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mathematics
precalculus 1st

Precalculus 1st Edition Jay Abramson - Solutions

For the following exercises, solve the system for x, y, and z.The top three oil producers in the United States in a certain year are the Gulf of Mexico, Texas, and Alaska. The three regions were responsible for 64% of the United States oil production. The Gulf of Mexico and Texas combined for 47%
For the following exercises, use a system of linear equations with two variables and two equations to solve.A jeep and BMW enter a highway running eastwest at the same exit heading in opposite directions. The jeep entered the highway 30 minutes before the BMW did, and traveled 7 mph slower than
For the following exercises, use this scenario: A health-conscious company decides to make a trail mix out of almonds, dried cranberries, and chocolate-covered cashews. The nutritional information for these items is shown in Table 1.For the “hiking” mix, there are 1,000 pieces in the mix,
For the following exercises, solve the system for x, y, and z.The top three sources of oil imports for the United States in the same year were Saudi Arabia, Mexico, and Canada. The three top countries accounted for 47% of oil imports. The United States imported 1.8% more from Saudi Arabia than they
For the following exercises, find the solutions by computing the inverse of the matrix. 4x + 3y - 3z = -4.3 5x4yz = -6.1 x+2=-0.7
For the following exercises, use a system of linear equations with two variables and two equations to solve.There were 130 faculty at a conference. If there were 18 more women than men attending, how many of each gender attended the conference?
For the following exercises, solve the system for x, y, and z.Last year, at Haven’s Pond Car Dealership, for a particular model of BMW, Jeep, and Toyota, one could purchase all three cars for a total of $140,000. This year, due to inflation, the same cars would cost $151,830. The cost of the BMW
For the following exercises, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule.Your garden produced two types of tomatoes, one green and one red. The red weigh 10 oz, and the green weigh 4 oz. You have 30 tomatoes, and a
For the following exercises, use Cramer’s Rule to solve the linear systems of equations. 4x − 2y = 23−5x − 10y = −35
For the following exercises, find the determinant. [Ve 2 0 गत 0V2 0 0 0 V2
For the following exercises, use a system of linear equations with two variables and two equations to solve.A store clerk sold 60 pairs of sneakers. The high-tops sold for $98.99 and the low-tops sold for $129.99. If the receipts for the two types of sales totaled $6,404.40, how many of each type
For the following exercises, find the determinant. -1 4 02 0 0 3] 3 -3.
For the following exercises, use a system of linear equations with two variables and two equations to solve.CDs cost $5.96 more than DVDs at All Bets Are Off Electronics. How much would 6 CDs and 2 DVDs cost if 5 CDs and 2 DVDs cost $127.73?
For the following exercises, find the determinant. 0.2 -0.61 0.7 -1.1.
For the following exercises, use a system of linear equations with two variables and two equations to solve.If an investor invests $23,000 into two bonds, one that pays 4% in simple interest, and the other paying 2% simple interest, and the investor earns $710.00 annual interest, how much was
For the following exercises, find the determinant. 100 0 [¹⁰⁰] 0
For the following exercises, use a system of linear equations with two variables and two equations to solve.If an investor invests a total of $25,000 into two bonds, one that pays 3% simple interest, and the other that pays 2 7/8 % interest, and the investor earns $737.50 annual interest, how much
For the following exercises, use a system of linear equations with two variables and two equations to solve.An investor who dabbles in real estate invested 1.1 million dollars into two land investments. On the first investment, Swan Peak, her return was a 110% increase on the money she invested. On
For the following exercises, solve the system for x, y, and z.Meat consumption in the United States can be broken into three categories: red meat, poultry, and fish. If fish makes up 4% less than one-quarter of poultry consumption, and red meat consumption is 18.2% higher than poultry consumption,
For the following exercises, write a system of equations to solve each problem. Solve the system of equations.A sorority held a bake sale to raise money and sold brownies and chocolate chip cookies. They priced the brownies at $2 and the chocolate chip cookies at $1. They raised $250 and sold 175
For the following exercises, use a system of linear equations with two variables and two equations to solve.An investor earned triple the profits of what she earned last year. If she made $500,000.48 total for both years, how much did she earn in profits each year?
