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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

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, find the partial fraction expansion. x²+4 (x + 1)³
For the following exercises, find the partial fraction expansion. x³ 4x² + 5x +4 (x - 2)³
For the following exercises, use the matrix below to perform the indicated operation on the given matrix. B2 1 0 0 1 B 0 0 Lo 1 0]
For the following exercises, construct a system of nonlinear equations to describe the given behavior, then solve for the requested solutions. Two numbers add up to 300. One number is twice the
For the following exercises, solve for the desired quantity. A stuffed animal business has a total cost of production C = 12x + 30 and a revenue function R = 20x. Find 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.A sorority held a bake sale to raise money and sold
For the following exercises, solve the system of linear equations using Gaussian elimination.3x − 4y = − 7−6x + 8y = 14
For the following exercises, solve the system for x, y, and z.Your roommate, John, offered to buy household supplies for you and your other roommate. You live near the border of three states, each of
For the following exercises, use the matrix below to perform the indicated operation on the given matrix. B3 [1 0 0 1 1 0 B=0 0 0
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 concert venue sells single tickets for $40
For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution.Bikes’R’Us manufactures bikes, which sell for $250. It costs the
For the following exercises, perform the operation and then find the partial fraction decomposition. 7 x + 8 + 5 x-2 x-1 x²6x16
For the following exercises, construct a system of nonlinear equations to describe the given behavior, then solve for the requested solutions.The squares of two numbers add to 360. The second number
For the following exercises, solve the system of linear equations using Gaussian elimination.3x − 4y = 1−6x + 8y = 6
For the following exercises, solve the system for x, y, and z.Three coworkers work for the same employer. Their jobs are warehouse manager, office manager, and truck driver. The sum of the annual
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 decide to paint your kitchen green. You
For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution.A major appliance store is considering purchasing vacuums from a small
For the following exercises, construct a system of nonlinear equations to describe the given behavior, then solve for the requested solutions.A laptop company has discovered their cost and revenue
For the following exercises, write the system of linear equations from the augmented matrix. Indicate whether there will be a unique solution. 10 51 -91 01 -2 4 00 0 0 3
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. x + Ay = 1 x+By = 1
For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. 5x+2 x(x²+4)²
For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 2,400 tickets were sold for a basketball game. If
For the following exercises, find the solutions to the nonlinear equations with two variables. x² - xy - 2y²-6=0 x² + y² = 1
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, use Gaussian elimination to solve the system. x-3 4 + y-1 3 + + 2z=-1 x+5 y+5 z+5 2 2 2 x+y+z=1 = 7
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, solve the system for x, y, and z.Three even numbers sum up to 108. The smaller is half the larger and the middle number is 3/4 the larger. What are the three numbers?
For the following exercises, write the system of linear equations from the augmented matrix. Indicate whether there will be a unique solution. 1 0-31 7 01 2-5 00 ol 0 0
For the following exercises, find the inverse of the given matrix. 1 0 0 0 0 0 07 0 1 0 0 0 0 0 0 0 0 0 1 1000 0 0 1 0 1 0 0 0 0 L1 1 1 1 1
