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mathematics
college algebra
College Algebra 12th edition Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels - Solutions
The graph depicts the distance y that a person driving a car on a straight road is from home after x hours. Interpret the graph. At what speeds did the car travel?Distance from Home 70 60 50 40 30 20 10 1 2 5 6. Time (in hours) Distance (in miles)
For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation.y = x3
Graph the line passing through the given point and having the indicated slope. Plot two points on the line.Through (-1, 3), m = 3/2
Determine whether each function is even, odd, or neither.ƒ(x) = x3 - x + 9
Write an equation (a) in standard form and (b) in slope-intercept form for each line described.Through (-5, 6), perpendicular to x = -2
Let ƒ(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find each of the following. Simplify if necessary.g (-1/4)
The figure shows the number of jobs gained or lost in a recent period from September to May.(a) Is this the graph of a function?(b) In what month were the most jobs lost? the most gained?(c) What was the largest number of jobs lost? of jobs gained?(d) Do these data show an upward or a downward
For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation.y = -x3
Graph the line passing through the given point and having the indicated slope. Plot two points on the line.Through (-2, 8), m = 2/5
Determine whether each function is even, odd, or neither.ƒ(x) = x4 - 5x + 8
Write an equation (a) in standard form and (b) in slope-intercept form for each line described.Through (4, -4), perpendicular to x = 4
Find the center-radius form of the circle described or graphed.A circle having a diameter with endpoints (-1, 2) and (11, 7)
Let ƒ(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find each of the following. Simplify if necessary.ƒ (p)
The percent of tax returns filed electronically in 2001 was 30.7%. In 2013, the figure was 82.9%. (a) Use the information given for the years 2001 and 2013, letting x = 0 represent 2001, x = 12 represent 2013, and y represent the percent of returns filed electronically, to find a linear
Answer the following.If a vertical line is drawn through the point (4, 3), at what point will it intersect the x-axis?
Graph the line passing through the given point and having the indicated slope. Plot two points on the line.Through (3, -4), m = -1/3
Work each problem.Find k so that the line through (4, -1) and (k, 2) is(a) Parallel to 3y + 2x = 6 (b) Perpendicular to 2y - 5x = 1.
Find the center-radius form of the circle described or graphed.A circle having a diameter with endpoints (5, 4) and (-3, -2)
Let ƒ(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find each of the following. Simplify if necessary.g (k)
In 1980 the median family income in the United States was about $21,000 per year. In 2013 it was about $63,800 per year. Find the average annual rate of change of median family income to the nearest dollar over that period.
Answer the following.If a horizontal line is drawn through the point (4, 3), at what point will it intersect the y-axis?
Find r so that the line through (2, 6) and (-4, r) is(a) Parallel to 2x - 3y = 4 (b) Perpendicular to x + 2y = 1.
Find the center-radius form of the circle described or graphed. (1, 4) (5, 1)
Let ƒ(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find each of the following. Simplify if necessary.f (-x)
For each line described, write an equation in (a) slope-intercept form, if possible, and (b) standard form.Through (3, -5) with slope -2
Graph the line passing through the given point and having the indicated slope. Plot two points on the line.Through (- 1/2, 4), m = 0
Solve each problem.Refer to the table that accompanies Figure 49 in.Figure 49 (a) Use the data points (0, 6312) and (3, 7703) to find a linear equation that models the data.(b) Use the equation from part (a) to estimate average tuition and fees for in-state students at public four-year
Find the center-radius form of the circle described or graphed. (-3, 10) х (5, -5)
Let ƒ(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find each of the following. Simplify if necessary.g (-x)
For each line described, write an equation in (a) slope-intercept form, if possible, and (b) standard form.Through (-2, 4) and (1, 3)
Answer the following.Show that the points (-2, 2), (13, 10), (21, -5), and (6, -13) are the vertices of a rhombus (all sides equal in length).
