Intermediate Algebra
19th Edition
ISBN: 9780998625720
Author: Lynn Marecek
Publisher: OpenStax College
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Textbook Question
Chapter 3, Problem 491RE
Atsushi he needs to exercise enough to burn 600 calories each day. He prefers to either run or bike and burns 20 calories per minute while running and 15 calories a minute while biking.
(a) If x is the number of minutes that Atsushi runs and yis the number minutes he bikes, find the inequality that models the situation.
(b) Graph the inequality.
(c) List three solutions to the inequality. What options do the solutions provide Atsushi?
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Students have asked these similar questions
Let
2
A =
4
3
-4
0
1
(a) Show that v =
eigenvalue.
()
is an eigenvector of A and find the corresponding
(b) Find the characteristic polynomial of A and factorise it. Hint: the answer to (a)
may be useful.
(c) Determine all eigenvalues of A and find bases for the corresponding eigenspaces.
(d) Find an invertible matrix P and a diagonal matrix D such that P-¹AP = D.
(c) Let
6
0 0
A =
-10 4 8
5 1 2
(i) Find the characteristic polynomial of A and factorise it.
(ii) Determine all eigenvalues of A and find bases for the corresponding
eigenspaces.
(iii) Is A diagonalisable? Give reasons for your answer.
most 2, and let
Let P2 denote the vector space of polynomials of degree at
D: P2➡ P2
be the transformation that sends a polynomial p(t) = at² + bt+c in P2 to its derivative
p'(t)
2at+b, that is,
D(p) = p'.
(a) Prove that D is a linear transformation.
(b) Find a basis for the kernel ker(D) of the linear transformation D and compute its
nullity.
(c) Find a basis for the image im(D) of the linear transformation D and compute its
rank.
(d) Verify that the Rank-Nullity Theorem holds for the linear transformation D.
(e) Find the matrix representation of D in the standard basis (1,t, t2) of P2.
Chapter 3 Solutions
Intermediate Algebra
Ch. 3.1 - Plot each point in a rectangular coordinate system...Ch. 3.1 - Plot each point in a rectangular coordinate system...Ch. 3.1 - Use graph of y=3x1 . For each ordered pair,...Ch. 3.1 - Use graph of y=3x1 . For each ordered pair,...Ch. 3.1 - Graph the equation by plotting points: y=2x3 .Ch. 3.1 - Graph the equation by plotting points: y=2x+4 .Ch. 3.1 - Graph the equation: y=13x1 .Ch. 3.1 - Graph the equation: y=14x+2 .Ch. 3.1 - Graph the equations: (a) x=5 (b) y=4 .Ch. 3.1 - Graph the equations: (a) x=2 (b) y=3
Ch. 3.1 - Graph the equations in the same rectangular...Ch. 3.1 - Graph the equations in the same rectangular...Ch. 3.1 - Find the x- and y-intercepts on the graph.Ch. 3.1 - Find the x- and y-intercepts on the graph.Ch. 3.1 - Find the intercepts: 3x+y=12 .Ch. 3.1 - Find the intercepts: x+4y=8 .Ch. 3.1 - Graph using the intercepts: x2y=4 .Ch. 3.1 - Graph using the intercepts: x+3y=6 .Ch. 3.1 - Graph using the intercepts: 5x2y=10 .Ch. 3.1 - Graph using the intercepts: 3x4y=12 .Ch. 3.1 - Graph using the intercepts: y=4x .Ch. 3.1 - Graph the intercepts: y=x .Ch. 3.1 - In the following exercises, plot each point in a...Ch. 3.1 - In the following exercises, plot each point in a...Ch. 3.1 - In the following exercises, plot each point in a...Ch. 3.1 - In the following exercises, plot each point in a...Ch. 3.1 - In the following exercises, for each ordered pair,...Ch. 3.1 - In the following exercises, for each ordered pair,...Ch. 3.1 - In the following exercises, for each ordered pair,...Ch. 3.1 - In the following exercises, for each ordered pair,...Ch. 3.1 - In the following exercises, graph by plotting...Ch. 3.1 - In the following exercises, graph by plotting...Ch. 3.1 - In the following exercises, graph by plotting...Ch. 3.1 - In the following exercises, graph by plotting...Ch. 3.1 - In the following exercises, graph by plotting...Ch. 3.1 - In the following exercises, graph by plotting...Ch. 3.1 - In the following exercises, graph by plotting...Ch. 3.1 - In the following exercises, graph by plotting...Ch. 3.1 - In the following exercises, graph by plotting...Ch. 3.1 - In the following exercises, graph by plotting...Ch. 3.1 - In the following exercises, graph by plotting...Ch. 3.1 - In the following exercises, graph by plotting...Ch. 3.1 - In the following exercises, graph by plotting...Ch. 3.1 - In the following exercises, graph by plotting...Ch. 3.1 - In the following exercises, graph by plotting...Ch. 3.1 - In the following