Intermediate Algebra (8th Edition)
8th Edition
ISBN: 9780134178967
Author: John Tobey Jr., Jeffrey Slater, Jamie Blair, Jenny Crawford
Publisher: PEARSON
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Chapter 3.4, Problem 9E
Graph each region.
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Assume {u1, U2, u3, u4} does not span R³.
Select the best statement.
A. {u1, U2, u3} spans R³ if u̸4 is a linear combination of other vectors in the set.
B. We do not have sufficient information to determine whether {u₁, u2, u3} spans R³.
C. {U1, U2, u3} spans R³ if u̸4 is a scalar multiple of another vector in the set.
D. {u1, U2, u3} cannot span R³.
E. {U1, U2, u3} spans R³ if u̸4 is the zero vector.
F. none of the above
Select the best statement.
A. If a set of vectors includes the zero vector 0, then the set of vectors can span R^ as long as the other vectors
are distinct.
n
B. If a set of vectors includes the zero vector 0, then the set of vectors spans R precisely when the set with 0
excluded spans Rª.
○ C. If a set of vectors includes the zero vector 0, then the set of vectors can span Rn as long as it contains n
vectors.
○ D. If a set of vectors includes the zero vector 0, then there is no reasonable way to determine if the set of vectors
spans Rn.
E. If a set of vectors includes the zero vector 0, then the set of vectors cannot span Rn.
F. none of the above
Which of the following sets of vectors are linearly independent? (Check the boxes for linearly independent sets.)
☐ A.
{
7
4
3
13
-9
8
-17
7
☐ B.
0
-8
3
☐ C.
0
☐
D.
-5
☐ E.
3
☐ F.
4
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Chapter 3 Solutions
Intermediate Algebra (8th Edition)
Ch. 3.1 - Verbal and Writing Skills, Exercises 1-4
1. Graphs...Ch. 3.1 - Verbal and Writing Skills, Exercises 1-4
2. The...Ch. 3.1 - Verbal and Writing Skills, Exercises 1-4 Explain...Ch. 3.1 - Verbal and Writing Skills, Exercises 1-4 (5, 1) is...Ch. 3.1 - Find the missing coordinate. ( − 2 , _ _ _ _ ) is...Ch. 3.1 - Find the missing coordinate. ( − 5 , _ _ _ _ ) is...Ch. 3.1 - Find the missing coordinate.
7. is a solution of...Ch. 3.1 - Find the missing coordinate. ( _ _ _ _ _ , 2 3 )...Ch. 3.1 - Graph each equation. y = 2 x − 3Ch. 3.1 - Graph each equation.
10.
Ch. 3.1 - Graph each equation. y = 1 − 3 xCh. 3.1 - Graph each equation.
12.
Ch. 3.1 - Graph each equation.
12.
Ch. 3.1 - Graph each equation. y = 5 2 x + 1Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify each equation if possible. Then graph the...Ch. 3.1 - Simplify each equation if possible. Then graph the...Ch. 3.1 - Simplify each equation if possible. Then graph the...Ch. 3.1 - Simplify each equation if possible. Then graph the...Ch. 3.1 - Simplify each equation if possible. Then graph the...Ch. 3.1 - Graph each equation. Use appropriate scales on...Ch. 3.1 - Graph each equation. Use appropriate scales on...Ch. 3.1 - Income of Men Versus Women The following graph...Ch. 3.1 - Income of Men Versus Women The following graph...Ch. 3.1 - Income of Men Versus Women The following graph...Ch. 3.1 - Income of Men Versus Women The following graph...Ch. 3.1 - Income of Men Versus Women The following graph...Ch. 3.1 - Prob. 42ECh. 3.1 - 43. Baseball If a baseball is thrown vertically...Ch. 3.1 - 44. Gasoline Storage Tank A full storage tank on...Ch. 3.1 - [1.3.3] Evaluate 36 ÷ ( 8 − 6 ) 2 + 3 ( − 4 )Ch. 3.1 - Prob. 46ECh. 3.1 - 47. [2.4.1.] Balloon Giveaway A novelty company is...Ch. 3.1 - Prob. 48ECh. 3.1 - Prob. 1QQCh. 3.1 - Prob. 2QQCh. 3.1 - Prob. 3QQCh. 3.1 - Prob. 4QQCh. 3.2 - Verbal and Writing Skills, Exercises 1-6 Slope...Ch. 3.2 - Verbal and Writing Skills, Exercises 1-6 A...Ch. 3.2 - Verbal and Writing Skills, Exercises 1-6 The slope...Ch. 3.2 - Verbal and Writing Skills, Exercises 1-6
4. Two...Ch. 3.2 - Verbal and Writing Skills, Exercises 1-6