For the following exercises, find the solutions to the nonlinear equations with two variables. x² - xy + y² -2 = 0 x + 3y = 4
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. x+y=A x=y=B
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, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. 2x³ + 11x + 7x + 70 (2x²+x+14)²
For the following exercises, use Gaussian elimination to solve the system. x-3 10 x+5 4 x-1 4 + + y+3 2 y-1 8 y+4 2 -2z=3 + z = +3z= 3/23/2
For the following exercises, solve the system for x, y, and z. 나의 + - 1 y+3 2+2 1 3 4 6 + 4x + 3y - 2z = 11 0.02x + 0.015y - 0.01z = 0.065
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. Two
For the following exercises, perform the requested operations on the given matrices.A3 6 7 9 [7 4 - All !!!!! - ¹ = [₁ B 11 –7 ], E = 2 - 1 3 L14 0 5 |0 6 7 -3 11 -2 4. 1 -4 D 10 5 2 8 -14 37 -1
For the following exercises, find the inverse of the given matrix. [1 202 2 1 0 0 0 0 3 0 0 2 0 0 LO 0 1 2 31 0 1 1 1 0]
For the following exercises, find the solutions to the nonlinear equations with two variables. = 8 || 8
For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth. -0.71x + 0.92y = 0.13 0.83x + 0.05y = 2.1
For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. x²+25 (x² + 3x +25)²
For the following exercises, use Gaussian elimination to solve the system. x-3 4 x + 5 2 + y-1 3 y + 5 2 + 2z = -1 z+5 2 x+y+z=1 + =8
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.A(BC) A-9-8---8 = [₁₂₁₂ 3] B
For the following exercises, solve the system for x, y, and z. x-3 y+2 + 6 2 y-5 2 y-3 2 x+2 4 + x+6 2 2-3 3 z +4 2 +z+1=9 + = 2 = 1
For the following exercises, perform the requested operations on the given matrices.CE A 4 -2 = [₁ −3], B =[₁ 7 -2 ------ C: 11 0. -3 1 -4 [7 97 5-7, E= 2 8 5 LO 10 -14 3 -1 3 1 9
For the following exercises, find the inverse of the given matrix. 1 0 1 -5 -2 1 040 0 3 07 02 -2 3 1 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. Two
For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth. 0.15x + 0.27y= 0.39 -0.34x+0.56y= 1.8
For the following exercises, find the solutions to the nonlinear equations with two variables. จน เก + | = 24 +4=0
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.(AB)C 9²-33-20 C 1 A 1 = [ 2 3 ]- B
For the following exercises, use Gaussian elimination to solve the system. x-1 4 x + 5 2 y+1 4 + y + 7 4 + 3z = -1 - z = 4 -2 x+y=z=2 22² = 1
For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. x² + 2x² + 4x (x² + 2x + 9)²
For the following exercises, use the determinant function on a graphing utility. 1 2 4 5 6 7 8 0 0 00 30 0 60 9 9 0
For the following exercises, solve the system for x, y, and z. x + 4 7 x-2 ++3 4 x+6 + y-1 6 y + 1 8 y + 2 3 + + 2+2 3 z+8 12 z +4 2 = 1 = 0 = 3
For the following exercises, perform the requested operations on the given matrices.EC 6 71 1 -4 9 4 -2 -3 A= 7 3c- စ- ဒါ-။ ဒါမျိုး A : = [₁ −3], B = [16 C: 11 -2 10 5
For the following exercises, find the inverse of the given matrix. -1 0 0 1 0 0 2 -3 2 51 02 1 0 0 1.
For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth. 0.5x + 0.3y = 4 0.25x 0.9y = 0.46
For the following exercises, graph the inequality. y≤ -log(x) y≤ et
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.D3 -2 3 A=
For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. +5x+5 (x + 2)²
For the following exercises, use Gaussian elimination to solve the system. x - 1 7 + y-2 8 3 2-3 4 x+y+z=6 + = 0 x+2+2y+z==5 3
For the following exercises, use the determinant function on a graphing utility. 1 0 0 0 00 7 100 4 5 2 2,000 0 21
For the following exercises, solve the system for x, y, and z. 5x-3y - 6x+ z+1 2 y-9 2 x+8 2 || 72 + 2z = -3 - 4y+z=4
For the following exercises, perform the requested operations on the given matrices.ED A 4 -2 - [₁ -3] B =[i 1 6 7 -2 1 -4 97 7 ]}c စစ်ဦး 6 C 11 D = | 10 5 -7 , E =|2 L14 2 8 5] LO 0. -14
For the following exercises, find the inverse of the given matrix. 「10 1 0 0 0 0 1 1 0 07 1 10 1 1
