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mathematics
precalculus

Questions and Answers of Precalculus

In Problems 5 – 24, graph each equation of the system. Then solve the system to find the points of intersection. y = y = √4x² 2x + 4
If the only solution to a system of two linear equations containing two variables is x = 3, y = −2, then the graphs of the lines in the system intersect at the point ________.
In Problems 7 – 14, find the value of each determinant. 64 -1 3
In Problems 1 – 10, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, state that it is inconsistent. x + 2y - z = 6 2xy
Solve the inequality: x2 − 4 ≤ 5
In Problems 5 – 16, determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression.
In Problems 7 – 18, write the augmented matrix of the given system of equations. 3x + 4y = 7 4x − 2y = 5
In Problems 5 – 24, graph each equation of the system. Then solve the system to find the points of intersection. = √x y = y = 2 x
In Problems 7 – 18, write the augmented matrix of the given system of equations. 2x+3y - 6 = 0 6=0 4x - бу + 2 = 0
In Problems 7 – 14, find the value of each determinant. -3 4 -1 2
In Problems 7 – 14, find the value of each determinant. 8-3 4 2
In Problems 5 – 24, graph each equation of the system. Then solve the system to find the points of intersection. y = x y = 6 - x
To find the product AB of two matrices A and B, which statement must be true?(a) The number of columns in A must equal the number of rows in B.(b) The number of rows in A must equal the number of
In Problems 5 – 16, determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression. x3
In Problems 7 – 18, write the augmented matrix of the given system of equations. 0.01x - 0.03y = 0.06 0.13x + 0.10y = 0.20
In Problems 7 – 14, find the value of each determinant. -4 2 -5 3
In Problems 5 – 24, graph each equation of the system. Then solve the system to find the points of intersection. x = 2y x = y² - 2y
Graph each equation. (a) y = 3x + 6 (c) y = x³ (e) y = √x (g) y = ln x (i) x² 3y2 = 1 (b) x² + y² = 4 (d) y X (f) y = ex (h) 2x² + 5y² = 1 (j) x² - 2x - 4y + 1 = 0
The function is one-to-one. Find f−1. Find the domain and the range of f and the domain and the range of f−1. f(x) = 5 x + 2
In Problems 9 – 18, verify that the values of the variables listed are solutions of the system of equations. 3x - 4y = 4 =글 2 X - 3y = I x= 2, y = 1/1: (2, 1/1)
Find the center and radius of the circle x2 + y2 − 2x + 4y − 11 = 0 Graph the circle.
In Problems 7 – 18, write the augmented matrix of the given system of equations. 9x - y = 0 3x - y - 4 = 0
In Problems 11 – 22, graph each inequality. x 20
The graph of a linear equation is a line that separates the xy-plane into two regions called _________.
If a system of dependent equations containing three variables has the general solution {(x, y, z) x = −z + 4, y = − 2z + 5, z is any real n umber} then_______ is one of the infinite number of
In Problems 5 – 24, graph each equation of the system. Then solve the system to find the points of intersection. y = x - 1 y = x² - 6x + 9
In Problems 11 – 22, graph each inequality. y ≥ 0
In Problems 7 – 18, write the augmented matrix of the given system of equations. 314 23 = || || लोत नाल नौक 1 +
In Problems 5 – 24, graph each equation of the system. Then solve the system to find the points of intersection. x² + y² = 4 x² + 2x + y² = 0
In Problems 11 – 22, graph each inequality. x IV 4
In Problems 9 – 18, verify that the values of the variables listed are solutions of the system of equations. 1 -= 2x + x = = 3x - 4y = 1 2 y = 0 19 2 2; (-1/2, 2²)
In Problems 9 – 18, verify that the values of the variables listed are solutions of the system of equations. x - y = 3 1/2 x 5x + y = 3 x = 4, y = 1; (4,1)
In Problems 7 – 18, write the augmented matrix of the given system of equations. y + z = 10 3x + 3y = 5 x + y + 2z = 2 X
In Problems 7 – 14, find the value of each determinant. 4 6 1 -1 2 -1 0 -3 -3 4
In Problems 5 – 16, determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression. 5x3
In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection. x² + y² = 8 x² + y² + 4y = 0
In Problems 9–18, solve each linear programming problem. Maximize z = 5x + 3y subject to the constraints x ≥ 0, y ≥ 0, x + y ≥ 2, x + y ≤ 8, 2x + y ≤ 10
In Problems 9–18, solve each linear programming problem. Minimize z = 5x + 4y subject to the constraints x ≥ 0, y ≥ 0, x + y 22, 2x + 3y 12, 3x + y ≤ 12
In Problems 11 – 22, graph each inequality. y ≤ 2
In Problems 7 – 18, write the augmented matrix of the given system of equations. x+y - z = 2 3x-2y = 2 5x+3y-z= 1 =
In Problems 13 – 16, use the following matrices to compute each expression.AB A || 10 24 -1 2 B = 4 1 -3 0 1 1-2 C = 315 -4 5 52
In Problems 15–42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, write, “Not applicable.” x + y = x - y = 8 4
In Problems 9–18, solve each linear programming problem. Minimize z = 2x + 3y subject to the constraints x > 0, y ≥ 0, x + y ≥ 3, x + y ≤ 9, x + 3y ≥ 6
In Problems 11 – 22, graph each inequality. 2x + y 2 6
In Problems 5 – 24, graph each equation of the system. Then solve the system to find the points of intersection. x2 x² + y² = 10 y = x + 2
In Problems 5 – 16, determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression. x(x
In Problems 11 – 22, graph each inequality. 3x + 2y 5 6
In Problems 15–42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, write, “Not applicable.” x + 2y = 5 x - y = 3
