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college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

In Exercises 133–140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 5².5-2 > 25.2-5
In Exercises 84–88, find each product.(a - b)(a2 + ab + b2)
In Exercises 85–96, simplify each algebraic expression.2(5x - 1) + 14x
In Exercises 133–140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 8 × 1030 4 x 10-5 || 2 x 1025
In Exercises 65–92, factor completely, or state that the polynomial is prime.x2 y - 16y + 32 - 2x2
Explain how to simplify a rational expression.
In Exercises 137–138, fill in each box to make the statement true. Xx = 5x7
In Exercises 133–140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 534.7 5.347 = × 10³ x
Place the correct symbol, > or <, in the shaded area between the given numbers. Do not use a calculator. Then check your result with a calculator. a. 32 33 b. √7 + V18 V7 + 18
Explain how to multiply rational expressions.
In Exercises 138–141, factor completely (x − 5)¯7²/(x + 5)¯ - IN - (x + 5)²(x - 5)
Exercises 145–147 will help you prepare for the material covered.a.b.c.Based on your answers to parts (a) and (b), what can you conclude? Find V16. √4.
In Exercises 133–140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. (4 × 10³) + (3 x 10²) = 4.3 × 10³
In Exercises 133–140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. (7 × 105) + (2 x 10³) = 9 × 10²
In Exercises 138–141, factor completelyx2n + 6xn + 8
In Exercises 134–137, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.x2 + 36 = (x + 6)2
You can do this by using the Explaining the Concepts exercises that ask you to respond with verbal or written explanations. Speaking or writing about a new concept uses a different part of your brain
In Exercises 138–141, factor completely -x2 - 4x + 5
In Exercises 134–137, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.x3 - 64 = (x + 4)(x2 + 4x - 16)
An effective way to understand something is to explain it to someone else. You can do this by using the Explaining the Concepts exercises that ask you to respond with verbal or written explanations.
In Exercises 138–141, factor completelyx4 - y4 - 2x3 y + 2xy3
Exercises 144–146 will help you prepare for the material covered.Factor the numerator and the denominator. Then simplify by dividing out the common factor in the numerator and the denominator. x2 +
An effective way to understand something is to explain it to someone else. You can do this by using the Explaining the Concepts exercises that ask you to respond with verbal or written explanations.
The mad Dr. Frankenstein has gathered enough bits and pieces (so to speak) for 2-1 + 2-2 of his creature-to-be. Write a fraction that represents the amount of his creature that must still be obtained.
An effective way to understand something is to explain it to someone else. You can do this by using the Explaining the Concepts exercises that ask you to respond with verbal or written explanations.
Exercises 144–146 will help you prepare for the material covered in the next section.In Exercises 145–146, perform the indicated operation. Where possible, reduce the answer to its lowest terms.
Exercises 144–146 will help you prepare for the material covered in the next section.In Exercises 145–146, perform the indicated operation. Where possible, reduce the answer to its lowest terms.
An effective way to understand something is to explain it to someone else. You can do this by using the Explaining the Concepts exercises that ask you to respond with verbal or written explanations.
Our hearts beat approximately 70 times per minute. Express in scientific notation how many times the heart beats over a lifetime of 80 years. Round the decimal factor in your scientific notation
Exercises 145–147 will help you prepare for the material covered in the next section.a. Use a calculator to approximate √300 to two decimal places.b. Use a calculator to approximate 10√3
In Exercises 142–143, find all integers b so that the trinomial can be factored.x2 + bx + 15
Exercises 142–144 will help you prepare for the material covered in the next section.Use the distributive property to multiply: 2x4(8x4 + 3x).
An effective way to understand something is to explain it to someone else. You can do this by using the Explaining the Concepts exercises that ask you to respond with verbal or written explanations.
Exercises 142–144 will help you prepare for the material covered.Multiply: (2x3y2)(5x4y7).
Exercises 142–144 will help you prepare for the material covered.Simplify and express the answer in descending powers of x:2x(x2 + 4x + 5) + 3(x2 + 4x + 5).
