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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

For the following exercises, graph the following inequalities.x2 + y2 > 4y < x2 + 1
For the following exercises, solve the system of nonlinear equations using elimination. 4x²-9y² = 36 4x² +9y² = 36
For the following exercises, write the linear system from the augmented matrix. -2 6 5 5 18 26.
For the following exercises, use the matrices below and perform the matrix addition or subtraction. Indicate if the operation is undefined.D − B 10 14] 0 2 6 12 =} }}=3 •]c- ပါး- - A B 7 2
For the following exercises, solve each system by substitution. 3x - 4y + 2z = -15 2x + 4y + z = 16 2x + 3y + 5z - 20
For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. 32x - 11 20x²13x + 2
For the following exercises, find the determinant. 10 5 0.2 0.1
In the following exercises, show that matrix A is the inverse of matrix B. 1 A = 0 0 0 01 1 1 -1, B 0 1 1 -1
For the following exercises, write a system of equations to solve each problem. Solve the system of equations.A performer charges C(x) = 50x + 10,000, where x is the total number of attendees at a
For the following exercises, graph the following inequalities. y < x2 + 9
For the following exercises, solve the system of nonlinear equations using substitution. x = 2 x² - y² = 9
For the following exercises, determine whether the given ordered pair is a solution to the system of equations.x + 8y = 433x − 2y = −1 and (3, 5)
For the following exercises, write the augmented matrix for the linear system. 6x +12y + 16z = 4 19x - 5y + 3z = -9 x + 2y = -8
For the following exercises, use the matrices below and perform the matrix addition or subtraction. Indicate if the operation is undefined.C + F 51 14] 0 4-6-8-12² 410-40-3 1-6 7-67 A = ,B= 방효 =
For the following exercises, determine whether the ordered triple given is the solution to the system of equations. -x-y + 2z=3 5x+8y3z=4 and (4, 1, -7) -x+3y- 5z = -5
For the following exercises, find the determinant. | 10 20 0-10
For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors.x/6x2 + 25x + 25
In the following exercises, show that matrix A is the inverse of matrix B. A=[ ²² ] B =[²₂] 3
For the following exercises, write a system of equations to solve each problem. Solve the system of equations. A factory has a cost of production C(x) = 150x + 15,000 and a revenue function R(x)
For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists.y2 + x2 = 25y2 − 2x2 = 1
For the following exercises, solve the system of nonlinear equations using substitution. y = -x x² + y² = 9
For the following exercises, write the augmented matrix for the linear system. x + 5y + 8z = 19 12x + 3y = 4 3x + 4y +9z = -7
For the following exercises, determine whether the given ordered pair is a solution to the system of equations.−2x + 5y = 72x + 9y = 7 and (−1, 1)
For the following exercises, determine whether the ordered triple given is the solution to the system of equations. x - y = 0 x-z=5 and (4, 4, -1) x-y+z=-1
For the following exercises, use the matrices below and perform the matrix addition or subtraction. Indicate if the operation is undefined.B − E 1 51 10 *- *-[2²4c-]-[ 14-9-- [₁ 6 12 A = C= 8
For the following exercises, find the determinant. 1 3 01 -41
For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors.10x + 47/x2 + 7x + 10
In the following exercises, show that matrix A is the inverse of matrix B. 4 A = [₂5]. B L7 B = 1 L5 4 35
For the following exercises, use addition to solve the system of equations.8x + 4y = 26x − 5y = 0.7
For the following exercises, solve the system of nonlinear equations using substitution. y = x x² + y² = 9
For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists.y = x2 + 2x − 3y = x − 1
For the following exercises, determine whether the given ordered pair is a solution to the system of equations.3x + 7y = 12x + 4y = 0 and (2, 3)
For the following exercises, write the augmented matrix for the linear system. 3x + 2y + 10z = 3 -6x + 2y + 5z = 13 4x + z = 18
For the following exercises, use the matrices below and perform the matrix addition or subtraction. Indicate if the operation is undefined.A + C A = [ 1 2 ], B = | 22 1 C=
For the following exercises, determine whether the ordered triple given is the solution to the system of equations. 6x-7y+z=2 -x-y + 3z = 4 and (4, 2,-6) 2x+y=z=1
For the following exercises, find the determinant. -8 4 -1 5
For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors.−x − 24/x2 − 2x − 24
In the following exercises, show that matrix A is the inverse of matrix B. 1 2 _A = [ 3 4], B² = -2 N/WN 3 2 1 2
For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists. 5x - 4y3z=0 2x + y + 2z = 0 x - бy -7z = 0
For the following exercises, use addition to solve the system of equations.3x + 4y = 29x + 12y = 3
For the following exercises, solve the system of nonlinear equations using substitution. y=x-3 x² + y² = 9
For the following exercises, determine whether the given ordered pair is a solution to the system of equations.−3x − 5y = 13− x + 4y = 10 and (−6, 1)
For the following exercises, write the augmented matrix for the linear system. 16y=4 9x-y=2
For the following exercises, determine whether the ordered triple given is the solution to the system of equations. 6x - y + 3z=6 3x + 5y + 2z = 0 and (3, -3, -5) x+y=0
For the following exercises, use the matrices below and perform the matrix addition or subtraction. Indicate if the operation is undefined.C + D 1 5 81 A = [₁ ²], B =[₂2₂ ¹14]. C= - [₂2²4]
For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors.3x − 79/x2 − 5x − 24
For the following exercises, find the determinant. 2 -1 -5 6
For the following exercises, find the determinant. 2 -1 3-4
In the following exercises, show that matrix A is the inverse of matrix B. 1 0 1 0 A: A = [_]-³=[₁₂] , B= 1 1 -1
For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists. x+z=20 x+y+z=20 x +2y+z= 10
For the following exercises, use addition to solve the system of equations. 3x + 2y = −72x + 4y = 6
For the following exercises, determine whether the given ordered pair is a solution to the system of equations. 5x − y = 4x + 6y = 2 and (4, 0)
For the following exercises, solve the system of nonlinear equations using substitution. x + y = 4 x² + y² = 9
For the following exercises, write the augmented matrix for the linear system. 8x - 37y=8 2x + 12y = 3
For the following exercises, use the matrices below and perform the matrix addition or subtraction. Indicate if the operation is undefined. A + B 3 2 A = [₁ ²], B = [ ₂² 1 5 C = 8 92,
For the following exercises, determine whether the ordered triple given is the solution to the system of equations. 2x - 6y + 6z = -12 x + 4y + 5z = -1 and (0, 1, -1) -x+2y+3z=-1
For the following exercises, find the determinant. | 1 2 24 3 4
For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors.5x + 16/x2 + 10x + 24
Can a matrix with zeros on the diagonal have an inverse? If so, find an example. If not, prove why not. For simplicity, assume a 2 × 2 matrix.
