Posted: December 19th, 2022

Mat 121 college algebra written assignment 6

  

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MAT-121: COLLEGE ALGEBRA

Written Assignment 6

4 points each

  

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7.1

Algebraic

For the following exercises, determine whether the given ordered pair is a solution to the system of equations.

  1. and and (1, 8)  

For the following exercises, solve each system by substitution.

  1. and  

For the following exercises, solve each system by addition.

  1. and

For the following exercises, solve each system by any method.

  1. and

Graphical

For the following exercises, graph the system of equations and state whether the system is consistent, inconsistent, or dependent and whether the system has one solution, no solution, or infinite solutions.

  1. and  

Real-World Applications

For the following exercises, solve for the desired quantity.

  1. The top band in the state charges , where x is the total number      of attendees at the concert. The venue charges $70 per ticket. After how      many people buy tickets does the venue break even, and what is the value      of the total tickets sold at that point?

For the following exercises, use a system of linear equations with two variables and two equations to solve.

  1. The startup cost for a boutique      is $15,000, and each floral arrangement costs $17 for the boutique to      make. If each arrangement is then sold for $25, after how many      arrangements does the boutique break even? 
  2. If a scientist mixed 15% saline      solution with 48% saline solution to get 20 gallons of 35% saline      solution, how many gallons of 15% and 48% solutions were mixed? Round each      to the nearest whole gallon. 
  3. Admission into an amusement park      for 4 children and 2 adults is $133.50. For 6 children and 4 adults, the      admission is $235.50. Assuming a different price for children and adults,      what is the price of the child ticket and the price of the adult ticket? 

7.2

Algebraic

For the following exercises, determine whether the ordered triple given is the solution to the system of equations.

  1. , , and (-1, 1, 2) 

For the following exercises, solve each system by substitution.

  1. , ,

For the following exercises, solve each system by Gaussian elimination.

  1. , ,

For the following exercises, solve each system by any method.

  1. , ,

Real-World Applications

  1. An animal shelter has a total of      254 animals comprised of cats, dogs, and guinea pigs. If the number of      guinea pigs is one third the number of dogs, and there are 40 more dogs      than cats, how many of each animal are at the shelter? 
  2. The top three countries in oil      consumption in a certain year are as follows: the United States, China,      and Japan. In millions of barrels per day, the three top countries      consumed 32.2 million barrels of the world’s oil. The United States      consumes 12 million more barrels a day than China. China consumes 3.2      million barrels a day than Japan. How many barrels of the world oil      consumption did the United States, Japan, and China consume?

7.3

Algebraic

For the following exercises, solve the system of nonlinear equations using substitution. Simplify any fractions or radicals to lowest terms.

  1. and

For the following exercises, solve the system of nonlinear equations using elimination.

  1. and

For the following exercises, use any method to solve the system of nonlinear equations.

  1. and
  2. and  

  

Graphical

For the following exercises, graph the inequality.

  1. and

  

Extensions

For the following exercises, graph the inequality.

  

Real-World Applications

For the following exercises, construct a system of nonlinear equations to describe the given behavior, then solve for the requested solutions.

  1. Two numbers add up to 144. One      number is half the square of the other number. What are the numbers?
  2. The squares of two numbers add      to 1,156. The second number is the square root of three times the square      of the first number. What are the numbers?

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