exercises, graph by plotting...Ch. 3.1 - In the following exercises, graph each equation....Ch. 3.1 - In the following exercises, graph each equation....Ch. 3.1 - In the following exercises, graph each equation....Ch. 3.1 - In the following exercises, graph each equation....Ch. 3.1 - In the following exercises, graph each pair of...Ch. 3.1 - In the following exercises, graph each pair of...Ch. 3.1 - In the following exercises, graph each pair of...Ch. 3.1 - In the following exercises, graph each pair of...Ch. 3.1 - In the following exercises, find the x- and...Ch. 3.1 - In the following exercises, find the x- and...Ch. 3.1 - In the following exercises, find the x- and...Ch. 3.1 - In the following exercises, find the x- and...Ch. 3.1 - In the following exercises, find the intercepts...Ch. 3.1 - In the following exercises, find the intercepts...Ch. 3.1 - In the following exercises, find the intercepts...Ch. 3.1 - In the following exercises, find the intercepts...Ch. 3.1 - In the following exercises, find the intercepts...Ch. 3.1 - In the following exercises, find the intercepts...Ch. 3.1 - In the following exercises, find the intercepts...Ch. 3.1 - In the following exercises, find the intercepts...Ch. 3.1 - In the following exercises, graph using the...Ch. 3.1 - In the following exercises, graph using the...Ch. 3.1 - In the following exercises, graph using the...Ch. 3.1 - In the following exercises, graph using the...Ch. 3.1 - In the following exercises, graph using the...Ch. 3.1 - In the following exercises, graph using the...Ch. 3.1 - In the following exercises, graph using the...Ch. 3.1 - In the following exercises, graph using the...Ch. 3.1 - In the following exercises, graph using the...Ch. 3.1 - In the following exercises, graph using the...Ch. 3.1 - In the following exercises, graph using the...Ch. 3.1 - In the following exercises, graph using the...Ch. 3.1 - In the following exercises, graph using the...Ch. 3.1 - In the following exercises, graph using the...Ch. 3.1 - In the following exercises, graph using the...Ch. 3.1 - In the following exercises, graph using the...Ch. 3.1 - In the following exercises, graph each equation....Ch. 3.1 - In the following exercises, graph each equation....Ch. 3.1 - In the following exercises, graph each equation....Ch. 3.1 - In the following exercises, graph each equation....Ch. 3.1 - In the following exercises, graph each equation....Ch. 3.1 - In the following exercises, graph each equation....Ch. 3.1 - In the following exercises, graph each equation....Ch. 3.1 - In the following exercises, graph each equation....Ch. 3.1 - Explain how you would choose three x-values to...Ch. 3.1 - What is the difference between the equations of a...Ch. 3.1 - Do you prefer to use the method of plotting points...Ch. 3.1 - Do you prefer to use the method of plotting points...Ch. 3.2 - Find the slope of the line shown.Ch. 3.2 - Find the slope of the line shown.Ch. 3.2 - Find the slope of the line: x=4 .Ch. 3.2 - Find the slope of the line: y=7 .Ch. 3.2 - Use the slope formula to find the slope of the...Ch. 3.2 - Use the slope formula to find the slope of the...Ch. 3.2 - Graph the line passing through the point (2,2)...Ch. 3.2 - Graph the line passing through the point (2,3)...Ch. 3.2 - Identify the slope and y-intercept from the...Ch. 3.2 - Identify the slope and y-intercept from the...Ch. 3.2 - Graph the line of the equation y=x3 using its...Ch. 3.2 - Graph the line of the equation y=x1 using its...Ch. 3.2 - Determine the most convenient method to graph each...Ch. 3.2 - Determine the most convenient method to graph each...Ch. 3.2 - The equation h=2s+50 is used to estimate a woman’s...Ch. 3.2 - The equation T=14n+40 is used to estimate the...Ch. 3.2 - Stella has a home business selling gourmet pizzas....Ch. 3.2 - Loreen has a calligraphy business. The equation...Ch. 3.2 - Use slopes and y-intercepts to determine if the...Ch. 3.2 - Use slopes and y-intercepts to determine if the...Ch. 3.2 - Use slopes and y-intercepts to determine if the...Ch. 3.2 - Use slopes and y-intercepts to determine if the...Ch. 3.2 - Use slopes to determine if the lines are...Ch. 3.2 - Use slopes to determine if the lines are...Ch. 3.2 - In the following exercises, find the slope of each...Ch. 3.2 - In the following exercises, find the slope of each...Ch. 3.2 - In the following exercises, find the slope of each...Ch. 3.2 - In the following exercises, find the slope of each...Ch. 