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Intermediate Algebra 13th Edition Margaret Lial, John Hornsby, Terry McGinnis - Solutions

Find the length and width of a rectangular room whose perimeter is 50 m and whose area is 100 m2. L P = 50 m A = 100 m² W
A company has determined that the cost y to make x (thousand) computer tablets isand that the revenue y from the sale of x (thousand) tablets isFind the break-even point, where cost equals revenue. y = 4x² + 36x + 20,
Graph each ellipse. x² 49 + y² 81 = 1
A lithotripter is a machine used to crush kidney stones using shock waves. The patient is in an elliptical tub with the kidney stone at one focus of the ellipse. Each beam is projected from the other focus to the tub so that it reflects to hit the kidney stone. See the figure.Rework Exercise 55 if
A company has found that the price p (in dollars) of its scientific calculator is related to the supply x (in thousands) by the equationThe price is related to the demand x (in thousands) for the calculator by the equationThe equilibrium price is the value of p where demand equals supply. Find the
Graph each ellipse. y2 25 1- 49
Match each system of inequalities in Column I with the quadrant that represents its graph in Column II. (a) x < 0 y > 0 (c) x < 0 y < 0 (b) x > 0 y < 0 (d) x > 0 y > 0 II A. Quadrant I B. Quadrant II C. Quadrant III D. Quadrant IV
Graph each ellipse. (x + 1)² (y-2)² + 64 49 1
Graph each ellipse. (x-4)² (y + 2)² + 9 4 = 1
Graph each ellipse. 9 = 1 16
Graph each ellipse. (x - 2)² 16 + (y-1)² 9 1
A lithotripter is a machine used to crush kidney stones using shock waves. The patient is in an elliptical tub with the kidney stone at one focus of the ellipse. Each beam is projected from the other focus to the tub so that it reflects to hit the kidney stone. See the figure.Suppose a lithotripter
Graph each ellipse. (x+3)² (y + 2)² + 25 36 = 1
An arch has the shape of half an ellipse. The equation of the ellipse, where x and y are in meters, is(a) How high is the center of the arch?(b) How wide is the arch across the bottom? 100x² + 324y² = 32,400.
Work each of the following.(a) The Roman Colosseum is an ellipse with a = 310 ft and b = 513/2 ft. Find the distance, to the nearest tenth, between the foci of this ellipse.(b) The approximate perimeter of an ellipse is given bywhere a and b are the lengths given in part (a). Use this formula to
A one-way street passes under an overpass, which is in the form of the top half of an ellipse, as shown in the figure. Suppose that a truck 12 ft wide passes directly under the overpass. What is the maximum possible height of this truck? 15 ft 20 ft Not to scale
A satellite is in an elliptical orbit around Earth with least distance (perigee) of 160 km and greatest distance (apogee) of 16,000 km. Earth is located at a focus of the elliptical orbit. See the figure. Find the equation of the ellipse. Use the fact that c2 = a2 - b2 here. Perigee 160
Match each equation with the correct graph. A. C. # y H 3 y 0 X X B. D. y 0 #
Without actually plotting points, match each function defined by the absolute value expression with its graph. A. C. ⠀⠀⠀ ⠀⠀⠀⠀ .......... ⠀⠀ ..... . LULL... a .... 2. ........ ...... : X B. D. -02 X
Solve. |2p - 5 > 15
Match each equation with the correct graph. A. C. # y H 3 y 0 X X B. D. y 0 #
Graph each hyperbola. x² 25 9 y² || 1
Evaluate each expression. [-4.75]
Graph. 1 VI
Without actually plotting points, match each function defined by the absolute value expression with its graph. A. C. ⠀⠀⠀ ⠀⠀⠀⠀ .......... ⠀⠀ ..... . LULL... a .... 2. ........ ...... : X B. D. -02 X
Which one of the following is a description of the graph of the solution set of the following system?A. All points outside the circle x2 + y2 = 25 and above the line y = -2B. All points outside the circle x2 + y2 = 25 and below the line y = -2C. All points inside the circle x2 + y2 = 25 and above
Evaluate each expression. [-21]
Graph each hyperbola. x² 16 y2 9 = 1 ||
Which one of the following equations is represented by the graph of a circle?For the equation that is represented by a circle, what are the coordinates of the center? What is the radius? A. x² + y² = 0 C. x² + y² = x² - y² B. x² + y² = -1 D. x² + y² = 1
Solve. |5x|– 6 =14
Suppose that a nonlinear system is composed of equations whose graphs are those described, and the number of points of intersection of the two graphs is as given. Make a sketch satisfying these conditions. (There may be more than one way to do this.)A line and an ellipse; no points
Graph. x² + y² = 25
Find the center and radius of the circle with equation x2 + y2 + 8x - 2y = 8.