5. Does...Ch. 3.2 - Prob. 6ECh. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - 19. Snowboarding Find the slope (grade) of a...Ch. 3.2 - 20. Grade of a Road Find the grade of a mountain...Ch. 3.2 - Rock Formation Find the slope (pitch) of a...Ch. 3.2 - Pitch of a Roof Find the slope (pitch) of a roof...Ch. 3.2 - 23. Slope of Street Baldwin Street in Dunedin, New...Ch. 3.2 - 24. Slope of a Roller Coaster Goliath at Six Flags...Ch. 3.2 - Find the slope of a line parallel to the line that...Ch. 3.2 - Find the slope of a line parallel to the line that...Ch. 3.2 - Find the slope of a line parallel to the line that...Ch. 3.2 - Find the slope of a line parallel to the line that...Ch. 3.2 - Prob. 29ECh. 3.2 - Find the slope of a line parallel to the line that...Ch. 3.2 - Find the slope of a line perpendicular to the line...Ch. 3.2 - Find the slope of a line perpendicular to the line...Ch. 3.2 - Find the slope of a line perpendicular to the line...Ch. 3.2 - Find the slope of a line perpendicular to the line...Ch. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - A line k passes through the points ( − 3 , − 9 )...Ch. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - 40. Do the points , and C(8,1) lie on a straight...Ch. 3.2 - 41. Architect Most new buildings are required to...Ch. 3.2 - Rate of Climb of Aircraft A small Cessna plane...Ch. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Prob. 1QQCh. 3.2 - Prob. 2QQCh. 3.2 - Prob. 3QQCh. 3.2 - Prob. 4QQCh. 3.3 - Verbal and Writing Skills, Exercises 1 and 2 You...Ch. 3.3 - Verbal and Writing Skills, Exercises 1 and 2
2....Ch. 3.3 - Write an equation of the line with the given slope...Ch. 3.3 - Write an equation of the line with the given slope...Ch. 3.3 - Write an equation of the line with the given slope...Ch. 3.3 - Write an equation of the line with the given slope...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Write each equation in slope-intercept form. Then...Ch. 3.3 - Prob. 17ECh. 3.3 - Write each equation in slope-intercept form. Then...Ch. 3.3 - Write each equation in slope-intercept form. Then...Ch. 3.3 - Write each equation in slope-intercept form. Then...Ch. 3.3 - Write each equation in slope-intercept form. Then...Ch. 3.3 - For each equation find the slope and the...Ch. 3.3 - Prob. 23ECh. 3.3 - For each equation find the slope and the...Ch. 3.3 - For each equation find the slope and the...Ch. 3.3 - Prob. 26ECh. 3.3 - Find an equation of the line that passes through...Ch. 3.3 - Find an equation of the line that passes through...Ch. 3.3 - Find an equation of the line that passes through...Ch. 3.3 - Find an equation of the line that passes through...Ch. 3.3 - Find an equation of the line that passes through...Ch. 3.3 - Find an equation of the line passing through the...Ch. 3.3 - Find an equation of the line passing through the...Ch. 3.3 - Find an equation of the line passing through the...Ch. 3.3 - Find an equation of the line passing through the...Ch. 3.3 - Find an equation of the line passing through the...Ch. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Find an equation of the line satisfying the...Ch. 3.3 - Find an equation of the line satisfying the...Ch. 3.3 - Find an equation of the line satisfying the...Ch. 3.3 - Find an equation of the line satisfying the...Ch. 3.3 - Prob. 44ECh. 3.3 - Find an equation of the line satisfying the...Ch. 3.3 - Prob. 46ECh. 3.3 - Without graphing, determine whether the following...Ch. 3.3 - Prob. 48ECh. 3.3 - Without graphing, determine whether the following...Ch. 3.3 - Prob. 50ECh. 3.3 - Without graphing, determine whether the following...Ch. 3.3 - Prob. 52ECh. 3.3 - Prob. 53ECh. 3.3 - Prob. 54ECh. 3.3 - Prob. 55ECh. 3.3 - Prob. 56ECh. 3.3 - Cost of Homes The median sale price of...Ch. 3.3 - Prob. 58ECh. 3.3 - Prob. 59ECh. 3.3 - Prob. 60ECh. 3.3 - Prob. 61ECh. 3.3 - Prob. 1QQCh. 3.3 - Prob. 2QQCh. 3.3 - Prob. 3QQCh. 3.3 - Prob. 4QQCh. 3.4 - Verbal and Writing Skills, Exercises 1-6 Explain...Ch. 3.4 - Prob. 2ECh. 3.4 - Verbal and Writing Skills, Exercises 1-6 When...Ch. 3.4 - Prob. 4ECh. 3.4 - Verbal and Writing Skills, Exercises 1-6
5. When...Ch. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Graph each region.
9.
Ch. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Graph each region. 6 y − x ≤ 12Ch. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Graph each region.
17.
