
Algebra and Trigonometry
1st Edition
ISBN: 9781938168376
Author: Jay Abramson
Publisher: OpenStax
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Chapter 4.1, Problem 115SE
A gym membership with two personal trainingsessions costs
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(1) Let F be a field, show that the vector space F,NEZ* be a finite dimension.
(2) Let P2(x) be the vector space of polynomial of degree equal or less than two
and M={a+bx+cx²/a,b,cЄ R,a+b=c),show that whether Mis hyperspace or not.
(3) Let A and B be a subset of a vector space such that ACB, show that whether:
(a) if A is convex then B is convex or not. (b) if B is convex then A is convex or not.
(4) Let R be a field of real numbers and X=R, X is a vector space over R show that by
definition the norms/II.II, and II.112 on X are equivalent where
Ilxll₁ = max(lx,l, i=1,2,...,n) and llxll₂=(x²).
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(5) Let Ⓡ be a field of real numbers, Ⓡis a normed space under usual operations and
norm, let E=(2,5,8), find int(E), b(E) and D(E).
(6) Write the definition of bounded linear function between two normed spaces and
write with prove the relation between continuous and bounded linear function
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b- Let f be a function from a normed space X into a normed space Y, show that f
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c-Show that every finite dimension normed space is a Banach.
Q/a- Let A and B two open sets in a normed space X, show that by definition
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Chapter 4 Solutions
Algebra and Trigonometry
Ch. 4.1 - If f(x) is a linear function, and (2,3) and (0,4)...Ch. 4.1 - The population of a small town increased from...Ch. 4.1 - If f(x) is a linear function, with f(2)=11, and...Ch. 4.1 - A new plant food was introduced to a young tree to...Ch. 4.1 - Graph f(x)=34x+6 by plotting points.Ch. 4.1 - Find a point on the graph we drew in Example 12...Ch. 4.1 - Graph f(x)=4+2x, using transformations.Ch. 4.1 - Find the x-intercept of f(x)=14x4.Ch. 4.1 - Given the function h(x)=2x4, write an equation for...Ch. 4.1 - A line passes through the points, (2,15) and...
Ch. 4.1 - Terry is skiing down a steep hill. Terry’s...Ch. 4.1 - Jessica is walking home from a friend’s...Ch. 4.1 - A boat is 100 miles away from the marina,...Ch. 4.1 - If the graphs of two linear functions...Ch. 4.1 - Ifa horizontal line has the equation f(x)=a and...Ch. 4.1 - For the following exercises, determine whether the...Ch. 4.1 - For the following exercises, determine whether the...Ch. 4.1 - For the following exercises, determine whether the...Ch. 4.1 - For the following exercises, determine whether the...Ch. 4.1 - For the following exercises, determine whether the...Ch. 4.1 - For the following exercises, determine whether the...Ch. 4.1 - For the following exercises, determine whether the...Ch. 4.1 - For the following exercises, determine whether the...Ch. 4.1 - For the following exercises, determine whether...Ch. 4.1 - For the following exercises, determine whether...Ch. 4.1 - For the following exercises, determine whether...Ch. 4.1 - For the following exercises, determine whether...Ch. 4.1 - For the following exercises, determine whether...Ch. 4.1 - For the following exercises, determine whether...Ch. 4.1 - For the following exercises, determine whether...Ch. 4.1 - For the following exercises, determine whether...Ch. 4.1 - For the following exercises, determine whether...Ch. 4.1 - For the following exercises, determine whether...Ch. 4.1 - For the following exercises, find the slope of the...Ch. 4.1 - For the following exercises, find the slope of the...Ch. 4.1 - For the following exercises, find the slope of the...Ch. 4.1 - For the following exercises, find the slope of the...Ch. 4.1 - For the following exercises, find the slope of the...Ch. 4.1 - For the following exercises, given each set of...Ch. 4.1 - For the following exercises, given each set of...Ch. 4.1 - For the following exercises, given each set of...Ch. 4.1 - For the following exercises, given each set of...Ch. 4.1 - For the following exercises, given each set of...Ch. 4.1 - For the following exercises, given each set of...Ch. 4.1 - For the following exercises, given each set of...Ch. 4.1 - For the following exercises, given each set of...Ch. 4.1 - For the following exercises, determine whether the...Ch. 4.1 - For the following exercises, determine whether the...Ch. 4.1 - For the following