3.2 - In the following exercises, find the slope of each...Ch. 3.2 - In the following exercises, find the slope of each...Ch. 3.2 - In the following exercises, find the slope of each...Ch. 3.2 - In the following exercises, find the slope of each...Ch. 3.2 - In the following exercises, find the slope of each...Ch. 3.2 - In the following exercises, find the slope of each...Ch. 3.2 - In the following exercises, find the slope of each...Ch. 3.2 - In the following exercises, find the slope of each...Ch. 3.2 - In the following exercises, use the slope formula...Ch. 3.2 - In the following exercises, use the slope formula...Ch. 3.2 - In the following exercises, use the slope formula...Ch. 3.2 - In the following exercises, use the slope formula...Ch. 3.2 - In the following exercises, use the slope formula...Ch. 3.2 - In the following exercises, use the slope formula...Ch. 3.2 - In the following exercises, use the slope formula...Ch. 3.2 - In the following exercises, use the slope formula...Ch. 3.2 - In the following exercises, graph each line with...Ch. 3.2 - In the following exercises, graph each line with...Ch. 3.2 - In the following exercises, graph each line with...Ch. 3.2 - In the following exercises, graph each line with...Ch. 3.2 - In the following exercises, graph each line with...Ch. 3.2 - In the following exercises, graph each line with...Ch. 3.2 - In the following exercises, graph each line with...Ch. 3.2 - In the following exercises, graph each line with...Ch. 3.2 - In the following exercises, identify the slope and...Ch. 3.2 - In the following exercises, identify the slope and...Ch. 3.2 - In the following exercises, identify the slope and...Ch. 3.2 - In the following exercises, identify the slope and...Ch. 3.2 - In the following exercises, identify the slope and...Ch. 3.2 - In the following exercises, identify the slope and...Ch. 3.2 - In the following exercises, identify the slope and...Ch. 3.2 - In the following exercises, identify the slope and...Ch. 3.2 - In the following exercises, graph the line of each...Ch. 3.2 - In the following exercises, graph the line of each...Ch. 3.2 - In the following exercises, graph the line of each...Ch. 3.2 - In the following exercises, graph the line of each...Ch. 3.2 - In the following exercises, graph the line of each...Ch. 3.2 - In the following exercises, graph the line of each...Ch. 3.2 - In the following exercises, graph the line of each...Ch. 3.2 - In the following exercises, graph the line of each...Ch. 3.2 - In the following exercises, determine the most...Ch. 3.2 - In the following exercises, determine the most...Ch. 3.2 - In the following exercises, determine the most...Ch. 3.2 - In the following exercises, determine the most...Ch. 3.2 - In the following exercises, determine the most...Ch. 3.2 - In the following exercises, determine the most...Ch. 3.2 - In the following exercises, determine the most...Ch. 3.2 - In the following exercises, determine the most...Ch. 3.2 - The equation P=31+1.75w models the relation...Ch. 3.2 - The equation P=28+2.54w models the relation...Ch. 3.2 - Bruce drives his car for his job. The equation...Ch. 3.2 - Janelle is planning to rent a car while on...Ch. 3.2 - Cherie works in retail and her weekly salary...Ch. 3.2 - Patel’s weekly salary includes a base pay plus...Ch. 3.2 - Costa is planning a lunch banquet. The equation...Ch. 3.2 - Margie is planning a dinner banquet. The equation...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - In the following exercises, use slopes and...Ch. 3.2 - How does the graph of a line with slope m=12...Ch. 3.2 - Why is the slope of a vertical line “undefined”?Ch. 3.2 - Explain how you can graph a line given a point and...Ch. 3.2 - Explain in your own words how to decide which...Ch. 3.3 - Find an equation of a line with slope 25 and...Ch. 3.3 - Find an equation of a line with slope 1 and...Ch. 3.3 - Find the equation of the line shown in the graph.Ch. 3.3 - Find the equation of the line shown in the graph.Ch. 3.3 - Find the equation of a line with slope m=25 and...Ch. 3.3 - Find the equation of a line with slope m=34 , and...Ch. 3.3 - Find an equation of a horizontal line containing...Ch. 3.3 - Find an equation of a horizontal line containing...Ch. 3.3 - Find an equation of a line containing the points...Ch. 3.3 - Find an equation of a line containing the points...Ch. 3.3 - Find an equation of a line containing the points...Ch. 3.3 - Find an equation of