For the following exercises, perform the operation and then find the partial fraction decomposition. 1 x-4 3 x+6 2x + 7 x² + 2x - 24
For the following exercises, use the matrix below to perform the indicated operation on the given matrix. B4 [10 0 0 001 1 0 B= 0 0
For the following exercises, construct a system of nonlinear equations to describe the given behavior, then solve for the requested solutions.A cell phone company has the following cost and revenue functions: C(x) = 8x2 − 600x + 21,500 and R(x) = −3x2 + 480x. What is the range of cell phones
For the following exercises, solve for the desired quantity.A cell phone factory has a cost of production C(x) = 150x + 10,000 and a revenue function R(x) = 200x. What is the break-even point?
For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix.Anna, Ashley, and Andrea weigh a combined 370 lb. If Andrea weighs 20 lb more than Ashley, and Anna weighs 1.5 times as much as Ashley, how much does each
For the following exercises, solve the system of linear equations using Gaussian elimination.−1.1x − 2.3y = 6.2−5.2x − 4.1y = 4.3
For the following exercises, solve the system for x, y, and z.At a carnival, $2,914.25 in receipts were taken at the end of the day. The cost of a child’s ticket was $20.50, an adult ticket was $29.75, and a senior citizen ticket was $15.25. There were twice as many senior citizens as adults in
For the following exercises, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule.You sold two types of scarves at a farmers’ market and would like to know which one was more popular. The total number of scarves sold was 56,
For the following exercises, use the matrix below to perform the indicated operation on the given matrix. B5 [10 0 B 0 0 1 = 01 10 0]
For the following exercises, perform the operation and then find the partial fraction decomposition. 2x - 16 1-2x x² + 6x + 8 x-5 x² - 4x
For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution.The three most popular ice cream flavors are chocolate, strawberry, and vanilla, comprising 83% of the flavors sold at an ice cream shop. If vanilla sells 1% more than twice
For the following exercises, solve the system of linear equations using Gaussian elimination. 2x + 3y + 2z=1 -4x6y4z=-2 10x + 15y + 10z = 0
For the following exercises, solve for the desired quantity.A musician charges C(x) = 64x + 20,000, where x is the total number of attendees at the concert. The venue charges $80 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold
For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix.Three roommates shared a package of 12 ice cream bars, but no one remembers who ate how many. If Tom ate twice as many ice cream bars as Joe, and Albert ate
For the following exercises, use the matrix below to perform the indicated operation on the given matrix. Using the above questions, find a formula for Bn . Test the formula for B201 and B202, using a calculator. Γ1 0 07 1 B=|0 0 [0 I 07
For the following exercises, solve the system of linear equations using Gaussian elimination. -x+2y-4z = 8 3y + 8z = - 4 -7x+y+ 2z = 1
For the following exercises, solve the system for x, y, and z.A local band sells out for their concert. They sell all 1,175 tickets for a total purse of $28,112.50. The tickets were priced at $20 for student tickets, $22.50 for children, and $29 for adult tickets. If the band sold twice as many
For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution.At an ice cream shop, three flavors are increasing in demand. Last year, banana, pumpkin, and rocky road ice cream made up 12% of total ice cream sales. This year, the same
For the following exercises, solve for the desired quantity.A guitar factory has a cost of production C(x) = 75x + 50,000. If the company needs to break even after 150 units sold, at what price should they sell each guitar? Round up to the nearest dollar, and write the revenue function.
For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix.A farmer constructed a chicken coop out of chicken wire, wood, and plywood. The chicken wire cost $2 per square foot, the wood $10 per square foot, and the
For the following exercises, solve the system for x, y, and z.In a bag, a child has 325 coins worth $19.50. There were three types of coins: pennies, nickels, and dimes. If the bag contained the same number of nickels as dimes, how many of each type of coin was in the bag?
For the following exercises, find the inverse of the matrix. -0.2 1.4] 1.2 -0.4
For the following exercises, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule.At a market, the three most popular vegetables make up 53% of vegetable sales. Corn has 4% higher sales than broccoli, which has 5% more sales
For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution.A bag of mixed nuts contains cashews, pistachios, and almonds. There are 1,000 total nuts in the bag, and there are 100 less almonds than pistachios. The cashews weigh 3 g,
For the following exercises, use a system of linear equations with two variables and two equations to solve. Find two numbers whose sum is 28 and difference is 13.
