Introductory Algebra for College Students (7th Edition)
7th Edition
ISBN: 9780134178059
Author: Robert F. Blitzer
Publisher: PEARSON
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Chapter 4.3, Problem 79ES
Make Sense? In Exercises 76-79, determine whether each statement makes sense or does not make sense, and explain your reasoning
79. I find it easiest to use the addition method when one of the equation has a variable on one side by itself.
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Question 1. Solve the system
-
x1 x2 + 3x3 + 2x4
-x1 + x22x3 + x4
2x12x2+7x3+7x4
Question 2. Consider the system
= 1
=-2
= 1
3x1 - x2 + ax3
= 1
x1 + 3x2 + 2x3
x12x2+2x3
= -b
= 4
1 For what values of a, b will the system be inconsistent?
2 For what values of a, b will the system have only one solution?
For what values of a, b will the saystem have infinitely many solutions?
Chapter 4 Solutions
Introductory Algebra for College Students (7th Edition)
Ch. 4.1 - Prob. 1CAVCCh. 4.1 - Fill in each blank so that the resulting statement...Ch. 4.1 - Prob. 3CAVCCh. 4.1 - Prob. 4CAVCCh. 4.1 - Prob. 1ESCh. 4.1 - Prob. 2ESCh. 4.1 - Prob. 3ESCh. 4.1 - In Exercises 1-10, determine whether the given...Ch. 4.1 - Prob. 5ESCh. 4.1 - Prob. 6ES
Ch. 4.1 - Prob. 7ESCh. 4.1 - Prob. 8ESCh. 4.1 - Prob. 9ESCh. 4.1 - Prob. 10ESCh. 4.1 - Prob. 11ESCh. 4.1 - Prob. 12ESCh. 4.1 - Prob. 13ESCh. 4.1 - Prob. 14ESCh. 4.1 - In Exercises 11-42, solve each system by graphing....Ch. 4.1 - Prob. 16ESCh. 4.1 - Prob. 17ESCh. 4.1 - Prob. 18ESCh. 4.1 - Prob. 19ESCh. 4.1 - Prob. 20ESCh. 4.1 - Prob. 21ESCh. 4.1 - Prob. 22ESCh. 4.1 - In Exercises 11-42, solve each system by graphing....Ch. 4.1 - In Exercises 11-42, solve each system by graphing....Ch. 4.1 - Prob. 25ESCh. 4.1 - Prob. 26ESCh. 4.1 - In Exercises 11-42, solve each system by graphing....Ch. 4.1 - Prob. 28ESCh. 4.1 - Prob. 29ESCh. 4.1 - Prob. 30ESCh. 4.1 - Prob. 31ESCh. 4.1 - Prob. 32ESCh. 4.1 - Prob. 33ESCh. 4.1 - Prob. 34ESCh. 4.1 - Prob. 35ESCh. 4.1 - Prob. 36ESCh. 4.1 - Prob. 37ESCh. 4.1 - Prob. 38ESCh. 4.1 - Prob. 39ESCh. 4.1 - Prob. 40ESCh. 4.1 - Prob. 41ESCh. 4.1 - Prob. 42ESCh. 4.1 - Prob. 43ESCh. 4.1 - Prob. 44ESCh. 4.1 - In Exercises 43-50, find the slope the y-intercept...Ch. 4.1 - In Exercises 43-50, find the slope the y-intercept...Ch. 4.1 - Prob. 47ESCh. 4.1 - Prob. 48ESCh. 4.1 - Prob. 49ESCh. 4.1 - In Exercises 43-50, find the slope the y-intercept...Ch. 4.1 - A rental company charges 40.00 a day plus 0.35 per...Ch. 4.1 - Prob. 52ESCh. 4.1 - Prob. 53ESCh. 4.1 - What is a system of linear equations? Provide an...Ch. 4.1 - Prob. 55ESCh. 4.1 - Prob. 56ESCh. 4.1 - Explain