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mathematics
college algebra graphs and models
College Algebra 7th Edition Robert F Blitzer - Solutions
In Exercises 12–18, graph each equation.x + y = 4
In Exercises 79–82, determine whether each statement makes sense or does not make sense, and explain your reasoning.I used matrix multiplication to represent a system of linear equations.
Exercises 80–82 will help you prepare for the material covered in the first section.Divide both sides of 25x2 + 16y2 = 400 by 400 and simplify.
Consider a square matrix such that each element that is not on the diagonal from upper left to lower right is zero. Experiment with such matrices (call each matrix A) by finding AA. Then write a sentence or two describing a method for multiplying this kind of matrix by itself.
If AB = -BA, then A and B are said to be anticommutative.Are anticommutative? A ^-[i and B-[- = = 1 -1
In Exercises 79–82, determine whether each statement makes sense or does not make sense, and explain your reasoning.I made an encoding error by selecting the wrong square invertible matrix.
Exercises 80–82 will help you prepare for the material covered in the first section.Complete the square and write the circle’s equation in standard form:x2 + y2 - 2x + 4y = 4.
In Exercises 83–88, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.All square 2 × 2 matrices have inverses because there is a formula for finding these inverses.
The interesting and useful applications of matrix theory are nearly unlimited. Applications of matrices range from representing digital photographs to predicting long-range trends in the stock market. Members of the group should research an application of matrices that they find intriguing. The
In Exercises 83–88, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.Two 2 × 2 invertible matrices can have a matrix sum that is not invertible.
Solve: 32x-8 = 27.
Find the solution set and then use a calculator to obtain a decimal approximation to two decimal places for the solution: 7x-3 = 52x+4.
In Exercises 83–88, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.To solve the matrix equation AX = B for X, multiply A and the inverse of B.
In Exercises 83–88, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.(A + B)-1 = A-1 + B-1, assuming A, B, and A + B are invertible.
In Exercises 83–88, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.(AB)-1 = A-1 B-1, assuming A, B, and AB are invertible.
Exercises 88–90 will help you prepare for the material covered in the next section.Multiply:After performing the multiplication, describe what happens to the elements in the first matrix. 011 a12 [1 07 922. LO [421
Use Gauss-Jordan elimination to solve the system: -x 4x + 5y y - z = 1 = 0 y - 3z = 0.
Multiply and write the linear system represented by the following matrix multiplication: 11- y a1 b₁ az bz cz c3. az b3 C₁ X || d₁ dz Ld3_
Give an example of a 2 × 2 matrix that is its own inverse.
Each person in the group should work with one partner. Send a coded word or message to each other by giving your partner the coded matrix and the coding matrix that you selected. Once messages are sent, each person should decode the message received.
In Exercises 1–4, find the focus and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d).y2 = 4x ندی * -4-3-2 -4-3 8 X 8. 2- د D ه ن دا + I 4. b.
Exercises 96–98 will help you prepare for the material covered in the next section. Simplify the expression in each exercise. 2(-5)-1(-4) 5(-5) - 6(-4)
Solve: log2 x + log2 (x + 2) = 3.
In Exercises 1–18, graph each ellipse and locate the foci. x2 16 + 12 4 = 1 =
In Exercises 1–8, graph each ellipse and locate the foci. 36 25 1
Solve: log(x + 4) - log(x - 2) = log x.
In Exercises 1–4, find the vertices and locate the foci of each hyperbola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d). a. C. 4- 3- y 4- -3- 2- IN b. d. A رنا 3 2- ننا - 21 y e d sit y x
In Exercises 1–4, write the first five terms of each sequence. Assume that d represents the common difference of an arithmetic sequence and r represents the common ratio of a geometric sequence. H1_ n (n − 1)! an = (-1)+1. =
In Exercises 1–5, graph the conic section with the given equation. For ellipses, find the foci. For hyperbolas, find the foci and give the equations of the asymptotes. For parabolas, find the vertex, focus, and directrix.9x2 - 4y2 = 36
Exercises 96–98 will help you prepare for the material covered in the next section. Simplify the expression in each exercise.2(-30 - (-3)) - 3(6 - 9) + (-1)(1 - 15)
Solve each equation or inequality in Exercises 1–7.2(x - 3) + 5x = 8(x - 1)
In Exercises 1–5, graph each ellipse. Give the location of the foci. x 25 4 = 1
Exercises 96–98 will help you prepare for the material covered in the next section. Simplify the expression in each exercise.2(-5) - (-3)(4)
Fill in each blank so that the resulting statement is true.The set of all points in a plane the sum of whose distances from two fixed points is constant is a/an_________ . The two fixed points are called the_________ . The midpoint of the line segment connecting the two fixed points is the_________
Fill in each blank so that the resulting statement is true.The set of all points in a plane the difference of whose distances from two fixed points is constant is a/an________ . The two fixed points are called the________ . The line through these points intersects the graph at two points, called
Fill in each blank so that the resulting statement is true.The set of all points in a plane that are equidistant from a fixed line and a fixed point is a/an________ . The fixed line is called the_______ and the fixed point is called the_________ .