Refer to the basic graphs in A–F to answer each of the following.Which is the graph of ƒ(x) = 1/x ? The lines with equations x = 0 and y = 0 are called its ___________. A. D. 32 A 123 12 X X B. E. 2 ++ -2 A 111 +12 X C. F. 4 X +
Suppose that a nonlinear system is composed of equations whose graphs are those described, and the number of points of intersection of the two graphs is as given. Make a sketch satisfying these conditions. (There may be more than one way to do this.)A line and a hyperbola; one point
A student incorrectly described the graph of the functionas a circle centered at the origin with radius 7. Give the correct description of the graph. f(x) = √49 - x²
Solve. -4x + 7 = 6x + 1
Evaluate each expression. 3 2- 4
Complete each statement. Choices may be used once, more than once, or not at all.The equationrepresents a(n)______ with centerand______ equal to 2. circle foci parabolas center radius ellipse intercepts conic sections
Graph. f(x) = √4-x
Solve. 4- (2x + 3) + x = 5x - 3
Find the center and radius of the circle with equation (x - 2)2 + (y + 3)2 = 16. Sketch the graph.
Refer to the basic graphs in A–F to answer each of the following.Which is not the graph of a function? Why? A. D. 32 A 123 12 X X B. E. 2 ++ -2 A 111 +12 X C. F. 4 X +
Evaluate each expression. [12]
Write a system of inequalities for the indicated region.Quadrant II, not including the x-axis but including the y-axis
A student incorrectly described the graph of the equationas a vertical hyperbola with y-intercepts (0, -4) and (0, 4). Give the correct description of the graph. x²y² 9 16 1
Complete the following: The graph of a circle (is / is not) the graph of a function because it fails the conditions of the______ . The graph of an ellipse (is / is not) the graph of a function.
Graph. x²-9y² = 9
Suppose that a nonlinear system is composed of equations whose graphs are those described, and the number of points of intersection of the two graphs is as given. Make a sketch satisfying these conditions. (There may be more than one way to do this.)A line and a circle; one point
Based on the discussions of ellipses in the previous section and of hyperbolas in this section, match each equation with its graph. A. C. 19: 0 3 X X B. D. -3-0 X
Each sketch represents the graphs of a pair of equations in a system. How many ordered pairs of real numbers are in each solution set? y 0 >Х
Match each function in parts (a) – (d) with its graph from choices A–D. (a) f(x) = Vx -2 (b) f(x) = Vx + 2 (c) f(x) = Vx + 2 (d) f(x) = Vx - 2 A. C. -2 十吐2 |||| B. D. -2 2 >
Graph ƒ(x) =|x - 3| + 4. Give the domain and range.
Graph. x² +9y² = 9
Write a system of inequalities for the indicated region.Quadrant III, including the x-axis but not including the y-axis
Consider the circle whose equation is x2 + y2 = 25.(a) What are the coordinates of its center? (b) What is its radius?(c) Sketch its graph.
Refer to the basic graphs in A–F to answer each of the following.Which is the graph ofGive the domain and range. A. D. 32 A 123 12 X X B. E. 2 ++ -2 A 111 +12 X C. F. 4 X +
Refer to the basic graphs in A–F to answer each of the following.Which is the graph of ƒ(x) = √x ? Give the domain and range. A. D. 32 A 123 12 X X B. E. 2 ++ -2 A 111 +12 X C. F. 4 X +
Evaluate. (a) 6² (b)-6² (c) (-6)² (d) V36 (e) - V/36 (f) V-36
Suppose that a nonlinear system is composed of equations whose graphs are those described, and the number of points of intersection of the two graphs is as given. Make a sketch satisfying these conditions. (There may be more than one way to do this.)A line and a circle; no points
Complete each statement. Choices may be used once, more than once, or not at all.A set of all points in a plane the sum of whose distances from two fixed points is constant is a(n)______ . The fixed points are the _______. circle foci parabolas center radius ellipse intercepts conic sections
Each sketch represents the graphs of a pair of equations in a system. How many ordered pairs of real numbers are in each solution set? y ( X
Based on the discussions of ellipses in the previous section and of hyperbolas in this section, match each equation with its graph. A. C. 19: 0 3 X X B. D. -3-0 X
Match each number in Column I with the set (or sets) of numbers in Column II to which the number belongs. (a) 1 (c) 2/3 (e) - V49 I (b) 0 (d) TT (f) 2.75 A. Natural numbers C. Integers E. Irrational numbers II B. Whole numbers D. Rational numbers F. Real numbers
Graph each function. Give the domain and range. f(x) = 1 x - 4
Write a system of inequalities for the indicated region.Quadrant IV, not including the x- and y-axes
Each sketch represents the graphs of a pair of equations in a system. How many ordered pairs of real numbers are in each solution set? X 0 K
Match each system of inequalities in parts (a)–(d) with its graph in choices A–D. (a) x>-2 y≤2 A. C. LI ~ loi lai o O 1 N toi -2.. 1 (b) x < -2 y = 2 X -X (c) x ≥ 2 B. D. y -2
Simplify -|-1| - 5 + |4 - 10.