For the following exercises, use substitution to solve the system of equations.5x + 6y = 144x + 8y = 8
For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists. -x-4y= 2 4 2x + 16y=2
If you are solving a break-even analysis and get a negative break-even point, explain what this signifies for the company?
For the following exercises, find the area of each triangle. Round each answer to the nearest tenth.Brian’s house is on a corner lot. Find the area of the front yard if the edges measure 40 and 56
For the following exercises, graph the polar inequality.θ = π/4, r ≥ −3
For the following exercises, graph the polar inequality.0 ≤ θ ≤ π/3, r < 2
For the following exercises, graph the polar inequality.−π/6 < θ ≤ π/3 , −3 < r < 2 b
Can any quotient of polynomials be decomposed into at least two partial fractions? If so, explain why, and if not, give an example of such a fraction.
Can a linear system of three equations have exactly two solutions? Explain why or why not.
Can we add any two matrices together? If so, explain why; if not, explain why not and give an example of two matrices that cannot be added together.
Can any system of linear equations be written as an augmented matrix? Explain why or why not. Explain how to write that augmented matrix.
Is the following ordered pair a solution to the system of equations? −5x − y = 12x + 4y = 9 with ( − 3, 3)
Explain why we can always evaluate the determinant of a square matrix.
Can you explain why a partial fraction decomposition is unique?
Can any matrix be written as a system of linear equations? Explain why or why not. Explain how to write that system of equations.
For the following exercises, determine whether the ordered pair is a solution to the system of equations.6x − 2y = 24−3x + 3y = 18 and (9,15)
Can you explain how to verify a partial fraction decomposition graphically?
Explain whether a system of two nonlinear equations can have exactly two solutions. What about exactly three? If not, explain why not. If so, give an example of such a system, in graph form, and
Can a system of linear equations have exactly two solutions? Explain why or why not.
For the following exercises, determine whether the ordered pair is a solution to the system of equations. 3x − y = 4x + 4y = − 3 and ( − 1, 1)
In a previous section, we showed that matrix multiplication is not commutative, that is, AB ≠ BA in most cases. Can you explain why matrix multiplication is commutative for matrix inverses, that
If a given ordered triple solves the system of equations, is that solution unique? If so, explain why. If not, give an example where it is not unique.
Can we multiply any column matrix by any row matrix? Explain why or why not.
For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists. 2x-3y =4 2x 3 2 * - y = 0 - =
When graphing an inequality, explain why we only need to test one point to determine whether an entire region is the solution?
If you are performing a break-even analysis for a business and their cost and revenue equations are dependent, explain what this means for the company’s profit margins.
Examining Cramer’s Rule, explain why there is no unique solution to the system when the determinant of your matrix is 0. For simplicity, use a 2×2 matrix.
Does every 2 × 2 matrix have an inverse? Explain why or why not. Explain what condition is necessary for an inverse to exist.
Is there only one correct method of using row operations on a matrix? Try to explain two different row operations possible to solve the augmented matrix [² 30 -2 -26
If a given ordered triple does not solve the system of equations, is there no solution? If so, explain why. If not, give an example.
Can both the products AB and BA be defined? If so, explain how; if not, explain why.
When you graph a system of inequalities, will there always be a feasible region? If so, explain why. If not, give an example of a graph of inequalities that does not have a feasible region. Why does
For the following exercises, use substitution to solve the system of equations. 10x + 5y = −53x − 2y = −12
Can you explain whether a 2 × 2 matrix with an entire row of zeros can have an inverse?
Explain what it means in terms of an inverse for a matrix to have a 0 determinant.
You are unsure if you correctly decomposed the partial fraction correctly. Explain how you could double check your answer.
For the following exercises, use substitution to solve the system of equations. 43 70 x+ 2 응. - - - 를 -X = 6 3
Using the method of addition, is there only one way to solve the system?
Can any two matrices of the same size be multiplied? If so, explain why, and if not, explain why not and give an example of two matrices of the same size that cannot be multiplied together.
Can a matrix whose entry is 0 on the diagonal be solved? Explain why or why not. What would you do to remedy the situation?
If you graph a revenue and cost function, explain how to determine in what regions there is profit.

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