or does not make sense, and explain your reasoning.I factored 4x2 - 100 completely and obtained (2x + 10)(2x - 10).
In Exercises 133–140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. (-2)4 = 2-4
In Exercises 130–133, determine whether each statement makes sense or does not make sense, and explain your reasoning.First factoring out the greatest common factor makes it easier for me to determine how to factor the remaining factor, assuming that it is not prime.
In Exercises 134–137, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.x4 - 16 is factored completely as (x2 + 4)(x2 - 4).
In Exercises 133–136, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The cube root of -8 is not a real number.
In Exercises 134–137, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The trinomial x2 - 4x - 4 is a prime polynomial.
What is an algebraic expression? Give an example with your explanation.
Write out the terms of the series and then evaluate it. Σ5(2)=1
Find a general term a, for the geometric sequence. az = 2, a6 = =
At noon, car A is traveling north at 50 miles per hour and is located 30 miles north of car B. Car B is traveling east at 50 miles per hour. Approximate the distance between the cars at 1:45 P.M. to the near- est tenth of a mile.
Find a general term a, for the geometric sequence. a3 = 1, as = 1 az
The probability of a day being cloudy is 30%, and the probability of it being cloudy and windy is 12%. Given that the day is cloudy, what is the probability that it will be windy?
Write out the terms of the series and then evaluate it.
The probability the probability of a day being cloudy is 40%, and of it being cloudy and windy is 15%. Given that the day is cloudy, what is the probability that it will be windy?
The probability that the first serve of a tennis ball is out of bounds is 0.3, and the probability that the second serve of a tennis ball is in bounds, given that the first serve was out of bounds, is 0.8. Find the probability that the first serve is out of bounds and the second serve is in bounds.
Find a general term a, for the geometric sequence. a₂ = 4, as = 32
Write out the terms of the series and then evaluate it. M (5 - 2k)
A number from 1 to 20 is drawn at random. Find the probability that the number is prime.
Find a general term a, for the geometric sequence. az = 9, r =
Write out the terms of the series and then evaluate it. 8
A jar initially contains 10 red marbles and 23 blue marbles. What is the probability of drawing a blue marble, given that 2 red marbles and 4 blue marbles have already been drawn?
Find the probability of rolling a sum of 7 with two dice.
If possible, maximize and minimize z subject to the given constraints. z = 8x + 3y 4x + y = 12 x + 2y = 6 x = 0, y = 0
The table contains data on sales of three homes. Price P is measured in thousands of dollars, home size S is in square feet, and condition Cis rated on a scale from 1 to 10, where 10 represents excellent condition. The variables were found to be related by the equation P = a + bS + cC.(a) Use the
Use Gauss-Jordan elimination to solve the system of equations. x + z = 2 0 -2 x-y-z -2x + y
(a) Find a matrix A and a column matrix B that describe the following tables. (b) Find the matrix product AB, and interpret the result. Student 1 Student 2 College A College B College A 15 12 College B 2 4 Cost per Credit $90 $75
If possible, maximize and minimize z subject to the given constraints. z = 7x + 6y x+y≤8 x+y=4 x ≥ 0, y = 0
(a) Find a matrix A and a column matrix B that describe the following tables. (b) Find the matrix product AB, and interpret the result. Student 1 Student 2 College A College B College A 12 8 College B 4 7 Cost per Credit $55 $70
Use Gauss-Jordan elimination to solve the system of equations. x + 2y + z = 3 y-2=-2 -x-2y + 2z = 6
The figure at the top of the next column shows four one-way streets with intersections A, B, C, and D. Numbers indicate the average traffic flow in vehicles per minute. The variables x1, x2, x3, and x4 denote unknown traffic flows.(a) The number of vehicles per minute entering an intersection
Use Gauss-Jordan elimination to solve the system of equations. 2x + 3y = 1 x-2y = -3
Find the maximum value of P = 3x + 5y subject to the following constraints. 3x + y ≤ 8 x + 3y ≤ 8 x ≥ 0, y = 0 =
Complete the following. (a) Design a matrix A with dimension 4 X 4 that represents a digital image of the given letter. Assume that there are four gray levels from 0 to 3. (b) Find a matrix B such that B- A represents the negative image of the picture represented by matrix A from part
A music store marks its DVDs as A. B, or C to indicate one of three selling prices. The last column in the table shows the total cost of a purchase. Use this information to determine the cost of one DVD of each type by setting up a matrix equa- tion and solving it with an inverse. A | B 2