Graph the line passing through the given point and having the indicated slope. Plot two points on the line.Through (3/2, 2), m = 0
Refer to the table that accompanies Figure 49 in.Figure 49.(a) Use the data points for the years 2009 and 2011 to find a linear equation that models the data.(b) Use the equation from part (a) to estimate average tuition and fees for in-state students at public four-year colleges in 2013. How does
The table lists average annual cost (in dollars) of tuition and fees at private four-year colleges for selected years.(a) Determine a linear function ƒ(x) = ax + b that models the data, where x = 0 represents 2009, x = 1 represents 2010, and so on. Use the points (0, 22,036) and (4, 24,525) to
Let ƒ(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find each of the following. Simplify if necessary.f (x + 2)
For each line described, write an equation in (a) slope-intercept form, if possible, and (b) standard form.Through (2, -1), parallel to 3x - y = 1
Answer the following.Are the points A(1, 1), B(5, 2), C(3, 4), and D(-1, 3) the vertices of a parallelogram (opposite sides equal in length)? of a rhombus (all sides equal in length)?
Give a rule for each piecewise-defined function. Also give the domain and range. y 2 -2 2.
Find the coordinates of the other endpoint of each line segment, given its midpoint and one endpoint.Midpoint (-9, 8), endpoint (-16, 9)
Decide whether or not each equation has a circle as its graph. If it does, give the center and radius. If it does not, describe the graph.4x2 + 4y2 + 4x - 4y - 7 = 0
Decide whether each relation defines y as a function of x. Give the domain and range.y = -6x + 4
If a walkway rises 2.5 ft for every 10 ft on the horizontal, which of the following express its slope (or grade)? (There are several correct choices.)A. 0.25 B. 4 C. 2.5/10D. 25%E. 1/4F. 10/2.5G. 400% H. 2.5%
Use the table in Exercise 37 to complete the following table.Exercise 37 (f + 8)(x) (f – 8)(*) (fg)(x) ()(*) | -2 f(x) g(x) -2 5 -2 4 10
Plot each point, and then plot the points that are symmetric to the given point with respect to the (a) x-axis, (b) y-axis, and (c) origin.(5, -3)
Give a rule for each piecewise-defined function. Also give the domain and range. y (2, 2) + T0 + -2 -1 2 A-1,-1)F-2
Find the coordinates of the other endpoint of each line segment, given its midpoint and one endpoint.Midpoint (a, b), endpoint (p, q)
Solve each problem. To visualize the situation, use graph paper and a compass to carefully graph each circle.Suppose that receiving stations X, Y, and Z are located on a coordinate plane at the points (7, 4), (-9, -4), and (-3, 9), respectively. The epicenter of an earthquake is determined to be 5
Decide whether each relation defines y as a function of x. Give the domain and range.x + y < 3
If the pitch of a roof is 1/4, how many feet in the horizontal direction correspond to a rise of 4 ft?
Plot each point, and then plot the points that are symmetric to the given point with respect to the (a) x-axis, (b) y-axis, and (c) origin.(-6, 1)
Find the slope and y-intercept of each line, and graph it.2y = x
Give a rule for each piecewise-defined function. Also give the domain and range. y +(1, 1) (4, 2) 0. 2 4 -2 -4 -2 (-3, –3) + 2.
Find the coordinates of the other endpoint of each line segment, given its midpoint and one endpoint.Midpoint (6a, 6b), endpoint (3a, 5b)
Decide whether each relation defines y as a function of x. Give the domain and range.x - y < 4
Find the slope of the line satisfying the given conditions.Through (2, -1) and (-3, -3)
How is the difference quotient related to slope?