how to solve a system of linear equations...Ch. 4.1 - Prob. 58ESCh. 4.1 - Prob. 59ESCh. 4.1 - Prob. 60ESCh. 4.1 - Prob. 61ESCh. 4.1 - Prob. 62ESCh. 4.1 - Make Sense? In Exercises 62-65 determine whether...Ch. 4.1 - Prob. 64ESCh. 4.1 - Prob. 65ESCh. 4.1 - Prob. 66ESCh. 4.1 - Prob. 67ESCh. 4.1 - Prob. 68ESCh. 4.1 - Prob. 69ESCh. 4.1 - Prob. 70ESCh. 4.1 - In Exercises 66-69 determine whether each...Ch. 4.1 - Prob. 72ESCh. 4.1 - Prob. 73ESCh. 4.1 - Prob. 74ESCh. 4.1 - Prob. 75ESCh. 4.1 - Prob. 76ESCh. 4.1 - Prob. 77ESCh. 4.1 - Prob. 78ESCh. 4.1 - Prob. 79ESCh. 4.1 - Prob. 80ESCh. 4.1 - Prob. 81ESCh. 4.1 - Prob. 82ESCh. 4.1 - Prob. 83ESCh. 4.1 - Prob. 84ESCh. 4.1 - Prob. 85ESCh. 4.1 - Prob. 86ESCh. 4.2 - Fill in each blank so that the resulting statement...Ch. 4.2 - Prob. 2CAVCCh. 4.2 - Prob. 3CAVCCh. 4.2 - Prob. 4CAVCCh. 4.2 - Prob. 5CAVCCh. 4.2 - Prob. 1ESCh. 4.2 - Prob. 2ESCh. 4.2 - In Exercises 1-32, solve each system by the...Ch. 4.2 - In Exercises 1-32, solve each system by the...Ch. 4.2 - Prob. 5ESCh. 4.2 - Prob. 6ESCh. 4.2 - Prob. 7ESCh. 4.2 - Prob. 8ESCh. 4.2 - Prob. 9ESCh. 4.2 - Prob. 10ESCh. 4.2 - Prob. 11ESCh. 4.2 - Prob. 12ESCh. 4.2 - Prob. 13ESCh. 4.2 - Prob. 14ESCh. 4.2 - Prob. 15ESCh. 4.2 - Prob. 16ESCh. 4.2 - Prob. 17ESCh. 4.2 - Prob. 18ESCh. 4.2 - Prob. 19ESCh. 4.2 - Prob. 20ESCh. 4.2 - Prob. 21ESCh. 4.2 - Prob. 22ESCh. 4.2 - Prob. 23ESCh. 4.2 - Prob. 24ESCh. 4.2 - Prob. 25ESCh. 4.2 - Prob. 26ESCh. 4.2 - Prob. 27ESCh. 4.2 - Prob. 28ESCh. 4.2 - Prob. 29ESCh. 4.2 - In Exercises 1-32, solve each system by the...Ch. 4.2 - Prob. 31ESCh. 4.2 - Prob. 32ESCh. 4.2 - Prob. 33ESCh. 4.2 - In Exercises 33-38,, write a system of equation...Ch. 4.2 - Prob. 35ESCh. 4.2 - In Exercises 33-38,, write a system of equation...Ch. 4.2 - Prob. 37ESCh. 4.2 - Prob. 38ESCh. 4.2 - Prob. 39ESCh. 4.2 - Prob. 40ESCh. 4.2 - The table shows the price of a gallon of unleaded...Ch. 4.2 - Prob. 42ESCh. 4.2 - Prob. 43ESCh. 4.2 - Prob. 44ESCh. 4.2 - Prob. 45ESCh. 4.2 - Prob. 46ESCh. 4.2 - Prob. 47ESCh. 4.2 - Prob. 48ESCh. 4.2 - Prob. 49ESCh. 4.2 - Make Sense? In Exercise 48-51, determine whether...Ch. 4.2 - Prob. 51ESCh. 4.2 - Prob. 52ESCh. 4.2 - Prob. 53ESCh. 4.2 - Prob. 54ESCh. 4.2 - Prob. 55ESCh. 4.2 - Prob. 56ESCh. 4.2 - Prob. 57ESCh. 4.2 - Prob. 58ESCh. 4.2 - Prob. 59ESCh. 4.2 - Prob. 60ESCh. 4.2 - Prob. 61ESCh. 4.2 - Prob. 62ESCh. 4.2 - Prob. 63ESCh. 4.3 - Prob. 1CAVCCh. 4.3 - Prob. 2CAVCCh. 4.3 - Prob. 3CAVCCh. 4.3 - Prob. 4CAVCCh. 