For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix.Jay has lemon, orange, and pomegranate trees in his backyard. An orange weighs 8 oz, a lemon 5 oz, and a pomegranate 11 oz. Jay picked 142 pieces of fruit
For the following exercises, find the inverse of the matrix. 1214 A |WN|T
For the following exercises, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule.At the same market, the three most popular fruits make up 37% of the total fruit sold. Strawberries sell twice as much as oranges, and kiwis sell
For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution.A bag of mixed nuts contains cashews, pistachios, and almonds. Originally there were 900 nuts in the bag. 30% of the almonds, 20% of the cashews, and 10% of the pistachios were
For the following exercises, use a system of linear equations with two variables and two equations to solve.A number is 9 more than another number. Twice the sum of the two numbers is 10. Find the two numbers.
For the following exercises, find the inverse of the matrix. 12 -1 -4 9 3 -3 -67 2 2]
For the following exercises, solve the system for x, y, and z.A recent college graduate took advantage of his business education and invested in three investments immediately after graduating. He invested $80,500 into three accounts, one that paid 4% simple interest, one that paid 4% simple
For the following exercises, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule.Three bands performed at a concert venue. The first band charged $15 per ticket, the second band charged $45 per ticket, and the final band
For the following exercises, use a system of linear equations with two variables and two equations to solve.The startup cost for a restaurant is $120,000, and each meal costs $10 for the restaurant to make. If each meal is then sold for $15, after how many meals does the restaurant break even?
For the following exercises, find the inverse of the matrix. 2 1 12 L3 2 3] 3 1
For the following exercises, solve the system for x, y, and z.You inherit one million dollars. You invest it all in three accounts for one year. The first account pays 3% compounded annually, the second account pays 4% compounded annually, and the third account pays 2% compounded annually. After
For the following exercises, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule.A movie theatre sold tickets to three movies. The tickets to the first movie were $5, the tickets to the second movie were $11, and the third
For the following exercises, use a system of linear equations with two variables and two equations to solve.A moving company charges a flat rate of $150, and an additional $5 for each box. If a taxi service would charge $20 for each box, how many boxes would you need for it to be cheaper to use the
For the following exercises, solve the system for x, y, and z.You inherit one hundred thousand dollars. You invest it all in three accounts for one year. The first account pays 4% compounded annually, the second account pays 3% compounded annually, and the third account pays 2% compounded annually.
For the following exercises, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule.Men aged 20–29, 30–39, and 40–49 made up 78% of the population at a prison last year. This year, the same age groups made up 82.08% of the
For the following exercises, use a system of linear equations with two variables and two equations to solve.A total of 1,595 first- and second-year college students gathered at a pep rally. The number of freshmen exceeded the number of sophomores by 15. How many freshmen and sophomores were in
For the following exercises, find the solutions by computing the inverse of the matrix. 0.3x − 0.1y = −10−0.1x + 0.3y = 14
For the following exercises, solve the system for x, y, and z.The top three countries in oil consumption in a certain year are as follows: the United States, Japan, and China. In millions of barrels per day, the three top countries consumed 39.8% of the world’s consumed oil. The United States
For the following exercises, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule.At a women’s prison down the road, the total number of inmates aged 20–49 totaled 5,525. This year, the 20–29 age group increased by 10%,
For the following exercises, use a system of linear equations with two variables and two equations to solve.276 students enrolled in a freshman-level chemistry class. By the end of the semester, 5 times the number of students passed as failed. Find the number of students who passed, and the number
For the following exercises, find the solutions by computing the inverse of the matrix.0.4x − 0.2y = −0.6−0.1x + 0.05y = 0.3
For the following exercises, solve the system for x, y, and z.The top three countries in oil production in the same year are Saudi Arabia, the United States, and Russia. In millions of barrels per day, the top three countries produced 31.4% of the world’s produced oil. Saudi Arabia and the United
For the following exercises, use this scenario: A health-conscious company decides to make a trail mix out of almonds, dried cranberries, and chocolate-covered cashews. The nutritional information for these items is shown in Table 1.For the special “low-carb” trail mix, there are 1,000 pieces
For the following exercises, find the solutions to the nonlinear equations with two variables. x² + 4xy-2y²-6=0 x = y + 2
For the following exercises, solve the system for x, y, and z.Three numbers sum up to 147. The smallest number is half the middle number, which is half the largest number. What are the three numbers?