For the following exercises, solve each system by addition. -0.1x + 0.2y = 0.6 5x - 10y = 1
For the following exercises, use any method to solve the nonlinear system. - x² + y = 2 2y = -x
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. AB -2 3 ^-(1978-1-1-0-| A =
For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth. -0.01x + 0.12y = 0.62 0.15x + 0.20y = 0.52
For the following exercises, graph the inequality. y≥ et y ≤ ln(x) + 5
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.A2 - A = [2 3] B =[
For the following exercises, solve the system by Gaussian elimination. - 1 x − 1² y + 1² = 2 x+y=1/7 z= 6 - ²x + ² y + 1/0² 8 29 6 431 210 49 45
For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. x²-x²+x-1 (x² - 3)²
For the following exercises, use the determinant function on a graphing utility. 1 0 0-9 3 0 2 1 0-2 1 1 1 3 -1 1-2
For the following exercises, solve the system for x, y, and z. x-1 2 x-2 3 + + y-3 2 x+y+z=3 z+1 2 y+4 3 = 0 + +² 4+² = ³ = 3 3 2 3
For the following exercises, perform the requested operations on the given matrices.DE 6 71 -----⠀H⠀ C 11 2],D=| 10 5 , E = 2 14 0 4 7 -3 ^- -- - - - : B -2 4 1 1 -4 -4 9] 2 8 5 7 LO -14 31 -1
For the following exercises, use a calculator to solve the system of equations with matrix inverses. 0.5x3y + 6z= -0.8 0.7x2y=-0.06 0.5x + 4y + 5z = 0
For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth. 0.1x+0.2y = 0.3 -0.3x + 0.5y =1
For the following exercises, graph the system of inequalities. Label all points of intersection. x² + 3y² > 16 3x² - y²
For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. x² +6x² + 5x +9 (x² + 1)²
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.D2 -4=[23] B =[²² A -2
For the following exercises, solve the system by Gaussian elimination. - 1 1/2 x + √ √ 2 y + 1²/²/2 = - 53 14 1x-1²y+z=3 23 1x + ²y + ½z= 15
For the following exercises, solve each system by Gaussian elimination. 0.8x + 0.8y + 0.8z = 2.4 0.3x0.5y + 0.2z = 0 0.1x + 0.2y + 0.3z = 0.6
For the following exercises, perform the requested operations on the given matrices.CB 6 7 4 7 -3 - A =li 3 - a =3], B =[[ -2 11 14 -2|, D= | 10 D=110 2 10 -4 91 7 = 5 -7|, E= | 2 8 5. LO -14 31 -1
For the following exercises, use the determinant function on a graphing utility. 1 0 0 2 1 0 0 2 8 9 1 0 3 0 4 3
For the following exercises, use a calculator to solve the system of equations with matrix inverses. 12.3x - 2y - 2.5z = 2 36.9x + 7y - 7.5z = -7 8y- 5z = -10
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
For the following exercises, graph the system of inequalities. Label all points of intersection. x-y> > -4 ㎡ + y < 12
For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. 3x3 + 2x² + 14x + 15 - (x2²+4)²
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.DC -2 4-6-34-38 A= [2 3], B -1 1
For the following exercises, solve the system by Gaussian elimination. 1x-²-z=-1 3 4 2 { x + ² y = / 3 y-1/2 = 2 3
For the following exercises, solve each system by Gaussian elimination. 0.3x + 0.3y+0.5z = 0.6 0.4x + 0.4y+ 0.4z = 1.8 0.4x + 0.2y + 0.1z = 1.6
For the following exercises, solve the system of linear equations using Cramer’s Rule. 4x 6y + 8z = 10 -2x+3y-4z = -5 12x + 18y-24z = - 30
For the following exercises, perform the requested operations on the given matrices.BC 1 -4 97 [ 7 4 -2 ---? - - - = [₁ −3], B =[₁ 7 -3 C: 11 10 5 –7 ], E = 2 0. 2 8 5] |0 A 11 -2 -14 3 -1
For the following exercises, use a calculator to solve the system of equations with matrix inverses. 3 43 -글x-클 - - 옮 = 20 31 2 + 5
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
For the following exercises, graph the system of inequalities. Label all points of intersection. x² + y² 12
For the following exercises, solve the system by Gaussian elimination. x+y+z= 100 x + 2z = 125 -y + 2z=25
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.BD -2 3 A=[2₂3], B = [² ³

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