4.3 - Prob. 1ESCh. 4.3 - Prob. 2ESCh. 4.3 - Prob. 3ESCh. 4.3 - Prob. 4ESCh. 4.3 - Prob. 5ESCh. 4.3 - Prob. 6ESCh. 4.3 - Prob. 7ESCh. 4.3 - Prob. 8ESCh. 4.3 - Prob. 9ESCh. 4.3 - Prob. 10ESCh. 4.3 - Prob. 11ESCh. 4.3 - Prob. 12ESCh. 4.3 - Prob. 13ESCh. 4.3 - Prob. 14ESCh. 4.3 - Prob. 15ESCh. 4.3 - Prob. 16ESCh. 4.3 - Prob. 17ESCh. 4.3 - Prob. 18ESCh. 4.3 - Prob. 19ESCh. 4.3 - Prob. 20ESCh. 4.3 - Prob. 21ESCh. 4.3 - Prob. 22ESCh. 4.3 - Prob. 23ESCh. 4.3 - Prob. 24ESCh. 4.3 - Prob. 25ESCh. 4.3 - Prob. 26ESCh. 4.3 - Prob. 27ESCh. 4.3 - Prob. 28ESCh. 4.3 - Prob. 29ESCh. 4.3 - Prob. 30ESCh. 4.3 - Prob. 31ESCh. 4.3 - Prob. 32ESCh. 4.3 - Prob. 33ESCh. 4.3 - Prob. 34ESCh. 4.3 - Prob. 35ESCh. 4.3 - Prob. 36ESCh. 4.3 - Prob. 37ESCh. 4.3 - Prob. 38ESCh. 4.3 - Prob. 39ESCh. 4.3 - Prob. 40ESCh. 4.3 - In Exercise 1-44, solve each sytem by the addition...Ch. 4.3 - In Exercise 1-44, solve each sytem by the addition...Ch. 4.3 - Prob. 43ESCh. 4.3 - In Exercise 1-44, solve each sytem by the addition...Ch. 4.3 - Prob. 45ESCh. 4.3 - Prob. 46ESCh. 4.3 - In Exercise 45-56, solve each sytem by the method...Ch. 4.3 - In Exercise 45-56, solve each sytem by the method...Ch. 4.3 - Prob. 49ESCh. 4.3 - Prob. 50ESCh. 4.3 - Prob. 51ESCh. 4.3 - Prob. 52ESCh. 4.3 - Prob. 53ESCh. 4.3 - Prob. 54ESCh. 4.3 - In Exercise 45-56, solve each sytem by the method...Ch. 4.3 - In Exercise 45-56, solve each sytem by the method...Ch. 4.3 - In Exercise 57-60, write a system of equations...Ch. 4.3 - In Exercise 57-60, write a system of equations...Ch. 4.3 - In Exercise 57-60, write a system of equations...Ch. 4.3 - In Exercise 57-60, write a system of equations...Ch. 4.3 - In Exercise 61-68, solve each system or state that...Ch. 4.3 - In Exercise 61-68, solve each system or state that...Ch. 4.3 - In Exercise 61-68, solve each system or state that...Ch. 4.3 - In Exercise 61-68, solve each system or state that...Ch. 4.3 - In Exercise 61-68, solve each system or state that...Ch. 4.3 - In Exercise 61-68, solve each system or state that...Ch. 4.3 - In Exercise 61-68, solve each system or state that...Ch. 4.3 - In Exercise 61-68, solve each system or state that...Ch. 4.3 - We opened this section with a study showing that...Ch. 4.3 - The bar graph shows the percentage of U.S. income...Ch. 4.3 - Explain how to solve a system of equations using...Ch. 4.3 - When using the addition method, how can you tell...Ch. 4.3 - When using the addition method, how can you tell...Ch. 4.3 - Prob. 74ESCh. 4.3 - The formula 3239x+96y=134,014 models the number of...Ch. 4.3 - Make Sense? In Exercises 76-79, determine whether...Ch. 4.3 - Prob. 77ESCh. 4.3 - Make Sense? In Exercises 76-79, determine whether...Ch. 4.3 - Make Sense? In Exercises 76-79, determine whether...Ch. 4.3 - In Exercises 80-83, determine whether each...Ch. 4.3 - In Exercises 