exercises, determine whether the...Ch. 4.1 - For the following exercises, determine whether the...Ch. 4.1 - For the following exercises, find the x-and...Ch. 4.1 - For the following exercises, find the x- and...Ch. 4.1 - For the following exercises, find the x-and...Ch. 4.1 - For the following exercises, find the x-and...Ch. 4.1 - For the following exercises, find the x-and...Ch. 4.1 - For the following exercises, find the x-and...Ch. 4.1 - For the following exercises, use the descriptions...Ch. 4.1 - For the following exercises, use the descriptions...Ch. 4.1 - For the following exercises, use the descriptions...Ch. 4.1 - For the following exercises, use the descriptions...Ch. 4.1 - For the following exercises, use the descriptions...Ch. 4.1 - For the following exercises, write an equation for...Ch. 4.1 - For the following exercises, write an equation for...Ch. 4.1 - For the following exercises, write an equation for...Ch. 4.1 - For the following exercises, write an equation for...Ch. 4.1 - For the following exercises, find the slope of the...Ch. 4.1 - For the following exercises, find the slope of the...Ch. 4.1 - For the following exercises, write an equation for...Ch. 4.1 - For the following exercises, write an equation for...Ch. 4.1 - For the following exercises, write an equation for...Ch. 4.1 - For the following exercises, write an equation for...Ch. 4.1 - For the following exercises, write an equation for...Ch. 4.1 - For the following exercises, write an equation for...Ch. 4.1 - For the following exercises, match the given...Ch. 4.1 - For the following exercises, match the given...Ch. 4.1 - For the following exercises, match the given...Ch. 4.1 - For the following exercises, match the given...Ch. 4.1 - For the following exercises, match the given...Ch. 4.1 - For the following exercises, match the given...Ch. 4.1 - For the following exercises, sketch a line with...Ch. 4.1 - For the following exercises, sketch a line with...Ch. 4.1 - For the following exercises, sketch a line with...Ch. 4.1 - For the following exercises, sketch a line with...Ch. 4.1 - For the following exercises, sketch a line with...Ch. 4.1 - For the following exercises, sketch a line with...Ch. 4.1 - For the following exercises, sketch the graph of...Ch. 4.1 - For the following exercises, sketch the graph of...Ch. 4.1 - For the following exercises, sketch the graph of...Ch. 4.1 - For the following exercises, sketch the graph of...Ch. 4.1 - For the following exercises, sketch the graph of...Ch. 4.1 - For the following exercises, sketch the graph of...Ch. 4.1 - For the following exercises, sketch the graph of...Ch. 4.1 - For the following exercises, sketch the graph of...Ch. 4.1 - For the following exercises, sketch the graph of...Ch. 4.1 - For the following exercises, write the equation of...Ch. 4.1 - For the following exercises, write the equation of...Ch. 4.1 - For the following exercises, write the equation of...Ch. 4.1 - For the following exercises, write the equation of...Ch. 4.1 - For the following exercises, which of the tables...Ch. 4.1 - For the following exercises, which of the tables...Ch. 4.1 - For the following exercises, which of the tables...Ch. 4.1 - For the following exercises, which of the tables...Ch. 4.1 - For the following exercises, which of the tables...Ch. 4.1 - For the following exercises, which of the tables...Ch. 4.1 - For the following exercises, which of the tables...Ch. 4.1 - For the following exercises, which of the tables...Ch. 4.1 - For the following exercises, use a calculator or...Ch. 4.1 - For the following exercises, use a calculator or...Ch. 4.1 - For the following exercises, use a calculator or...Ch. 4.1 - For the following exercises, use a calculator or...Ch. 4.1 - For the following exercises, use a calculator or...Ch. 4.1 - For the following exercises, use a calculator or...Ch. 4.1 - For the following exercises, use a calculator or...Ch. 4.1 - For the following exercises, use a calculator or...Ch. 4.1 - Find the value ofx if a linear function goes...Ch. 4.1 - Find the value ofy if a linear function goes...Ch. 4.1 - Find the equation of the line that passes...Ch. 4.1 - Find the equation of the line that passes...Ch. 4.1 - Find the equation of the line that passes...Ch. 4.1 - Find the equation of the line parallel to the line...Ch. 4.1 - Find the equation of the line perpendicular to the...Ch. 4.1 - For the following exercises, use the functions...Ch. 4.1 - For the following exercises, use the functions...Ch. 4.1 - At noon, a barista notices that