a line containing the points...Ch. 3.3 - Find an equation of a line parallel to the line...Ch. 3.3 - Find an equation of a line parallel to the line...Ch. 3.3 - Find an equation of a line perpendicular to the...Ch. 3.3 - Find an equation of a line perpendicular to the...Ch. 3.3 - Find an equation of a line that is perpendicular...Ch. 3.3 - Find an equation of a line that is perpendicular...Ch. 3.3 - Find an equation of a line that is perpendicular...Ch. 3.3 - Find an equation of a line that is perpendicular...Ch. 3.3 - In the following exercises, find the equation of a...Ch. 3.3 - In the following exercises, find the equation of a...Ch. 3.3 - In the following exercises, find the equation of a...Ch. 3.3 - In the following exercises, find the equation of a...Ch. 3.3 - In the following exercises, find the equation of a...Ch. 3.3 - In the following exercises, find the equation of a...Ch. 3.3 - In the following exercises, find the equation of a...Ch. 3.3 - In the following exercises, find the equation of a...Ch. 3.3 - In the following exercises, find the equation of...Ch. 3.3 - In the following exercises, find the equation of...Ch. 3.3 - 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Hugh works two part time jobs. One at a grocery...Ch. 3.4 - Veronica works two part time jobs in order to earn...Ch. 3.4 - In the following exercises, determine whether each...Ch. 3.4 - In the following exercises, determine whether each...Ch. 3.4 - In the following exercises, determine whether each...Ch. 3.4 - In the following exercises, determine whether each...Ch. 3.4 - In the following exercises, determine whether each...Ch. 3.4 - In the following exercises, determine whether each...Ch. 3.4 - In the following exercises, write the inequality...Ch. 3.4 - In the following exercises, write the inequality...Ch. 3.4 - In the following exercises, write the inequality...Ch. 3.4 - In the following exercises, write the inequality...Ch. 3.4 - In the following exercises, write the inequality...Ch. 3.4 - In the following exercises, write the inequality...Ch. 3.4 - In the following exercises, write the inequality...Ch. 3.4 - In the following exercises, write the inequality...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - In the following exercises, graph each linear...Ch. 3.4 - Harrison works two part time jobs. One at a gas...Ch. 3.4 - Elena needs to earn at least $450 a week during...Ch. 3.4 - The doctor tells Laura she needs to exercise...Ch. 3.4 - Armando’s workouts consist of kickboxing and...Ch. 3.4 - Lester thinks that the solution of any inequality...Ch. 3.4 - Explain why, in some graphs of linear...Ch. 3.5 - For the relation...Ch. 3.5 - For the relation {(1,3),(2,6),(3,9),(4,12),(5,15)}...Ch. 3.5 - Use the mapping of the relation shown to (a) list...Ch. 3.5 - Use the mapping of the relation shown to (a) list...Ch. 3.5 - Use the graph of the relation to (a) list the...Ch. 3.5 - Use the graph of the relation to (a) list the...Ch. 3.5 - Use the set of ordered pairs to (i) determine...Ch. 3.5 - Use the set of ordered pairs to (i) determine...Ch. 3.5 - Use the mapping to (a) determine whether the...Ch. 3.5 - Use the mapping to (a) determine whether the...Ch. 3.5 - Determine whether each equation is a function. (a)...Ch. 3.5 - Determine whether each equation is a function. (a)...Ch. 3.5 - For the function f(x)=3x22x+1 , evaluate the...Ch. 3.5 - For the function f(x)=2x2+4x3 , evaluate the...Ch. 3.5 - For the function g(x)=4x7 , evaluate the function....Ch. 3.5 - For the function h(x)=2x+1 , evaluate the...Ch. 3.5 - The number of unread emails in Bryan’s account is...Ch. 3.5 - The number of unread emails in Anthony’s account...Ch. 3.5 - In the following exercises, for each relation (a)...Ch. 3.5 - In the following exercises, for each relation (a)...Ch. 3.5 - In the following exercises, for each relation (a)...Ch. 3.5 - In the following exercises, for each relation (a)...Ch. 3.5 - In the following exercises, use the mapping of the...Ch. 3.5 - In the following exercises, use the mapping of the...Ch. 3.5 - In the following exercises, use the mapping of the...Ch. 3.5 - In the following exercises, use the mapping of the...Ch. 3.5 - In the following exercises, use the graph of the...Ch. 3.5 - In the following exercises, use the graph of the...Ch. 3.5 - In the following exercises, use the graph of the...Ch. 3.5 - In the following exercises, use the graph of the...Ch. 3.5 - In the following exercises, use