80-83, determine whether each...Ch. 4.3 - In Exercises 80-83, determine whether each...Ch. 4.3 - In Exercises 80-83, determine whether each...Ch. 4.3 - Solve by expressing x and y in terms of a and b:...Ch. 4.3 - The point of interesection of the graphs of the...Ch. 4.3 - For which number is 5 times the number equal to...Ch. 4.3 - Prob. 87ESCh. 4.3 - Prob. 88ESCh. 4.3 - Prob. 89ESCh. 4.3 - Exercises 89-91 will help you prepare for the...Ch. 4.3 - Prob. 91ESCh. 4.4 - Prob. 1CAVCCh. 4.4 - Prob. 2CAVCCh. 4.4 - Prob. 3CAVCCh. 4.4 - Prob. 4CAVCCh. 4.4 - Prob. 5CAVCCh. 4.4 - In Exercises 1-4, let x represent one number and...Ch. 4.4 - In Exercises 1-4, let x represent one number and...Ch. 4.4 - In Exercises 1-4, let x represent one number and...Ch. 4.4 - In Exercises 1-4, let x represent one number and...Ch. 4.4 - The bar graph shows the average time per day that...Ch. 4.4 - The bar graph shows the average time per day that...Ch. 4.4 - Prob. 7ESCh. 4.4 - Looking for Mr. Goobar? It’s probably not a good...Ch. 4.4 - Prob. 9ESCh. 4.4 - Prob. 10ESCh. 4.4 - Prob. 11ESCh. 4.4 - Prob. 12ESCh. 4.4 - Prob. 13ESCh. 4.4 - Prob. 14ESCh. 4.4 - Prob. 15ESCh. 4.4 - Prob. 16ESCh. 4.4 - You are choosing between two cellphone plans. Data...Ch. 4.4 - You are choosing between two cellphone plans. Data...Ch. 4.4 - Prob. 19ESCh. 4.4 - You are choosing between two plans at a discunt...Ch. 4.4 - A community center sells a total of 301 tickets...Ch. 4.4 - On a special day, tickets for a minor league...Ch. 4.4 - Prob. 23ESCh. 4.4 - Prob. 24ESCh. 4.4 - Prob. 25ESCh. 4.4 - Prob. 26ESCh. 4.4 - Prob. 27ESCh. 4.4 - Prob. 28ESCh. 4.4 - Prob. 29ESCh. 4.4 - Exercises 29-36 involve dual investments. You...Ch. 4.4 - Exercises 29-36 involve dual investments. A bank...Ch. 4.4 - Prob. 32ESCh. 4.4 - Prob. 33ESCh. 4.4 - Prob. 34ESCh. 4.4 - Prob. 35ESCh. 4.4 - Exercises 29-36 involve dual investments. You...Ch. 4.4 - Prob. 37ESCh. 4.4 - Exercises 37-42 involve mixtures. A candy company...Ch. 4.4 - Prob. 39ESCh. 4.4 - Exercises 37-42 involve mixtures. A lab technician...Ch. 4.4 - Exercises 37-42 involve mixtures. A lab technician...Ch. 4.4 - Exercises 37-42 involve mixtures. A lab technician...Ch. 4.4 - Describe the conditions in a problem that enable...Ch. 4.4 - Use Figure 4.11 on page 313 to write a world...Ch. 4.4 - Prob. 45ESCh. 4.4 - Prob. 46ESCh. 4.4 - Prob. 47ESCh. 4.4 - Prob. 48ESCh. 4.4 - Prob. 49ESCh. 4.4 - Prob. 50ESCh. 4.4 - Prob. 51ESCh. 4.4 - Prob. 52ESCh. 4.4 - Prob. 53ESCh. 4.4 - Prob. 54ESCh. 4.4 - Prob. 55ESCh. 4.4 - Prob. 56ESCh. 4.4 - Prob. 57ESCh. 4.4 - Select any two problems that you sdved from...Ch. 4.4 - Prob. 59ESCh. 4.4 - Prob. 60ESCh. 4.4 - Prob. 61ESCh. 4.4 - Prob. 62ESCh. 4.4 - Prob. 63ESCh. 4.4 - Prob. 64ESCh. 4.5 - Fill in each blank so that the resulting statement...Ch. 4.5 - Prob. 2CAVCCh. 