she has 20 in...Ch. 4.1 - A gym membership with two personal...Ch. 4.1 - A clothing business finds there is a...Ch. 4.1 - A phone company charges for service accordingto...Ch. 4.1 - A farmer finds there is a linear relationship...Ch. 4.1 - A city’s population in the year 1960 was...Ch. 4.1 - A town’s population has been growing linearly.In...Ch. 4.1 - Suppose that average annual income (in dollars)...Ch. 4.1 - When temperature is 0 degrees Celsius,...Ch. 4.2 - A company sells doughnuts. They incur a fixed cost...Ch. 4.2 - A city’s population has been growing linearly. In...Ch. 4.2 - Try it #3 There is a straight road leading from...Ch. 4.2 - Explain how to find the input variable in a word...Ch. 4.2 - Explain how to find the output variable in a wordp...Ch. 4.2 - Explain how to interpret the initial value in a...Ch. 4.2 - Explain how to determine the slope in a...Ch. 4.2 - Find the area of a parallelogram bounded by...Ch. 4.2 - Find the area of a triangle bounded by the...Ch. 4.2 - Find the area of a triangle bounded by the...Ch. 4.2 - Find the area of a parallelogram bounded by...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, consider this...Ch. 4.2 - For the following exercises, use the graph in...Ch. 4.2 - For the following exercises, use the graph in...Ch. 4.2 - For the following exercises, use the graph in...Ch. 4.2 - For the following exercises, use the graph in...Ch. 4.2 - For the following exercises, use the graph in...Ch. 4.2 - For the following exercises, use the graph in...Ch. 4.2 - For the following exercises, use the graph in...Ch. 4.2 - For the following exercises, use the graph in...Ch. 4.2 - For the following exercises, use the median home...Ch. 4.2 - For the following exercises, use the median home...Ch. 4.2 - NUMERIC For the following exercises, use the...Ch. 4.2 - For the following exercises, use the median home...Ch. 4.2 - For the following exercises, use the median home...Ch. 4.2 - For the following exercises, use the median home...Ch. 4.2 - In 2004, a school population was 1,001. By 2008the...Ch. 4.2 - In 2003, a town’s population was 1,431. By 2007the...Ch. 4.2 - A phone company has a monthly cellular plan where...Ch. 4.2 - A phone company has a monthly cellular data plan...Ch. 4.2 - In 1991, the moose population in a park...Ch. 4.2 - In 2003, the owl population in a park was measured...Ch. 4.2 - The Federal Helium Reserve held about 16...Ch. 4.2 - Suppose the world’s oil reserves in 2014 are 1,820...Ch. 4.2 - You are choosing between two different prepaid...Ch. 4.2 - You are choosing between two different...Ch. 4.2 - When hired at a new job selling jewelry, you...Ch. 4.2 - When hired at a new job selling electronics, you...Ch. 4.2 - When hired at a new job selling electronics, you...Ch. 4.2 - When hired at a new job selling electronics, you...Ch. 4.3 - According to the data from Table 1, what...Ch. 4.3 - Use the model we created using technology in...Ch. 4.3 - Describe what it means if there is a model...Ch. 4.3 - What is interpolation when using a linear model?Ch. 4.3 - What is extrapolation when using a linear model?Ch. 4.3 - Explain the difference between a positive and...Ch. 4.3 - Explain how to interpret the absolute value of...Ch. 4.3 - A regression was run to determine whether there...Ch. 4.3 - A regression was run to determine whether there is...Ch. 4.3 - For the following exercises, draw a scatter plot...Ch. 4.3 - For the following exercises, draw a scatter plot...Ch. 4.3 - For the following exercises, draw a scatter plot...Ch. 4.3 - For the following exercises, draw a scatter plot...Ch. 4.3 - For the following exercises, draw a scatter plot...Ch. 4.3 - For the following exercises, draw a scatter plot...Ch. 4.3 - For the following exercises, match each...Ch. 4.3 - For the following exercises, match each...Ch. 4.3 - For the following exercises, match each...Ch. 4.3 - For the following exercises, match each...Ch. 4.3 - For the following exercises, draw a best-fit line...Ch. 4.3 - For the following exercises, draw a best-fit line...Ch. 4.3 - For the following exercises, draw a best-fit line...Ch. 4.3 - For the following exercises, draw a best-fit line...Ch. 4.3 - The U.S. Census tracks the percentage of persons...Ch. 4.3 - The US. import of wine (in hectoliters) for...Ch. 4.3 - Table 6 shows the year and the number ofpeople...Ch. 4.3 - For the following exercises, use each set of data...Ch. 4.3 - For the following exercises, use each set of data...Ch. 4.3 - For the following exercises, use each set of data...Ch. 