For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. x² + x³ + 8x²² + 6x +36 z(9 + zx)x
For the following exercises, solve each system in terms of A, B, C, D, E, and F where A – F are nonzero numbers. Note that A ≠ B and AE ≠ BD. Ax + y = 0 Bx + y = 1
For the following exercises, create a system of linear equations to describe the behavior. Then, calculate the determinant. Will there be a unique solution? If so, find the unique solution.Three numbers add to 216. The sum of the first two numbers is 112. The third number is 8 less than the first
For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. Every day, a cupcake store sells 5,000 cupcakes in chocolate and vanilla flavors. If the chocolate flavor is 3 times as popular as the vanilla flavor, how many of each
For the following exercises, write the augmented matrix from the system of linear equations. -2x+2y+z=7 2x - 8y + 5z = 0 19x 10y +22z = 3
For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. In the previous exercise, if you were told there were 400 more tickets sold for floor 2 than floor 1, how much was the price of each ticket?
For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. Use a calculator to verify your solution. BC A = -2 1 |0.5 0 91 8-3, B 4 5] || 0.5 3 -4 1 8 01 6, C 7 2 C = [1 0 0 1 0 1 0 1] 0 1,
For the following exercises, solve the system for x, y, and z.At a family reunion, there were only blood relatives, consisting of children, parents, and grandparents, in attendance. There were 400 people total. There were twice as many parents as grandparents, and 50 more children than parents. How
For the following exercises, solve the system of inequalities. Use a calculator to graph the system to confirm the answer. xy < 1 y> Vx
For the following exercises, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. You invest $10,000 into two accounts, which receive 8% interest and 5% interest. At the end of a year, you had $10,710 in your combined
For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution.At a competing cupcake store, $4,520 worth of cupcakes are sold daily. The chocolate cupcakes cost $2.25 and the red velvet cupcakes cost $1.75. If the total number of cupcakes
For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. 2x – 9 (x2 - x)2
For the following exercises, solve for the desired quantity. A fast-food restaurant has a cost of production C(x) = 11x + 120 and a revenue function R(x) =5x. When does the company start to turn a profit?
For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix.A clothing store needs to order new inventory. It has three different types of hats for sale: straw hats, beanies, and cowboy hats. The straw hat is priced at
For the following exercises, write the augmented matrix from the system of linear equations. x + 3z = 12 -x + 4y = 0 y + 2z = -7
For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution.You invested $2,300 into account 1, and $2,700 into account 2. If the total amount of interest after one year is $254, and account 2 has 1.5 times the interest rate of account
For the following exercises, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule.A movie theater needs to know how many adult tickets and children tickets were sold out of the 1,200 total tickets. If children’s tickets are
For the following exercises, solve the system for x, y, and z.Your roommate, Sarah, offered to buy groceries for you and your other roommate. The total bill was $82. She forgot to save the individual receipts but remembered that your groceries were $0.05 cheaper than half of her groceries, and that
For the following exercises, solve each system in terms of A, B, C, D, E, and F where A – F are nonzero numbers. Note that A ≠ B and AE ≠ BD. Ax+ By = C Dx + Ey = F
For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. Students were asked to bring their favorite fruit to class. 95% of the fruits consisted of banana, apple, and oranges. If oranges were twice as popular
For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution.You invested $10,000 into two accounts: one that has simple 3% interest, the other with 2.5% interest. If your total interest payment after one year was $283.50, how much was in
For the following exercises, solve each system in terms of A, B, C, D, E, and F where A – F are nonzero numbers. Note that A ≠ B and AE ≠ BD. Ax+By = C x+y=1
For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. 5x³ - 2x + 1 (x² + 2x)²
For the following exercises, write the augmented matrix from the system of linear equations. 4x + 2y3z 14 -12x + 3y + z = 100 9x6y + 2z = 31
For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. A food drive collected two different types of canned goods, green beans and kidney beans. The total number of collected cans was 350 and the total
For the following exercises, solve the system for x, y, and z.An animal shelter has a total of 350 animals comprised of cats, dogs, and rabbits. If the number of rabbits is 5 less than one-half the number of cats, and there are 20 more cats than dogs, how many of each animal are at the shelter?
For the following exercises, solve the system of inequalities. Use a calculator to graph the system to confirm the answer. x² + y 2x
For the following exercises, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule.You invest $80,000 into two accounts, $22,000 in one account, and $58,000 in the other account. At the end of one year, assuming simple interest,
For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. Use a calculator to verify your solution. ABC A = -2 0 9 18-3, 5] 0.5 4 0.5 3 3 0 1 -4 1 B= -4 6, C = 87 2 0 1 0 1 0 0 1

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