4.5 - Prob. 3CAVCCh. 4.5 - Prob. 4CAVCCh. 4.5 - In Exercises 1-36, graph the solution set of each...Ch. 4.5 - In Exercise 1-36, graph the solution set of each...Ch. 4.5 - Prob. 3ESCh. 4.5 - Prob. 4ESCh. 4.5 - Prob. 5ESCh. 4.5 - Prob. 6ESCh. 4.5 - Prob. 7ESCh. 4.5 - Prob. 8ESCh. 4.5 - Prob. 9ESCh. 4.5 - In Exercises 1-36, graph the solution set of each...Ch. 4.5 - Prob. 11ESCh. 4.5 - Prob. 12ESCh. 4.5 - Prob. 13ESCh. 4.5 - Prob. 14ESCh. 4.5 - In Exercises 1-36, graph the solution set of each...Ch. 4.5 - Prob. 16ESCh. 4.5 - Prob. 17ESCh. 4.5 - Prob. 18ESCh. 4.5 - Prob. 19ESCh. 4.5 - In Exercises 1-36, graph the solution set of each...Ch. 4.5 - Prob. 21ESCh. 4.5 - Prob. 22ESCh. 4.5 - Prob. 23ESCh. 4.5 - Prob. 24ESCh. 4.5 - Prob. 25ESCh. 4.5 - Prob. 26ESCh. 4.5 - In Exercises 1-36, graph the solution set of each...Ch. 4.5 - Prob. 28ESCh. 4.5 - Prob. 29ESCh. 4.5 - Prob. 30ESCh. 4.5 - In Exercises 1-36, graph the solution set of each...Ch. 4.5 - Prob. 32ESCh. 4.5 - Prob. 33ESCh. 4.5 - Prob. 34ESCh. 4.5 - Prob. 35ESCh. 4.5 - Prob. 36ESCh. 4.5 - Prob. 37ESCh. 4.5 - Prob. 38ESCh. 4.5 - Prob. 39ESCh. 4.5 - Prob. 40ESCh. 4.5 - Prob. 41ESCh. 4.5 - Prob. 42ESCh. 4.5 - Prob. 43ESCh. 4.5 - Prob. 44ESCh. 4.5 - Prob. 45ESCh. 4.5 - Prob. 46ESCh. 4.5 - Prob. 47ESCh. 4.5 - Prob. 48ESCh. 4.5 - Prob. 49ESCh. 4.5 - What does the graph of a sytem of linear...Ch. 4.5 - Look at the shaded region on the previous page...Ch. 4.5 - Mak Sense?In Exercise 52-55, determine whether...Ch. 4.5 - Prob. 53ESCh. 4.5 - Mak Sense?In Exercise 52-55, determine whether...Ch. 4.5 - Prob. 55ESCh. 4.5 - Prob. 56ESCh. 4.5 - Prob. 57ESCh. 4.5 - Prob. 58ESCh. 4.5 - Prob. 59ESCh. 4.5 - Prob. 60ESCh. 4.5 - Prob. 61ESCh. 4.5 - Prob. 62ESCh. 4.5 - Prob. 63ESCh. 4.5 - Prob. 64ESCh. 4.5 - Prob. 65ESCh. 4.5 - Prob. 66ESCh. 4.5 - Prob. 67ESCh. 4 - In Exercises 1-3, solve each system by graphing....Ch. 4 - Prob. 2MCPCh. 4 - Prob. 3MCPCh. 4 - Prob. 4MCPCh. 4 - Prob. 5MCPCh. 4 - Prob. 6MCPCh. 4 - Prob. 7MCPCh. 4 - Prob. 8MCPCh. 4 - Prob. 9MCPCh. 4 - Prob. 10MCPCh. 4 - Prob. 11MCPCh. 4 - sIn Exercises 4-15, solve each system by the...Ch. 4 - In Exercises 4-15, solve each system by the method...Ch. 4 - Prob. 14MCPCh. 