Ch. 3.4 - Graph each region. x − 3 y ≥ 0Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Prob. 22ECh. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Prob. 27ECh. 3.4 - Prob. 28ECh. 3.4 - Prob. 29ECh. 3.4 - Prob. 1QQCh. 3.4 - Prob. 2QQCh. 3.4 - Prob. 3QQCh. 3.4 - Prob. 4QQCh. 3.5 - Verbal and Writing Skills, Exercises 1-4 Explain...Ch. 3.5 - Prob. 2ECh. 3.5 - Verbal and Writing Skills, Exercises 1-4 What are...Ch. 3.5 - Prob. 4ECh. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - Prob. 10ECh. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - Prob. 12ECh. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - Prob. 14ECh. 3.5 - Prob. 15ECh. 3.5 - Prob. 16ECh. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a...Ch. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a...Ch. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a...Ch. 3.5 - Prob. 26ECh. 3.5 - Given the function defined by , find the...Ch. 3.5 - Prob. 28ECh. 3.5 - Given the function defined by , find the...Ch. 3.5 - Prob. 30ECh. 3.5 - Given the function defined by h ( x ) = 3 4 x + 1...Ch. 3.5 - Prob. 32ECh. 3.5 - Prob. 33ECh. 3.5 - Prob. 34ECh. 3.5 - Given the function defined by r ( x ) = 2 x 2 − 4...Ch. 3.5 - Prob. 36ECh. 3.5 - Given the function defined by , find the...Ch. 3.5 - Prob. 38ECh. 3.5 - Given the function defined by t ( x ) = x 3 − 3 x...Ch. 3.5 - Given the function defined by t ( x ) = x 3 − 3 x...Ch. 3.5 - Given the function defined by t ( x ) = x 3 − 3 x...Ch. 3.5 - 42. If , find
Ch. 3.5 - 43. If , find
Ch. 3.5 - Prob. 44ECh. 3.5 - 45. If , find g (2).
Ch. 3.5 - Prob. 46ECh. 3.5 - Find the range of the function for the given...Ch. 3.5 - Prob. 48ECh. 3.5 - Find the domain of the function for the given...Ch. 3.5 - Prob. 50ECh. 3.5 - Prob. 51ECh. 3.5 - Prob. 52ECh. 3.5 - Prob. 1QQCh. 3.5 - Prob. 2QQCh. 3.5 - Prob. 3QQCh. 3.5 - Prob. 4QQCh. 3.6 - Graph each function. f ( x ) = 3 4 x + 2Ch. 3.6 - Prob. 2ECh. 3.6 - Graph each function.
3.
Ch. 3.6 - Prob. 4ECh. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Wildlife Biologist Ning is a wildlife biologist...Ch. 3.6 - Insulation in a House The R value of insulation in...Ch. 3.6 - Graph each function.
9.
Ch. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - Prob. 12ECh. 3.6 - Graph each function.
13.
Ch. 3.6 - Prob. 14ECh. 3.6 - Prob. 15ECh. 3.6 - Prob. 16ECh. 3.6 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Graph each function.
19.
Ch. 3.6 - Prob. 20ECh. 3.6 - Graph each function.
21.
Ch. 3.6 - Prob. 22ECh. 3.6 - Prob. 23ECh. 3.6 - Prob. 24ECh. 3.6 - Prob. 25ECh. 3.6 - Prob. 26ECh. 3.6 - In each of the following problems, a table of...Ch. 3.6 - Prob. 28ECh. 3.6 - Prob. 29ECh. 3.6 - Prob. 30ECh. 3.6 - In each of the following problems, a table of...Ch. 3.6 - Prob. 32ECh. 3.6 - Computer Manufacturing The following table shows...Ch. 3.6 - Prob. 34ECh. 3.6 - Prob. 35ECh. 3.6 - Prob. 36ECh. 3.6 - Prob. 37ECh. 3.6 - Prob. 38ECh. 3.6 - Prob. 1QQCh. 3.6 - Prob. 2QQCh. 3.6 - Prob. 3QQCh. 3.6 - Concept Check Explain how you would find f ( 1 4 )...Ch. 3 - Graph the straight line determined by each of the...Ch. 3 - Graph the straight line determined by each of the...Ch. 3 - Prob. 3RPCh. 3 - Prob. 4RPCh. 3 - Prob. 5RPCh. 3 - Prob. 6RPCh. 3 - Prob. 7RPCh. 3 - 8. Find the slope of a line perpendicular to the...Ch. 3 - 9. A line has a slope of and a y-intercept of (0,...Ch. 3 - Find the standard form of the equation of the line...Ch. 3 - 11. Find the standard form of the equation of the...Ch. 3 - 12. Computer Company Profit A computer company's...Ch. 3 - In exercises 13 - 16, find an equation of the line...Ch. 3 - In exercises 13 - 16, find an equation of the line...Ch. 3 - Prob. 15RPCh. 3 - In exercises 13 - 16, find an equation of the line...Ch. 3 - In exercises 17 - 18, find the slope and...Ch. 3 - In exercises 17 -18, find the slope and...Ch. 3 - Prob. 19RPCh. 3 - Graph the region described by the inequality.
