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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

For the following exercises, find the solutions by computing the inverse of the matrix. -2x - 3y + 2z=3 -x + 2y + 4z = -5 -2y + 5z = -3
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
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
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 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
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
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
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,
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
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
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
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,
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
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
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.
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
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
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
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
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’
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
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
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
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,
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
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,
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
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,
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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 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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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

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