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mathematics
college algebra
College Algebra 12th edition Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels - Solutions
This chapter has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer’s rule. Use each method at least once when solving the systems below. Include solutions with nonreal complex number
This chapter has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer’s rule. Use each method at least once when solving the systems below. Include solutions with nonreal complex number
This chapter has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer’s rule. Use each method at least once when solving the systems below. Include solutions with nonreal complex number
This chapter has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer’s rule. Use each method at least once when solving the systems below. Include solutions with nonreal complex number
This chapter has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer’s rule. Use each method at least once when solving the systems below. Include solutions with nonreal complex number
This chapter has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer’s rule. Use each method at least once when solving the systems below. Include solutions with nonreal complex number
This chapter has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer’s rule. Use each method at least once when solving the systems below. Include solutions with nonreal complex number
This chapter has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer’s rule. Use each method at least once when solving the systems below. Include solutions with nonreal complex number
This chapter has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer’s rule. Use each method at least once when solving the systems below. Include solutions with nonreal complex number
This chapter has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer’s rule. Use each method at least once when solving the systems below. Include solutions with nonreal complex number
This chapter has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer’s rule. Use each method at least once when solving the systems below. Include solutions with nonreal complex number
This chapter has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer’s rule. Use each method at least once when solving the systems below. Include solutions with nonreal complex number
This chapter has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer’s rule. Use each method at least once when solving the systems below. Include solutions with nonreal complex number
This chapter has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer’s rule. Use each method at least once when solving the systems below. Include solutions with nonreal complex number
This chapter has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer’s rule. Use each method at least once when solving the systems below. Include solutions with nonreal complex number
Consider the following nonlinear system.y = |x - 1|y = x2 - 4Use the values of x found in Exercise to find the solution set of the system.
Consider the following nonlinear system.y = |x - 1|y = x2 - 4Use the quadratic formula to solve both equations from Exercise. Pay close attention to the restriction on x.
Consider the following nonlinear system.y = |x - 1|y = x2 - 4Write two quadratic equations that will be used to solve the system.
Consider the following nonlinear system.y = |x - 1|y = x2 - 4Use the definition of absolute value to write y = |x - 1| as a piecewise-defined function.
Consider the following nonlinear system.y = |x - 1|y = x2 - 4How is the graph of y = x2 - 4 obtained by transforming the graph of y = x2?
Consider the following nonlinear system.y = |x - 1|y = x2 - 4How is the graph of y = |x - 1| obtained by transforming the graph of y = |x|?
The following equations model the percents of revenue from both sources in Exercise 73. Use the equations to determine the year and percent when the amounts from both sources were equal.S = 32(0.9637)x-2003 State sourcesT = 17(1.0438)x-2003 TuitionExercise 73Public College Revenue from Tuition and
The percents of revenue for public colleges from state sources and tuition are modeled in the accompanying graph.(a) Interpret this graph. How are the sources of funding for public colleges changing with time?(b) During what time period was the revenue from state sources increasing?(c) Use the
In electronics, circuit gain is modeled bywhere R is the value of a resistor, t is temperature, Rt is the value of R at temperature t, and B is a constant. The sensitivity of the circuit to temperature is modeled byIf B = 3.7 and t is 90 K (kelvins), find the values of R and Rt that will result in
The supply and demand equations for a certain commodity are given.(a) Find the equilibrium demand. (b) Find the equilibrium price (in dollars). supply: p = V0.1q + 9 – 2 and demand: p = V25 – 0.1q
The supply and demand equations for a certain commodity are given.(a) Find the equilibrium demand.(b) Find the equilibrium price (in dollars). 7000 – 3q and demand: p = 29 2000 supply: p 2000 – 4
Solve each problem.Find the radius and height (to the nearest thousandth) of an open-ended cylinder with volume 50 in.3 and lateral surface area 65 in.2. 2nr
Solve each problem.A box with an open top has a square base and four sides of equal height. The volume of the box is 360 ft3. If the surface area is 276 ft2, find the dimensions of the box. (Round answers to the nearest thousandth, if necessary.) х х y х х
Suppose we are given the equations of two circles that are known to intersect in exactly two points. How would we find the equation of the only chord common to these circles? y х
Answer each question.A line passes through the points of intersection of the graphs of y = x2 and x2 + y2 = 90. What is the equation of this line? 4 8 +8 -4 -4 -8- 7² + y² = 90
Answer each question.For what value(s) of b will the line x + 2y = b touch the circle x2 + y2 = 9 in only one point?