the set of ordered...Ch. 3.5 - In the following exercises, use the set of ordered...Ch. 3.5 - In the following exercises, use the set of ordered...Ch. 3.5 - In the following exercises, use the set of ordered...Ch. 3.5 - In the following exercises, use the mapping to (a)...Ch. 3.5 - In the following exercises, use the mapping to (a)...Ch. 3.5 - In the following exercises, use the mapping to (a)...Ch. 3.5 - In the following exercises, use the mapping to (a)...Ch. 3.5 - In the following exercises, determine whether each...Ch. 3.5 - In the following exercises, determine whether each...Ch. 3.5 - In the following exercises, determine whether each...Ch. 3.5 - In the following exercises, determine whether each...Ch. 3.5 - In the following exercises, evaluate the function:...Ch. 3.5 - In the following exercises, evaluate the function:...Ch. 3.5 - In the following exercises, evaluate the function:...Ch. 3.5 - In the following exercises, evaluate the function:...Ch. 3.5 - In the following exercises, evaluate the function:...Ch. 3.5 - In the following exercises, evaluate the function:...Ch. 3.5 - In the following exercises, evaluate the function:...Ch. 3.5 - In the following exercises, evaluate the function:...Ch. 3.5 - In the following exercises, evaluate the function:...Ch. 3.5 - In the following exercises, evaluate the function:...Ch. 3.5 - In the following exercises, evaluate the function:...Ch. 3.5 - In the following exercises, evaluate the function:...Ch. 3.5 - In the following exercises, evaluate the function:...Ch. 3.5 - ?y13In the following exercises, evaluate the...Ch. 3.5 - In the following exercises, evaluate the function....Ch. 3.5 - In the following exercises, evaluate the function....Ch. 3.5 - In the following exercises, evaluate the function....Ch. 3.5 - In the following exercises, evaluate the function....Ch. 3.5 - In the following exercises, evaluate the function....Ch. 3.5 - In the following exercises, evaluate the function....Ch. 3.5 - In the following exercises, evaluate the function....Ch. 3.5 - In the following exercises, evaluate the function....Ch. 3.5 - In the following exercises, solve. 329. 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Is every function a...Ch. 3.5 - How do you find the value of a function?Ch. 3.6 - Determine whether each graph is the graph of a...Ch. 3.6 - Determine whether each graph is the graph of a...Ch. 3.6 - Graph: f(x)=3x1Ch. 3.6 - Graph: f(x)=4x5Ch. 3.6 - Graph: f(x)=2Ch. 3.6 - Graph: f(x)=3 .Ch. 3.6 - Graph: f(x)=x2 .Ch. 3.6 - Graph: f(x)=x2Ch. 3.6 - Graph: f(x)=x3 .Ch. 3.6 - Graph: f(x)=x3 .Ch. 3.6 - Graph: f(x)=x .Ch. 3.6 - Graph: f(x)=x .Ch. 3.6 - Graph: f(x)=|x| .Ch. 3.6 - Graph: f(x)=|x| .Ch. 3.6 - Use the graph of the function to find its domain...Ch. 3.6 - Use the graph of the function to find its domain...Ch. 3.6 - Use the graph of the function to find the...Ch. 3.6 - Use the graph of the function to find the...Ch. 3.6 - In the following exercises, determine whether each...Ch. 3.6 - In the following exercises, determine whether each...Ch. 3.6 - In the following exercises, determine whether each...Ch. 3.6 - In the following exercises, determine whether each...Ch. 3.6 - In the following exercises, (a) graph each...Ch. 3.6 - 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In the following exercises, use the graph of the...Ch. 3.6 - In the following exercises, use the graph of the...Ch. 3.6 - In the following exercises, use the graph of the...Ch. 3.6 - In the following exercises, use the graph of the...Ch. 3.6 - In the following exercises, use the graph of the...Ch. 3.6 - In the following exercises, use the graph of the...Ch. 3.6 - In the following exercises, use the graph of the...Ch. 3.6 - In the following exercises, use the graph of the...Ch. 3.6 - Explain in your own words how to find the domain...Ch. 3.6 - Explain in your own words how to find the range...Ch. 3.6 - Explain in your own words how to use the vertical...Ch. 3.6 - Draw a sketch of the square and cube functions....Ch. 3 - In the following exercises, plot each point in a...Ch. 3 - In the following exercises, plot each point in a...Ch. 3 - In the following exercises, plot each point in a...Ch. 3 - In the following exercises, plot each point in a...Ch. 3 - In the following exercises, graph by plotting...Ch. 3 - 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Katherine is a private chef. 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