In Problems 9–18, solve each linear programming problem. Maximize z = 5x + 2y subject to the constraints x ≥ 0, y ≥ 0, x + y ≤ 10, 2x + y 2 10, x + 2y > 10
In Problems 15–42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, write, “Not applicable.” 5x - y = 2x + 3y = 13 12
In Problems 5 – 24, graph each equation of the system. Then solve the system to find the points of intersection. x² + y² = 4 y² - x = 4
In Problems 9–18, solve each linear programming problem. Maximize z = 2x + 4y subject to the constraints x ≥ 0, y ≥ 0, 2x + y ≥ 4, x + y ≤ 9
In Problems 11 – 22, graph each inequality. x² + y² > 1 2
In Problems 5 – 24, graph each equation of the system. Then solve the system to find the points of intersection. x² + y² = 16 x² - 2y = 8
In Problems 17–50, find the partial fraction decomposition of each rational expression. 4 x(x - 1)
In Problems 17–50, find the partial fraction decomposition of each rational expression. 3x (x + 2)(x-1)
In Problems 15–42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, write, “Not applicable.” x + 3y = 5 2x - 3y = -8
In Problems 11 – 22, graph each inequality. x2 x² + y2 ≤ 9
In Problems 17–50, find the partial fraction decomposition of each rational expression. 1 x(x² + 1) 2
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. x + y = 8 x - y = 4
In Problems 15–42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, write, “Not applicable.” 3x = x + 2y = 24 0
In Problems 11 – 22, graph each inequality. 2 y ≤ x² - 1
In Problems 20–25, solve each system of equations using matrices. If the system has no solution, state that it is inconsistent. 3x - 2y = 1 10x +10y = 5
In Problems 5 – 24, graph each equation of the system. Then solve the system to find the points of intersection. x² = = y xy = 1
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. x + 2y = x + y = -7 -3
In Problems 15–42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, write, “Not applicable.” 4x + 5y = -3 -2y = -4
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 5x - y = 2x + 3y = 12 21
In Problems 11 – 22, graph each inequality. 2 y > x² + 2
In Problems 9 – 26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, write “not defined”BA
In Problems 19 – 26, write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. 1 -3 4 3 -5 -5
In Problems 11 – 22, graph each inequality. xy > 4
In Problems 11 – 22, graph each inequality. xy ≤ 1
In Problems 9 – 26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, write “not defined”C (A
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. x + 3y = 5 2x — 3y = −8
In Problems 15–42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, write, “Not applicable.” 4х 4x - бу = -42 7x +4y = -1
In Problems 19 – 26, write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. 1-3 -4 -5 -3 -3 -2
In Problems 23 – 34, graph each system of linear inequalities. x + y ≤2 2x + y 24
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 3x = 24 x + 2y = 0
In Problems 15–42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, write, “Not applicable.” 2x + 4y = 16 3x-5y=-9
Graph the system of inequalities: x² + у2 х2 4x - 3у ≤ 100 < 20
In Problems 5 – 24, graph each equation of the system. Then solve the system to find the points of intersection. y = = x² - 4 y = 6x13
In Problems 19 – 26, write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. 1-3 2 2 -5 3 4 -3 -6 -6 -
In Problems 15–42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, write, “Not applicable.” 3x - 2y = 4 6x - 4y = 0
Open the “Slope” interactive figure, which is available in the Video & Resource Library of MyLab Math (under Interactive Figures) or at bit.ly/3raFUGB.(a) Be sure the “Show Slope” box is
Open the “Circle” interactive figure, which is available in the Video & Resource Library of MyLab Math (under Interactive Figures) or at bit.ly/3raFUGB.(a) Check the box “Equation of the
The x-intercepts of the graph of an equation are those x-values for which ________.
Open the “Circle” interactive figure, which is available in the Video & Resource Library of MyLab Math (under Interactive Figures) or at bit.ly/3raFUGB.(a) Check the boxes “Equation of the
In Problems 13–16,(a) Find the slope of the line(b) Interpret the slope. У (-2, 1) 2 -2 -1 (0,0) 2 х
In Problems 79–98, find the slope and y-intercept of each line. Graph the line. 1 2 -y = x - 1
In Problems 79–86,(a) Find the intercepts of each equation,(b) Test each equation for symmetry with respect to the x-axis, the y-axis, and the origin,(c) Graph each equation by hand by plotting
In Problems 79–86,(a) Find the intercepts of each equation,(b) Test each equation for symmetry with respect to the x-axis, the y-axis, and the origin,(c) Graph each equation by hand by plotting
In Problems 79–86,(a) Find the intercepts of each equation,(b) Test each equation for symmetry with respect to the x-axis, the y-axis, and the origin,(c) Graph each equation by hand by plotting
In Problems 79–98, find the slope and y-intercept of each line. Graph the line.x − y = 2
Solve the equation 2( x + 3) − 1 = −7.
To complete the square of x2 + 10x, you would_____ ( add / subtract ) the number ______.
In Problems 13–16,(a) Find the slope of the line(b) Interpret the slope. (-1, 1) -2 YA 2 -1 (2, 2) 181 2 X
Solve the equation x2 − 9 = 0.
Solve the equation: (x − 2)2 = 9.
In Problems 13 – 18, determine which of the given points are on the graph of the equation. Equation: x² + 4y² = 4 Points: (0, 1); (2, 0): (2, 1)
In Problems 13–16,(a) Find the slope of the line(b) Interpret the slope. YA 2 (0,0) -1 -2 (2, 1) 2 x

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