Answer each question.Does the straight line 3x - 2y = 9 intersect the circle x2 + y2 = 25?
Solve each problem using a system of equations in two variables.The longest side of a right triangle is 29 ft in length. One of the other two sides is 1 ft longer than the shortest side. Find the lengths of the two shorter sides of the triangle.
Solve each problem using a system of equations in two variables.The longest side of a right triangle is 13 m in length. One of the other sides is 7 m longer than the shortest side. Find the lengths of the two shorter sides of the triangle.
Solve each problem using a system of equations in two variables.Find two numbers whose ratio is 4 to 3 and are such that the sum of their squares is 100.
Solve each problem using a system of equations in two variables.Find two numbers whose ratio is 9 to 2 and whose product is 162.
Solve each problem using a system of equations in two variables.Find two numbers whose squares have a sum of 194 and a difference of 144.
Solve each problem using a system of equations in two variables.Find two numbers whose squares have a sum of 100 and a difference of 28.
Solve each problem using a system of equations in two variables.Find two numbers whose sum is -10 and whose squares differ by 20.
Solve each problem using a system of equations in two variables.Find two numbers whose sum is -17 and whose product is 42.
Many nonlinear systems cannot be solved algebraically, so graphical analysis is the only way to determine the solutions of such systems. Use a graphing calculator to solve each nonlinear system. Give x- and y coordinates to the nearest hundredth. y = Vx – 4 x² + y? = 6
Many nonlinear systems cannot be solved algebraically, so graphical analysis is the only way to determine the solutions of such systems. Use a graphing calculator to solve each nonlinear system. Give x- and y coordinates to the nearest hundredth.y = ex+12x + y = 3
Many nonlinear systems cannot be solved algebraically, so graphical analysis is the only way to determine the solutions of such systems. Use a graphing calculator to solve each nonlinear system. Give x- and y coordinates to the nearest hundredth.y = 5xxy = 1
Many nonlinear systems cannot be solved algebraically, so graphical analysis is the only way to determine the solutions of such systems. Use a graphing calculator to solve each nonlinear system. Give x- and y coordinates to the nearest hundredth.y = log (x + 5)y = x2
Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components.x2 + y2 = 9|x| = |y|
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.2x2 - y2 = 4|x| = |y|
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.2x + |y| = 4x2 + y2 = 5
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.x = |y|x2 + y2 = 18
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.x2 + y2 = 9|x| + y = 3
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.x2 + y2 = 25|x| - y = 5
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.x2 + 3xy - y2 = 12x2 - y2 = -12
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.x2 + 2xy - y2 = 14x2 - y2 = -16
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.3x2 + 2xy - y2 = 9x2 - xy + y2 = 9
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.x2 - xy + y2 = 52x2 + xy - y2 = 10
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.5x2 - 2y2 = 6xy = 2
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.3x2 - y2 = 11xy = 12
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.-5xy + 2 = 0x - 15y = 5
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.2xy + 1 = 0x + 16y = 2
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.xy = 83x + 2y = -16
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.xy = -154x + 3y = 3
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.5x2 - 2y2 = 2510x2 + y2 = 50
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.2x2 - 3y2 = 126x2 + 5y2 = 36
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.x2 + y2 = 45x2 + 5y2 = 28
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.2x2 + 2y2 = 204x2 + 4y2 = 30
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.3x2 + 5y2 = 172x2 - 3y2 = 5
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.2x2 + 3y2 = 53x2 - 4y2 = -1
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.x2 + 2y2 = 9x2 + y2 = 25
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.3x2 + y2 = 34x2 + 5y2 = 26
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.x2 + y2 = 02x2 - 3y2 = 0
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.5x2 - y2 = 03x2 + 4y2 = 0
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.x2 + y2 = 102x2 - y2 = 17
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.x2 + y2 = 8x2 - y2 = 0
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.x2 + y2 = 5-3x + 4y = 2
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.3x2 + 2y2 = 5x - y = -2
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.y = 6x + x24x - y = -3
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.y = x2 + 4x2x - y = -8
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.y = x2 + 6x + 9x + 2y = -2
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.y = x2 - 2x + 1x - 3y = -1
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.x2 + y = 2x - y = 0
Solve the nonlinear system of equations. Give all solutions, including those with nonreal complex components.x2 - y = 0x + y = 2
Answer the question.In Example 5, there were four solutions to the system, but there were no points of intersection of the graphs. If a nonlinear system has nonreal complex numbers as components of its solutions, will they appear as intersection points of the graphs?