Write a system of inequalities for the indicated region. Quadrant I, including the x- and y-axes
Fill in each blank with the correct response.The range of ƒ(x) = [x], the greatest integer function, is _________.
Refer to the basic graphs in A–F to answer each of the following.Which is the graph of ƒ(x) = x2? Give the domain and range. A. D. 32 A 123 12 X X B. E. 2 ++ -2 A 111 +12 X C. F. 4 X +
Based on the discussions of ellipses in the previous section and of hyperbolas in this section, match each equation with its graph. A. C. 19: 0 3 X X B. D. -3-0 X
Complete each statement. Choices may be used once, more than once, or not at all.A set of all points in a plane that lie a fixed distance from a fixed point is a(n) _______. The fixed distance is the_______ and the fixed point is the_______ .
Graph each function. Give the domain and range. f(x)=√x +3
Each sketch represents the graphs of a pair of equations in a system. How many ordered pairs of real numbers are in each solution set? y 0 a X
Match each inequality in parts (a)–(d) with its graph in choices A–D. (a) y = x² + 4 A. C. 0. FH A V O A N ........ N (b) y ≤ x² + 4 (c) y < x² + 4 B. D. V O N V X X (d) y > x² + 4
Find the center and radius of the circle with equation. x² + y² + 4x 10y - 7 = 0.
Refer to the basic graphs in A–F to answer each of the following.Which is the graph of ƒ(x) = |x| ? The lowest point on its graph has coordinates (______ , ________). A. D. 32 A 123 12 X X B. E. 2 ++ -2 A 111 +12 X C. F. 4 X +
Fill in each blank with the correct response.The range of the square root function ƒ(x) = √x is_______ .
Complete each statement. Choices may be used once, more than once, or not at all.When a plane intersects an infinite cone at different angles_______, such as________ , circles, ellipses, and hyperbolas result. circle foci parabolas center radius ellipse intercepts conic sections
True or false: The graph of y = -√1 - x2 is the graph of a function.
To see how exponential and logarithmic functions are related.Describe the symmetry between the graphs in Exercises 107 and 108.Data from in Exercises 107Complete the table of values, and sketch the graph of y = 10x. Give the domain and range of the function. Exercises 108Complete the table of
Graph each function. Give the domain and range. f(x) = x + 4|
To see how exponential and logarithmic functions are related.Complete the table of values, and sketch the graph of y = 10x. Give the domain and range of the function. X -2 -1 0 1 2 у
The population of deer (in thousands) in a certain area is approximated by the logarithmic functionwhere x is the number of years since 2017. During what year is the population expected to be 4 thousand deer? f(x) = logs (100x - 75),
To see how exponential and logarithmic functions are related.What can we conclude about the functions y = f(x) = 10x and y = g(x) = log10 x?
Fill in each blank with the correct response.For the reciprocal function defined by ƒ(x) = 1/x _________, is the only real number not in the domain.
To see how exponential and logarithmic functions are related.Complete the table of values, and sketch the graph of y = log10 x. Give the domain and range of the function. X 1 100 1 10 1 10 100 y II H
Sales (in thousands of units) of a new product are approximated by the logarithmic functionwhere t is the number of years after the product is introduced.(a) What were the sales, to the nearest unit, after 1 yr?(b) What were the sales, to the nearest unit, after 13 yr?(c) Graph y = S(t). S(t) = 100
A study showed that the number of mice in an old abandoned house was approximated by the logarithmic functionwhere t is measured in months and t = 0 corresponds to January 2018. Find the number of mice in the house for each month.(a) January 2018 (b) July 2018 (c) July 2020 (d) Graph y = M(t).
An online sales company finds that its sales (in millions of dollars) are approximated by the logarithmic functionwhere x is the number of advertisements placed on a popular website. How many advertisements must be placed to earn sales of $4 million? S(x) = log₂ (3x + 1),
Write 1/100 as a decimal and as a percent.
Why is loga a = 1 true for any value of a that is allowed as the base of a logarithm?
Why is loga 1 = 0 true for any value of a that is allowed as the base of a logarithm? Use a rule of exponents introduced earlier in the explanation.
Previously, we solved an equation such as 5x = 125 as follows.Solution set: {3}The method described in this section can also be used to solve this equation. Work Exercises in order, to see how this is done.Write the equation so that x is alone on the left. 5x 5 = 125 5 = 53 X x = 3
Use the graph at the right to predict the value of ƒ(t) for the given value of t.t = 60 f(t) 24 16 80 0 5... ⠀⠀ H CO .... LO THE ....60 -t
Use the graph at the right to predict the value of ƒ(t) for the given value of t.t = 10 f(t) 24 16 80 0 5... ⠀⠀ H CO .... LO THE ....60 -t
Graph each logarithmic function. f(x) = log1/5 x
Use the graph at the right to predict the value of ƒ(t) for the given value of t.t = 0 f(t) 24 16 80 0 5... ⠀⠀ H CO .... LO THE ....60 -t

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