An effective way to understand something is to explain it to someone else. You can do this by using the Explaining the Concepts exercises that ask you to respond with verbal or written explanations.
Exercises 159–161 will help you prepare for the material covered.In parts (a) and (b), complete each statement. a. b7 b3 b. 68 6² b·b·b·b·b·b·b b·b·b =
A large number can be put into perspective by comparing it with another number. For example, we put the $18.9 trillion national debt in perspective by comparing this number to the number of U.S.
In Exercises 144–147, determine whether each statement makes sense or does not make sense, and explain your reasoning.My mathematical model describes the data for tuition and fees at public
In Exercises 156–158, insert either in the shaded area between the numbers to make the statement true. 3.14 2 TT 2
In Exercises 156–158, insert either in the shaded area between the numbers to make the statement true. √2 1.5
Exercises 145–147 will help you prepare for the material covered in the next section.a. Simplify: 21x + 10x.b. Simplify: 21√2 + 10√2.
In Exercises 144–147, determine whether each statement makes sense or does not make sense, and explain your reasoning.A model that describes the average cost of tuition and fees at private U.S.
In Exercises 156–158, insert either in the shaded area between the numbers to make the statement true. ルー -3.5
In Exercises 144–147, determine whether each statement makes sense or does not make sense, and explain your reasoning.Just as the commutative properties change groupings, the associative properties
Exercises 159–161 will help you prepare for the material covered.In parts (a) and (b), complete each statement. a. b4. b³ = (b·b·b·b)(b·b·b) = b? b. b5 b5 = (b.b·b·b·b)(b·b·b·b·b) =
In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.Every rational number is an integer.
In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.Some whole numbers are not integers.
In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.Some rational numbers are not positive.
In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.Irrational numbers cannot be negative.
In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The term x has no coefficient.
In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.5 + 3(x - 4) = 8(x - 4) = 8x - 32
In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.-x - x = -x + (-x) = 0
In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.x - 0.02(x + 200) = 0.98x - 4
Exercises 159–161 will help you prepare for the material covered in the next section.If 6.2 is multiplied by 103, what does this multiplication do to the decimal point in 6.2?
In Exercises 88–89, write each equation as a quadratic equation in y and then use the quadratic formula to express y in terms of x. Graph the resulting two equations using a graphing utility. What
Use a graphing utility to graph any five of the parabolas that you graphed by hand in Exercises 5–16.Data from exercise 5-165.6.7.8.9. x = -44.Y (0, 0) 자 (4,8) 104 10 x (4, -8) y = 16x
Use a graphing utility to graph any three of the parabolas that you graphed by hand in Exercises 35–42. First solve the given equation for y, possibly using the square root property.Data from
An Earth satellite has an elliptical orbit described byThe coordinates of the center of Earth are (16, 0).a. The perigee of the satellite’s orbit is the point that is nearest Earth’s center. If
Where possible, find each product.a.b. 0 0][-1 -1 0 -1
What happens to the shape of the graph of as 2 x 2 a 62 D = 1
The equation of the red ellipse in the figure shown isWrite the equation for each circle shown in the figure. 25 + 9 1.
Use a graphing utility to graph the parabolas in Exercises 86–87. Write the given equation as a quadratic equation in y and use the quadratic formula to solve for y. Enter each of the equations to
In Exercises 81–84, determine whether each statement makes sense or does not make sense, and explain your reasoning.I graphed a hyperbola centered at the origin that was symmetric with respect to
Find the standard form of the equation of an ellipse with vertices at (0, -6) and (0, 6), passing through (2, -4).
In Exercises 85–88, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.If one branch of a hyperbola is removed
Use a graphing utility to graph the parabolas in Exercises 86–87. Write the given equation as a quadratic equation in y and use the quadratic formula to solve for y. Enter each of the equations to
Solve by eliminating variables: x - бу 2x + 4y - 3z 3x-2y + 5z = -17. 29 - : -22 =
In Exercises 83–86, determine whether each statement makes sense or does not make sense, and explain your reasoning.In a whispering gallery at our science museum, I stood at one focus, my friend
Exercises 94–96 will help you prepare for the material covered.Consider the equationa. Find the x-intercepts.b. Explain why there are no y-intercepts. 2 X 16 9 = 1.