4 - In Exercises 4-15, solve each system by the method...Ch. 4 - In Exercises 1-2, determine whether the given...Ch. 4 - In Exercises 1-2, deterine whether the given...Ch. 4 - Does the graphing-utility screen show the solution...Ch. 4 - In Exercises 4-14, solve each sytem by graphing....Ch. 4 - In Exercises 4-14, solve each sytem by graphing....Ch. 4 - In Exercises 4-14, solve each sytem by graphing....Ch. 4 - In Exercises 4-14, solve each sytem by graphing....Ch. 4 - In Exercises 4-14, solve each sytem by graphing....Ch. 4 - In Exercises 4-14, solve each sytem by graphing....Ch. 4 - In Exercises 4-14, solve each sytem by graphing....Ch. 4 - In Exercises 4-14, solve each sytem by graphing....Ch. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - In Exercises 25-35, solve each sytem by the...Ch. 4 - In Exercises 25-35, solve each sytem by the...Ch. 4 - In Exercises 25-35, solve each sytem by the...Ch. 4 - In Exercises 25-35, solve each sytem by the...Ch. 4 - In Exercises 25-35, solve each sytem by the...Ch. 4 - In Exercises 25-35, solve each sytem by the...Ch. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Health experts agree that cholesterol intake...Ch. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - A chemist needs to mix a 75% saltwater solution...Ch. 4 - Prob. 51RECh. 4 - Prob. 52RECh. 4 - Prob. 53RECh. 4 - In Exercises 51-57, graph the solution set of each...Ch. 4 - In Exercises 51-57, graph the solution set of each...Ch. 4 - In Exercises 51-57, graph the solution set of each...Ch. 4 - In Exercises 51-57, graph the solution set of each...Ch. 4 - Prob. 1TCh. 4 - In Exercisses 1-2, determine whether the given...Ch. 4 - In Exercisses 3-4, solve each system by graphing....Ch. 4 - Prob. 4TCh. 4 - In Exercisses 5-7, solve each system by the...Ch. 4 - In Exercisses 5-7, solve each system by the...Ch. 4 - Prob. 7TCh. 4 - Prob. 8TCh. 4 - Prob. 9TCh. 4 - In Exercisses 8-10, solve each system by the...Ch. 4 - Our Dogs, OurseIves. Dogs rely on a dazzling sense...Ch. 4 - A rectangular garden has perimeter of 34 yards,...Ch. 4 - You are choosing between two cellphone plans Data...Ch. 4 - You invested $6000 in two accounts paying 9% and...Ch. 4 - A chemist needs to mix a 50% acid solution with an...Ch. 4 - Prob. 16TCh. 4 - Prob. 17TCh. 4 - Perform the indicated operations: 14[18(610)].Ch. 4 - Simplify: 6(3x2)(x1).Ch. 4 - Prob. 3CRECh. 4 - In Exercises 3-4, solve each equation. 4 x41=x5Ch. 4 - In Exercises 3-4, solve each equation. 5. Solve...Ch. 4 - Prob. 6CRECh. 4 - In Exercise 7-9, graph each equation in the...Ch. 4 - In Exercise 7-9, graph each equation in the...Ch. 4 - Prob. 9CRECh. 4 - Prob. 10CRECh. 4 - Prob. 11CRECh. 4 - Prob. 12CRECh. 4 - Prob. 13CRECh. 4 - Prob. 14CRECh. 4 - Prob. 15CRECh. 4 - Prob. 16CRECh. 4 - Prob. 17CRECh. 4 - Prob. 18CRECh. 4 - Prob. 19CRECh. 4 - Prob. 20CRE
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