Solve each equation or inequality in Exercises 1–7.-3(2x - 4) 7 2(6x - 12)
In Exercises 1–8, graph each ellipse and locate the foci. x2 25 16 읽 || 1
In Exercises 1–18, graph each ellipse and locate the foci. x2 25 + y2 16 || 1
In Exercises 1–4, find the vertices and locate the foci of each hyperbola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d). a. C. 4- 3- y 4- -3- 2- IN b. d. A رنا 3 2- ننا - 21 y e d sit y x
In Exercises 1–4, find the focus and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d).x2 = -4y ندی * -4-3-2 -4-3 8 X 8. 2- د D ه ن دا + I 4. b.
Fill in each blank so that the resulting statement is true.The equation of the parabola is of the forma. y2 = 4px.b. x2 = 4py_____. y X
In Exercises 1–5, graph each ellipse. Give the location of the foci. 9x² + 4y² = 36
Solve each equation or inequality in Exercises 1–7. x-5 = √x + 7
Fill in each blank so that the resulting statement is true.Consider the following equation in standard form:The value of a2 is______ , so the y-intercepts are______ and_________ . The graph passes through_________ and___________ , which are the vertices. The value of b2 is_________ , so the
In Exercises 1–5, graph the conic section with the given equation. For ellipses, find the foci. For hyperbolas, find the foci and give the equations of the asymptotes. For parabolas, find the vertex, focus, and directrix. (x + 2)² (y - 5)² + 25 9 1
In Exercises 1–4, find the vertices and locate the foci of each hyperbola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d). a. C. 4- 3- y 4- -3- 2- IN b. d. A رنا 3 2- ننا - 21 y e d sit y x
In Exercises 1–18, graph each ellipse and locate the foci. X है। 9 + 36 = 1
Fill in each blank so that the resulting statement is true.The vertices of x2/25 - y2/9 = 1 are_______ and________ . The foci are located at________ and________ .
In Exercises 1–4, write the first five terms of each sequence. Assume that d represents the common difference of an arithmetic sequence and r represents the common ratio of a geometric sequence.a1 = 5, d = -3
In Exercises 1–4, find the focus and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d).y2 = -4x ندی * -4-3-2 -4-3 8 X 8. 2- د D ه ن دا + I 4. b.
In Exercises 1–8, graph each ellipse and locate the foci.4x2 + y2 = 16
Fill in each blank so that the resulting statement is true.If 4p = -28, then the coordinates of the focus are____________ .
In Exercises 1–18, graph each ellipse and locate the foci. 2 X 16 + 49 = 1
In Exercises 1–4, find the vertices and locate the foci of each hyperbola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d). a. C. 4- 3- y 4- -3- 2- IN b. d. A رنا 3 2- ننا - 21 y e d sit y x
In Exercises 1–5, graph each ellipse. Give the location of the foci. (x + 2)² (y 1)² − + 25 16 = 1
Fill in each blank so that the resulting statement is true.The vertices of y2/25 - x2/9 = 1 are_______ and________ . The foci are located at________ and_______ .
In Exercises 1–4, write the first five terms of each sequence. Assume that d represents the common difference of an arithmetic sequence and r represents the common ratio of a geometric sequence.a1 = 5, r = -3
Solve each equation or inequality in Exercises 1–7.(x - 2)2 = 20
In Exercises 1–5, graph the conic section with the given equation. For ellipses, find the foci. For hyperbolas, find the foci and give the equations of the asymptotes. For parabolas, find the vertex, focus, and directrix.4x2 - y2 + 8x + 2y + 7 = 0
In Exercises 1–8, graph each ellipse and locate the foci.4x2 + 9y2 = 36
Solve each equation or inequality in Exercises 1–7. |2x - 1 ≥ 7
Fill in each blank so that the resulting statement is true.If 4p = -28, then the equation of the directrix is_______ . -X
In Exercises 1–8, graph each ellipse and locate the foci. (x - 1)² (y + 2)² 16 9 = 1
In Exercises 1–18, graph each ellipse and locate the foci. x 25 64 = 1
Fill in each blank so that the resulting statement is true.Consider an ellipse centered at the origin whose major axis is vertical. The equation of this ellipse in standard form indicates that a2 = 9 and b2 = 4. Thus, c2 =_______ . The foci are located at________ and________ .