Answer each question.In Example 1, we solved the following system. How can we tell, before doing any work, that this system cannot have more than two solutions?x2 - y = 4x + y = -2
A nonlinear system is given, along with the graphs of both equations in the system. Verify that the points of intersection specified on the graph are solutions of the system by substituting directly into both equations. 4 y = 9. x2 + y? = 25 х 3 5 (3, -4) (-3, –4) y = -r2 2+ у? в 25 4-
A nonlinear system is given, along with the graphs of both equations in the system. Verify that the points of intersection specified on the graph are solutions of the system by substituting directly into both equations.y = 3x2x2 + y2 = 10 (-1, 3) 3 (1, 3) х y = 3x2 x²+ y² = 10T
A nonlinear system is given, along with the graphs of both equations in the system. Verify that the points of intersection specified on the graph are solutions of the system by substituting directly into both equations.x + y = -3x2 + y2 = 45 (-6, 3) 3 х 3 (3, –6) х +у3-3 x² + y² = 45
A nonlinear system is given, along with the graphs of both equations in the system. Verify that the points of intersection specified on the graph are solutions of the system by substituting directly into both equations.x2 + y2 = 5-3x + 4y = 2 38 41 25 25. (-2, –1) + x? + y² = 5 -3x + 4y = 2
A nonlinear system is given, along with the graphs of both equations in the system. Verify that the points of intersection specified on the graph are solutions of the system by substituting directly into both equations.2x2 = 3y + 23y = 2x - 5 (4, 3) 2x² = 3y + 23 (-1, –7) y = 2x – 5
A nonlinear system is given, along with the graphs of both equations in the system. Verify that the points of intersection specified on the graph are solutions of the system by substituting directly into both equations.x2 = y - 1y = 3x + 5 y (4, 17) 15+ 10+ x² = y – 1 y = 3x + 5 (-1, 2) i i ż 3
If we want to solve the following nonlinear system by eliminating the y2 terms, by what number should we multiply equation (2)?x2 + 3y2 = 4 (1)x2 - y2 = 0 (2)
If we want to solve the following nonlinear system by substitution and we decide to solve equation (2) for y, what will be the resulting equation when the substitution is made into equation (1)?x2 + y = 2 (1)x - y = 0 (2)
Refer to the system in Exercise 2. The other solution with real components has x-value -2. What is the y-value of this solution?Exercise 2The following nonlinear system has two solutions with real components, one of which is (2, ______).y = x2 + 6x2 - y2 = -96
Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence.The following nonlinear system has two solutions, one of which is (________ , 3).2x + y = 1x2 + y2 = 10
Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence.The following nonlinear system has two solutions with real components, one of which is (2, ______).y = x2 + 6x2 - y2 = -96
Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence.The following nonlinear system has two solutions, one of which is (3, _______).x + y = 7x2 + y2 = 25
Solve the problem.Find the partial fraction decomposition for each rational expression. 2x2 — 15х — 32 (х — 1) (х? + 6х + 8)
Solve the problem.Find the partial fraction decomposition for each rational expression. 10х + 13 х2 — х — 20
Solve each problem.Evaluate Use determinant theorems if desired. |-3 -2 -3 5| 2 -1
Solve the problem.Let -5 |A = 2 Find |A|. -1
Solve the problem.A sum of $5000 is invested in three accounts that pay 2%, 3%, and 4% interest rates. The amount of money invested in the account paying 4% equals the total amount of money invested in the other two accounts, and the total annual interest from all three investments is $165. Find
Solve each problem.In 2013, the amount spent by a typical American household on food was about $6602. For every $10 spent on food away from home, about $15 was spent on food at home. Find the amount of household spending on food in each category.
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