Use Gauss-Jordan elimination to solve the system of equations. x - y = 1 x + y = 5
Find the minimum value of C = 4x + 2y subject to the following constraints. x + y = 3 2x + 3y = 12 x ≥ 0, y = 0
(a) Let X represent the point (0, √2). If this point is rotated about the origin 45° clockwise and then translated 2 units to the right and 3 units upward, determine its new coordinates geometrically. (b) Compute Y = ABX, and explain the result. (c) Is ABX equal to BAX? Interpret your
Complete the following. (a) Design a matrix A with dimension 4 X 4 that represents a digital image of the given letter. Assume that there are four gray levels from 0 to 3. (b) Find a matrix B such that B- A represents the negative image of the picture represented by matrix A from part
The augmented matrix is in reduced row-echelon form and represents a system of linear equations. If possible, solve the system. 10 00 010 0 0 0 10 21 -2
Write a system of linear inequalities that describes the shaded region. 2 7 2 3 4
To win the jackpot in a lottery, one must select five different numbers from 1 to 39. How many ways are there to play this game?
Complete the following for the given system of linear equations. (a) Write the system in the form AX = B. (b) Solve the linear system by computing X = A-1B with a calculator. Approximate the solution to the nearest hundredth when appropriate. 3x - y + z= 49 5.8x - 2.1y
Shade the region of feasible solutions for the following constraints. 3x + 2y = 12 2x + 3y = 12 x ≥ 0, y = 0
The matrix A translates a point to the right 4 units and downward 2 units, and the matrix B translates a point to the left 3 units and upward 3 units, where(a) Let X represent the point (1, 1). Predict the result of Y = ABX. Check your prediction. (b) Find AB mentally, and then compute AB. (c)
The matrix B rotates the point (x, y) clockwise about the origin 45°, where B = -SH 15-12 0 and B-1 15-12 1-st 0 001 1 (a) Let X represent the point (-√2, -√2). Compute Y = BX. (b) Find B¹Y. Interpret what B¹ computes. 0
The graph shows a region of feasible solutions for C. Find the maximum and minimum values of C. (1, 10) (1.0) (7,9) (7.6) I
The digital image represents the letter F using 20 pixels in a 5 x 4 grid. Assume that there are four gray levels from 0 to 3.(a) Find a matrix B such that B- A represents the negative image of the picture represented by A. (b) Find a matrix C such that A + C represents a decrease in the contrast
The matrix product AX performs a translation on the point (x, y), where(a) Predict the new location of the point (x, y) when it is translated by A. Compute Y = AX to verify your prediction. (b) Make a conjecture as to what A-1Y represents. Find A-1 and calculate A-1Y to test your conjecture. (c)
The augmented matrix is in reduced row-echelon form and represents a system of linear equations. If possible, solve the system. 1 0 0 010 -1 0 00 ilm
The graph shows a region of feasible solutions for C. Find the maximum and minimum values of C. (1, 10) (1.0) (7,9) (7.6) I
The augmented matrix is in reduced row-echelon form and represents a system of linear equations. If possible, solve the system. 0 013 0 0 0 0 5 0
The augmented matrix is in reduced row-echelon form and represents a system of linear equations. If possible, solve the system. 1 0 01 0 2 -1 00 0 4 -3 0
The graph shows a region of feasible solutions for C. Find the maximum and minimum values of C. (1, 10) (1.0) (7,9) (7.6) I
The matrix product AX performs a translation on the point (x, y), where(a) Predict the new location of the point (x, y) when it is translated by A. Compute Y = AX to verify your prediction. (b) Make a conjecture as to what A-1Y represents. Find A-1 and calculate A-1Y to test your conjecture. (c)
The digital image represents the letter F using 20 pixels in a 5 x 4 grid. Assume that there are four gray levels from 0 to 3.Find a matrix A that represents this digital image of the letter F. E
Complete the following. (a) Design a matrix A with dimension 4 X 4 that represents a digital image of the given letter. Assume that there are four gray levels from 0 to 3. (b) Find a matrix B such that B- A represents the negative image of the picture represented by matrix A from part
Matrix A represents a digital photograph. Find a matrix B that represents the negative image of 1. 030 131 2 32
The augmented matrix is in reduced row-echelon form and represents a system of linear equations. If possible, solve the system. 1 0 0 0 1 0 -9 3 00 1
The graph shows a region of feasible solutions for C. Find the maximum and minimum values of C. (1, 10) (1.0) (7,9) (7.6) I
Predict the result of the computations BB-1 X and B-1BX for any point (x, y) given by X. Explain this result geometrically.