20....Ch. 3 - Graph the region described by the inequality. 3 x...Ch. 3 - Graph the region described by the inequality. x ≤...Ch. 3 - Prob. 23RPCh. 3 - Prob. 24RPCh. 3 - What is the domain and range of each relation? Is...Ch. 3 - What is the domain and range of each relation? Is...Ch. 3 - Determine whether the graph represents a function.Ch. 3 - Determine whether the graph represents a function.Ch. 3 - If f ( x ) = − 2 x + 10 , find f ( − 1 ) and f ( −...Ch. 3 - If h ( x ) = x 3 + 2 x 2 − 5 x + 8 , find h ( − 1...Ch. 3 - Graph each function. f ( x ) = 2 | x − 1 |Ch. 3 - Prob. 32RPCh. 3 - Prob. 33RPCh. 3 - Prob. 34RPCh. 3 - Prob. 35RPCh. 3 - Prob. 36RPCh. 3 - Complete the table of values for each...Ch. 3 - 38. Find the slope and y-intercept of .
Ch. 3 - A line n is perpendicular to the line passing...Ch. 3 - A line p is parallel to the line passing through...Ch. 3 - Find the standard form of the equation of the line...Ch. 3 - 42. Find an equation of the line parallel to and...Ch. 3 - Find the slope-intercept form of the equation of...Ch. 3 - Prob. 44RPCh. 3 - Prob. 45RPCh. 3 - Prob. 46RPCh. 3 - Prob. 47RPCh. 3 - Prob. 48RPCh. 3 - Prob. 1TCh. 3 - Prob. 2TCh. 3 - Prob. 3TCh. 3 - Prob. 4TCh. 3 - Find the slope of the line passing through ( 2 , −...Ch. 3 - Prob. 6TCh. 3 - Prob. 7TCh. 3 - Prob. 8TCh. 3 - Prob. 9TCh. 3 - Write an equation of the horizontal line passing...Ch. 3 - Prob. 11TCh. 3 - Prob. 12TCh. 3 - Prob. 13TCh. 3 - Prob. 14TCh. 3 - 15. If , find f .
Ch. 3 - Prob. 16TCh. 3 - Prob. 17TCh. 3 - Prob. 18TCh. 3 - Prob. 19TCh. 3 - Prob. 20TCh. 3 - Prob. 21TCh. 3 - Prob. 1CTCh. 3 - Evaluate the expression. 3 ( 4 − 6 ) 2 + 16 + 12 ÷...Ch. 3 - Prob. 3CTCh. 3 - Prob. 4CTCh. 3 - Prob. 5CTCh. 3 - Prob. 6CTCh. 3 - Prob. 7CTCh. 3 - Prob. 8CTCh. 3 - Prob. 9CTCh. 3 - Prob. 10CTCh. 3 - Prob. 11CTCh. 3 - Prob. 12CTCh. 3 - Prob. 13CTCh. 3 - Prob. 14CTCh. 3 - Prob. 15CTCh. 3 - Prob. 16CTCh. 3 - Prob. 17CTCh. 3 - Prob. 18CTCh. 3 - Prob. 19CTCh. 3 - Prob. 20CTCh. 3 - Prob. 21CTCh. 3 - Prob. 22CTCh. 3 - Prob. 23CTCh. 3 - Prob. 24CTCh. 3 - Prob. 25CT
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- 3 and = 5 3 ---8--8--8 Let = 3 U2 = 1 Select all of the vectors that are in the span of {u₁, u2, u3}. (Check every statement that is correct.) 3 ☐ A. The vector 3 is in the span. -1 3 ☐ B. The vector -5 75°1 is in the span. ГОЛ ☐ C. The vector 0 is in the span. 3 -4 is in the span. OD. The vector 0 3 ☐ E. All vectors in R³ are in the span. 3 F. The vector 9 -4 5 3 is in the span. 0 ☐ G. We cannot tell which vectors are i the span.arrow_forward(20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0; y₁ = e*, y2 = e¯x, y3 = e−2x (20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y"-2y-3y = 6; y(0) = 3, y'(0) = 11 yc = c₁ex + c2e³x; yp = −2 (60 p) 3. Find the general, and if possible, particular solutions of the linear systems of differential equations given below using the eigenvalue-eigenvector method. (See Section 7.3 in your textbook if you need a review of the subject.) = a) x 4x1 + x2, x2 = 6x1-x2 b) x=6x17x2, x2 = x1-2x2 c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0arrow_forwardFind the perimeter and areaarrow_forward
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