Plot each point, and then plot the points that are symmetric to the given point with respect to the (a) x-axis, (b) y-axis, and (c) origin.(-4, -2)
Graph each equation.ƒ(x) = x
Give a rule for each piecewise-defined function. Also give the domain and range. (2, 3) 3 (1, 2) -8 -6 -4 -2 2 (-1, –1)F-2 (-8, –2)
Solve each problem.The graph shows a straight line that approximates the percentage of Americans 25 years and older who had earned bachelor’s degrees or higher for the years 1990–2012. Use the midpoint formula and the two given points to estimate the percent in 2001. Compare the answer with the
Decide whether each relation defines y as a function of x. Give the domain and range.y = √x
Find the slope of the line satisfying the given conditions.Through (-3, 4) and (2, -8)
Refer to Figure 93. How is the secant line PQ related to the tangent line to a curve at point P?Figure 93. y y = f(x), Secant line Q (x + h, f(x +h)) P(x,f(x)) х
Find the slope and y-intercept of each line, and graph it.x + 3y = -9
Plot each point, and then plot the points that are symmetric to the given point with respect to the (a) x-axis, (b) y-axis, and (c) origin.(-8, 0)
Graph each equation.x - 4y = 8
Give a rule for each piecewise-defined function. Also give the domain and range. A (2, 3) ; 3 ++++ х 10 2 3 4 (1, –1) -4 -3 -2 -1 -3 -4
Solve each problem. To visualize the situation, use graph paper and a compass to carefully graph each circle.The locations of three receiving stations and the distances to the epicenter of an earthquake are contained in the following three equations: (x - 2)2 + (y - 4)2 = 25, (x - 1)2 + (y + 3)2 =
The graph shows a straight line that approximates national advertising revenue, in millions of dollars, for newspapers in the United States for the years 2006–2012. Use the midpoint formula and the two given points to estimate revenue in 2009. Compare the answer with the actual figure of 4424
Decide whether each relation defines y as a function of x. Give the domain and range.y = -√x
Find the slope of the line satisfying the given conditions.Through (5, 8) and (3, 12)
The graph of y = |x - 2| is symmetric with respect to a vertical line. What is the equation of that line?
Find the slope and y-intercept of each line, and graph it. 3 y=x-1=0 2
Graph each function. Give the domain and range.ƒ(x) = [[-x]]
Work each of the following.Find the center-radius form of the equation of a circle with center (3, 2) and tangent to the x-axis.
The table lists how poverty level income cutoffs (in dollars) for a family of four have changed over time. Use the midpoint formula to approximate the poverty level cutoff in 2012 to the nearest dollar.Year.................................. Income (in
Decide whether each relation defines y as a function of x. Give the domain and range.xy = 2
Decide whether each relation defines y as a function of x. Give the domain and range.xy = -6
Find the slope of the line satisfying the given conditions.Through (5, -3) and (1, -7)
For each function, find (a) ƒ(x + h),(b) ƒ(x + h) - ƒ(x), and (c) ƒ(x + h) - ƒ(x)/h.ƒ(x) = 1 - x
Repeat Exercise 43 for the graph of y = - |x + 1|.Exercise 43The graph of y = |x - 2| is symmetric with respect to a vertical line. What is the equation of that line?
The table represents a linear function ƒ.(a) Find the slope of the graph of y = ƒ(x).(b) Find the y-intercept of the line.(c) Write an equation for this line in slope-intercept form.x.................... y-2................ -11-1................. -80.................. -51..................
Graph each equation.ƒ(x) = 3
Graph each function. Give the domain and range.ƒ(x) = - [[x]]
Work each of the following.Find the equation of a circle with center at (-4, 3), passing through the point (5, 8). Write it in center-radius form.
Enrollments in public colleges for recent years are shown in the table. Assuming a linear relationship, estimate the enrollments for (a) 2003 and (b) 2009. Give answers to the nearest tenth of thousands if applicable.Year....................... Enrollment (in
Decide whether each relation defines y as a function of x. Give the domain and range.y = √4x + 1
Show that if M is the midpoint of the line segment with endpoints P(x1, y1) and Q(x2, y2), thend(P, M) + d(M, Q) = d(P, Q) and d(P, M) = d(M, Q).
Find the slope of the line satisfying the given conditions.Through (5, 9) and (-2, 9)
For each function, find (a) ƒ(x + h),(b) ƒ(x + h) - ƒ(x), and (c) ƒ(x + h) - ƒ(x)/h.ƒ(x) = 6x + 2
The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an equation that defines ƒ. :3 -3
Without graphing, determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.y = x2 + 5
Graph each equation.y + 2 = 0
Graph each function. Give the domain and range.ƒ(x) = [[2x]]
Work each of the following.Find all points (x, y) with x = y that are 4 units from (1, 3).
Decide whether each relation defines y as a function of x. Give the domain and range.y = √7 - 2x
Write the distance formulausing a rational exponent. d = V(x2 - x1)? + (y2 – Y1)²
Find the slope of the line satisfying the given conditions.Through (-2, 4) and (6, 4)
For each function, find (a) ƒ(x + h),(b) ƒ(x + h) - ƒ(x), and (c) ƒ(x + h) - ƒ(x)/h.ƒ(x) = 4x + 11
Without graphing, determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.y = 2x4 - 3
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