Complete the following for the given system of linear equations. (a) Write the system in the form AX = B. (b) Solve the linear system by computing X = A-1B with a calculator. Approximate the solution to the nearest hundredth when appropriate. 1.2x0.3y 0.7: = -0.5 - -0.4x + 1.3y + 0.4: = 0.9 1.7x
The augmented matrix is in reduced row-echelon form and represents a system of linear equations. If possible, solve the system. 1 0 0 010 00 1 417
The negative image of a picture interchanges black and white. The number 1 is represented by the matrix A. Determine a matrix B such that B - A represents the negative image of the picture represented by A. Evaluate B - A. 030 A = 0 3 0 030
The augmented matrix is in reduced row-echelon form and represents a system of linear equations. If possible, solve the system. [] 00
Find a 3 x 3 matrix A that performs the following translation of a point (x, y) represented by X. Find A-1 and describe what it computes.6 units to the right and 1 unit upward
The graph shows a region of feasible solutions for P. Find the maximum and minimum values of P. P = 6x + y (1,5) (1.2) (6,8) (9,1)
The graph shows a region of feasible solutions for P. Find the maximum and minimum values of P. P = 3x + 5y (1.4) (5, 10) (6.3)
Find a 3 x 3 matrix A that performs the following translation of a point (x, y) represented by X. Find A-1 and describe what it computes.3 units to the left and 5 units downward
The augmented matrix is in reduced row-echelon form and represents a system of linear equations. If possible, solve the system. 0 12 [13] Lo
Complete the following for the given system of linear equations. (a) Write the system in the form AX = B. (b) Solve the linear system by computing X = A-1B with a calculator. Approximate the solution to the nearest hundredth when appropriate. 17x22y 192 = -25.2 3x + 13y9z = 105.9 x - 2y + 6.1z =
We can calculate social distances between people using matrices. For example, people you like are a social distance of 1 from you. People your friends like are a social distance of 2 from you. A person can be a social distance of 1 and 2 from you if you like them and have a friend who also likes
Shade the region of feasible solutions for the following constraints. x + y ≤ 4 x + 4y = 4 x ≥ 0, y = 0
We can calculate social distances between people using matrices. For example, people you like are a social distance of 1 from you. People your friends like are a social distance of 2 from you. A person can be a social distance of 1 and 2 from you if you like them and have a friend who also likes
We can calculate social distances between people using matrices. For example, people you like are a social distance of 1 from you. People your friends like are a social distance of 2 from you. A person can be a social distance of 1 and 2 from you if you like them and have a friend who also likes
Complete the following for the given system of linear equations. (a) Write the system in the form AX = B. (b) Solve the linear system by computing X = A-1B with a calculator. Approximate the solution to the nearest hundredth when appropriate. 3.1x + 1.9y 6.3x z = 1.99 -3.78 - 9.9z -x+ 1.5y + 7 =
We can calculate social distances between people using matrices. For example, peo- ple you like are a social distance of 1 from you. People your friends like are a social distance of 2 from you. A person can be a social distance of 1 and 2 from you if you like them and have a friend who also likes
Shade the region of feasible solutions for the following constraints. x + 2y = 8 2x + y = 2 x = 0, y = 0
The following matrix represents a simple social network.Column 4 in the matrix contains only 0's. What does this tell us about Person 4? 0 0 1 1 0 0000 1100 10 10.
The following matrix represents a simple social network.If a column of a social network matrix contains only I's (except on the main diagonal), what can be said about the person represented by that column? 0 0 1 1 0 0000 1100 10 10.
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