4.3 - For the following exercises, use each set of data...Ch. 4.3 - For the following exercises, use each set of data...Ch. 4.3 - For the following exercises, use each set of data...Ch. 4.3 - For the following exercises, use each set of data...Ch. 4.3 - Graph f(x)=0.5x+10. Pick a set of 5 orderedpairs...Ch. 4.3 - Graph f(x)=2x10. Picka set of5 ordered pairs using...Ch. 4.3 - For the following exercises, consider this...Ch. 4.3 - For the following exercises, consider this...Ch. 4.3 - For the following exercises, consider this...Ch. 4.3 - For the following exercises, consider this...Ch. 4.3 - For the following exercises, consider this...Ch. 4.3 - For the following exercises, consider this...Ch. 4.3 - For the following exercises, consider this...Ch. 4.3 - For the following exercises, consider this...Ch. 4.3 - For the following exercises, consider this...Ch. 4 - Determine whether the algebraic equation is...Ch. 4 - Determine whether the algebraic equation is...Ch. 4 - Determine whether the function is increasing...Ch. 4 - Determine whether the function is increasing...Ch. 4 - Given each set of information, find a linear...Ch. 4 - Given each set of information, find a linear...Ch. 4 - Find the slope of the line shown in the graph.Ch. 4 - Find the slope of the line shown in the graph.Ch. 4 - Write an equation in slope-intercept form for the...Ch. 4 - Does the following table represent a linear...Ch. 4 - Does the following table represent a linear...Ch. 4 - On June 1st, a company has $4,000,000 profit.If...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, find the x-and...Ch. 4 - For the following exercises, find the x-and...Ch. 4 - For the following exercises, use the descriptions...Ch. 4 - For the following exercises, use the descriptions...Ch. 4 - For the following exercises, use the descriptions...Ch. 4 - For the following exercises, use the descriptions...Ch. 4 - For the following exercises, use the descriptions...Ch. 4 - For the following exercises, use the descriptions...Ch. 4 - For the following exercises, use the descriptions...Ch. 4 - Find the area of a triangle bounded by the y-axis,...Ch. 4 - A town’s population increases at a constant rate....Ch. 4 - The number of people afflicted with the common...Ch. 4 - For the following exercises, use the graph in...Ch. 4 - For the following exercises, use the graph in...Ch. 4 - For the following exercise, consider this...Ch. 4 - For the following exercises, consider this...Ch. 4 - For the following exercises, consider this...Ch. 4 - For the following exercises, consider this...Ch. 4 - For the following exercises, consider this...Ch. 4 - Draw a scatter plot for the data in Table 2. Then...Ch. 4 - Draw a scatter plot for the data in Table 3. If we...Ch. 4 - Eight students were asked to estimate their score...Ch. 4 - Draw a best-fit line for the plotted data.Ch. 4 - For the following exercises, consider the data in...Ch. 4 - For the following exercises, consider the data in...Ch. 4 - For the following exercises, consider the data in...Ch. 4 - For the following exercises, consider the data in...Ch. 4 - For the following exercises, consider this...Ch. 4 - For the following exercises, consider this...Ch. 4 - For the following exercises, consider this...Ch. 4 - For the following exercises, consider this...Ch. 4 - Determine whether the following algebraic...Ch. 4 - Determine whether the following function...Ch. 4 - Determine whether the following function...Ch. 4 - Given the following set of information, find a...Ch. 4 - Given the following set of information. find a...Ch. 4 - Find the slope ofthe line in Figure l.Ch. 4 - Write an equation for line in Figure 2.Ch. 4 - Does Table 1 represent a linear function? If so,...Ch. 4 - Does Table 2 represent a linear function? If so,...Ch. 4 - At 6 am, an online company has sold 120 items that...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, use the graph in...Ch. 4 - For the following exercises, use the graph in...Ch. 4 - For the following exercises, use the graph in...Ch. 4 - For the following exercises, use the graph in...Ch. 4 - For the following exercises, use the graph in...Ch. 4 - For the following exercises, use Table 4 which...Ch. 4 - For the following exercises, use Table 4 which...Ch. 4 - For the following exercises, use Table 4 which...Ch. 4 - For the following exercises, consider this...Ch. 4 - For the following exercises, consider this...Ch. 4 - For the following exercises, consider this...
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