Fill in each blank so that the resulting statement is true.The two branches of the graph of a hyperbola approach a pair of intersecting lines, called_________ . These intersecting lines pass through________ the of the hyperbola.
Fill in each blank so that the resulting statement is true.If 4p = -28, then the length of the latus rectum is_________ . The endpoints of the latus rectum are________ and_________ .
In Exercises 1–4, write the first five terms of each sequence. Assume that d represents the common difference of an arithmetic sequence and r represents the common ratio of a geometric sequence.a1 = 3, an = -an-1 + 4
In Exercises 1–5, graph the conic section with the given equation. For ellipses, find the foci. For hyperbolas, find the foci and give the equations of the asymptotes. For parabolas, find the vertex, focus, and directrix.(x + 5)2 = 8(y - 1)
In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola.y2 = 16x
Solve each equation or inequality in Exercises 1–7.3x3 + 4x2 - 7x + 2 = 0
In Exercises 1–8, graph each ellipse and locate the foci. (x + 1)² 9 (y-2)² 16 = 1
In Exercises 1–5, graph each ellipse. Give the location of the foci.x2 + 9y2 - 4x + 54y + 49 = 0
In Exercises 6–11, graph each hyperbola. Give the location of the foci and the equations of the asymptotes. 2 X 9 y2 = 1
In Exercises 5–12, find the standard form of the equation of each hyperbola satisfying the given conditions.Foci: (0, -3), (0, 3); vertices: (0, -1), (0, 1)
In Exercises 5–7, write a formula for the general term (the nth term) of each sequence. Then use the formula to find the indicated term.2, 6, 10, 14, . . . ; a20
In Exercises 1–18, graph each ellipse and locate the foci. 2 X 49 36 = 1
In Exercises 6–8, find the standard form of the equation of the conic section satisfying the given conditions.Ellipse; Foci: (-7, 0), (7, 0); Vertices: (-10, 0), (10, 0)
In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola.y2 = 4x
In Exercises 1–18, graph each ellipse and locate the foci. +² 49 y 81 = 1
Fill in each blank so that the resulting statement is true.If 4p = 4, then the coordinates of the focus are________ . (-2,-1)
Fill in each blank so that the resulting statement is true.If the center of an ellipse is (3, -2), the major axis is horizontal and parallel to the x-axis, and the distance from the center of the ellipse to its vertices is a = 5 units, then the coordinates of the vertices are_______ and________ .
In Exercises 5–12, find the standard form of the equation of each hyperbola satisfying the given conditions.Foci: (0, -6), (0, 6); vertices: (0, -2), (0, 2)
In Exercises 6–11, graph each hyperbola. Give the location of the foci and the equations of the asymptotes. y 9 x = 1
Fill in each blank so that the resulting statement is true.The equations for the asymptotes of x2/4 - y2/9 = 1 are________ and_______ .
In Exercises 5–7, write a formula for the general term (the nth term) of each sequence. Then use the formula to find the indicated term.3, 6, 12, 24, . . . ; a10
Solve each equation or inequality in Exercises 1–7.log2(x + 1) + log2(x - 1) = 3
In Exercises 6–8, find the standard form of the equation of the conic section satisfying the given conditions.Hyperbola; Foci: (0, -10), (0, 10); Vertices: (0, -7), (0, 7)
Solve each system in Exercises 8–10. 3x + 4y = 2 (2x + 5y = -1
In Exercises 5–7, write a formula for the general term (the nth term) of each sequence. Then use the formula to find the indicated term. 3 2² 1 1,2,0,... 30 ;
In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola.y2 = -8x
In Exercises 1–8, graph each ellipse and locate the foci.4x2 + 9y2 + 24x - 36y + 36 = 0
In Exercises 1–18, graph each ellipse and locate the foci. x2 2 + 64 100 = 1
Fill in each blank so that the resulting statement is true.If the foci of an ellipse are located at (-8, 6) and (10, 12), then the coordinates of the center of the ellipse are________ .
Fill in each blank so that the resulting statement is true.The equations for the asymptotes of y2/4 - x2 = 1 are______ and________ .
In Exercises 5–12, find the standard form of the equation of each hyperbola satisfying the given conditions.Foci: (-4, 0), (4, 0); vertices: (-3, 0), (3, 0)
In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola.y2 = -12x
Solve each system in Exercises 8–10. √2x² - y² = -8 lx - y = 6
In Exercises 6–8, find the standard form of the equation of the conic section satisfying the given conditions.Parabola; Focus: (50, 0); Directrix: x = -50
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