In Exercises 85–88, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.All points on the asymptotes of a
Graph the solution set of the system: 2x + y = 4 x>-3 y ≥ 1.
In Exercises 85–88, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.Two different hyperbolas can never share
In Exercises 88–89, write each equation as a quadratic equation in y and then use the quadratic formula to express y in terms of x. Graph the resulting two equations using a graphing utility. What
Exercises 94–96 will help you prepare for the material covered.Consider the equationa. Find the y-intercepts.b. Explain why there are no x-intercepts. y2 x 9 16 1.
In Exercises 85–88, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The graph of x2/9 - y2/4 = 1 does not
Find the standard form of the equation of the hyperbola with vertices (5, -6) and (5, 6), passing through (0, 9).
Consider the systema. Write the system as a matrix equation in the form AX = B.b. Solve the system using the fact that the inverse of x - y + z у+z X -2х = -2y + z = Зу -3 -6 -10.
Find the equation of a hyperbola whose asymptotes are perpendicular.
What happens to the shape of the graph of x2/a2 - y2/b2 = 1 as c/a →, where c2 = a2 + b2?
The top destinations for U.S. college students studying abroad are the United Kingdom, Italy, and Spain. The number of students studying in the U.K. exceeds the number studying in Spain by 10
The number of gallons of water, W, used when taking a shower varies directly as the time, t, in minutes, in the shower. A shower lasting 5 minutes uses 30 gallons of water. How much water is used in
In Exercises 90–93, determine whether each statement makes sense or does not make sense, and explain your reasoning.Knowing that a parabola opening to the right has a vertex at (-1, 1) gives me
Use Cramer’s Rule (determinants) to solve the system: x - y = -5 3x + 2y = 0.
Use the exponential decay model, A = A0ekt, to solve this exercise. The half-life of aspirin in your bloodstream is 12 hours. How long, to the nearest tenth of an hour, will it take for the aspirin
In Exercises 90–93, determine whether each statement makes sense or does not make sense, and explain your reasoning.I noticed that depending on the values for A and C, assuming that they are not
Exercises 94–96 will help you prepare for the material covered.Divide both sides of 4x2 - 9y2 = 36 by 36 and simplify. How does the simplified equation differ from that of an ellipse?
Exercises 95–97 will help you prepare for the material covered.In Exercises 95–96, graph each parabola with the given equation.y = x2 + 4x - 5
In Exercises 90–93, determine whether each statement makes sense or does not make sense, and explain your reasoning.I’m using a telescope in which light from distant stars is reflected to the
Exercises 104–106 will help you prepare for the material covered in the first section.Evaluate (-1)" 3n - 1 for n = 1, 2, 3, and 4.
Exercises 95–97 will help you prepare for the material covered.In Exercises 95–96, graph each parabola with the given equation.y = -3(x - 1)2 + 2
In Exercises 94–97, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The parabola whose equation is x = 2y - y2
The figure shows the graph of y = f(x) and its vertical asymptote. Use the graph to solve Exercises 1–9.Find the domain and the range of f. 200 y = f(x) -5-4-3-2-1 17 H cr |||| 2 3 4 5 T HH X
Exercises 95–97 will help you prepare for the material coveredIsolate the terms involving y on the left side of the equation:y2 + 2y + 12x - 23 = 0.Then write the equation in an equivalent form by
In Exercises 94–97, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.If the parabola whose equation is x = ay2
Find the focus and directrix of a parabola whose equation is of the form Ax2 + Ey = 0, A ≠ 0, E ≠ 0.
Write the standard form of the equation of a parabola whose points are equidistant from y = 4 and (-1, 0).
In Exercises 94–97, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.Some parabolas that open to the right have
Shown again is the table indicating the marital status of the U.S. population in 2010. Numbers in the table are expressed in millions. Use the data in the table to solve Exercises 1–10. Express
In Exercises 94–97, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The graph of x = a(y - k) + h is a

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