Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Factor the following expressions completely over the real numbers. \(x^{2}-16\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Factor the following expressions completely over the real numbers. \(x^{2}+10 x+25\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Factor the following expressions completely over the real numbers. \(81 y^{2}-4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Factor the following expressions completely over the real numbers. \(3 x^{3}-15 x^{2}+18 x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Factor the following expressions completely over the real numbers. \(16 h^{4}-81\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Factor the following expressions completely over the real numbers. \(x^{2}+2 x h+h^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Factor the following expressions completely over the real numbers. \(x^{2}+3 x-4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Factor the following expressions completely over the real numbers. \(x^{2}-3 x+4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Factor the following expressions completely over the real numbers. \(2 x^{2}-11 x+5\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Factor the following expressions completely over the real numbers. \(x^{4}+x^{2}-20\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, match the numerical model to the corresponding graphical model (aj) and algebraic model (kt). (k) \(y=x^{2}+x\) (l) \(y=40-x^{2}\) (m) y = (x + 1) (x - 1) (n) \(y=\sqrt{x-3}\) (o) y = 100 - 2x (p) y = 3x - 2 (

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, match the numerical model to the corresponding graphical model (aj) and algebraic model (kt). (k) \(y=x^{2}+x\) (l) \(y=40-x^{2}\) (m) y = (x + 1) (x - 1) (n) \(y=\sqrt{x-3}\) (o) y = 100 - 2x (p) y = 3x - 2 (

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, match the numerical model to the corresponding graphical model (aj) and algebraic model (kt). (k) \(y=x^{2}+x\) (l) \(y=40-x^{2}\) (m) y = (x + 1) (x - 1) (n) \(y=\sqrt{x-3}\) (o) y = 100 - 2x (p) y = 3x - 2 (

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, match the numerical model to the corresponding graphical model (aj) and algebraic model (kt). (k) \(y=x^{2}+x\) (l) \(y=40-x^{2}\) (m) y = (x + 1) (x - 1) (n) \(y=\sqrt{x-3}\) (o) y = 100 - 2x (p) y = 3x - 2 (

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, match the numerical model to the corresponding graphical model (aj) and algebraic model (kt). (k) \(y=x^{2}+x\) (l) \(y=40-x^{2}\) (m) y = (x + 1) (x - 1) (n) \(y=\sqrt{x-3}\) (o) y = 100 - 2x (p) y = 3x - 2 (

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, match the numerical model to the corresponding graphical model (aj) and algebraic model (kt). (k) \(y=x^{2}+x\) (l) \(y=40-x^{2}\) (m) y = (x + 1) (x - 1) (n) \(y=\sqrt{x-3}\) (o) y = 100 - 2x (p) y = 3x - 2 (q)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, match the numerical model to the corresponding graphical model (aj) and algebraic model (kt). (k) \(y=x^{2}+x\) (l) \(y=40-x^{2}\) (m) y = (x + 1) (x - 1) (n) \(y=\sqrt{x-3}\) (o) y = 100 - 2x (p) y = 3x - 2 (q)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, match the numerical model to the corresponding graphical model (aj) and algebraic model (kt). (k) \(y=x^{2}+x\) (l) \(y=40-x^{2}\) (m) y = (x + 1) (x - 1) (n) \(y=\sqrt{x-3}\) (o) y = 100 - 2x (p) y = 3x - 2 (q)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, match the numerical model to the corresponding graphical model (aj) and algebraic model (kt). (k) \(y=x^{2}+x\) (l) \(y=40-x^{2}\) (m) y = (x + 1) (x - 1) (n) \(y=\sqrt{x-3}\) (o) y = 100 - 2x (p) y = 3x - 2 (q)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 110, match the numerical model to the corresponding graphical model (aj) and algebraic model (kt). (k) \(y=x^{2}+x\) (l) \(y=40-x^{2}\) (m) y = (x + 1) (x - 1) (n) \(y=\sqrt{x-3}\) (o) y = 100 - 2x (p) y = 3x - 2 (q)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 1118 refer to the data in Table 1.6 below, showing the percentage of the female and male populations in the United States employed in the civilian work force in selected years from 1954 to 2004. (a) According to the numerical model, what has been the trend in females joining the

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 1118 refer to the data in Table 1.6 below, showing the percentage of the female and male populations in the United States employed in the civilian work force in selected years from 1954 to 2004. (a) According to the numerical model, what has been the trend in males joining the w

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 1118 refer to the data in Table 1.6 below, showing the percentage of the female and male populations in the United States employed in the civilian work force in selected years from 1954 to 2004. Model the data graphically with two scatter plots on the same graph, one showing the

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 1118 refer to the data in Table 1.6 below, showing the percentage of the female and male populations in the United States employed in the civilian work force in selected years from 1954 to 2004. Are the male percentages falling faster than the female percentages are rising, or v

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 1118 refer to the data in Table 1.6 below, showing the percentage of the female and male populations in the United States employed in the civilian work force in selected years from 1954 to 2004. Model the data algebraically with linear equations of the form y = mx + b. Write one

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 1118 refer to the data in Table 1.6 below, showing the percentage of the female and male populations in the United States employed in the civilian work force in selected years from 1954 to 2004. If the percentages continue to follow the linear models you found in Exercise 15, wh

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 1118 refer to the data in Table 1.6 below, showing the percentage of the female and male populations in the United States employed in the civilian work force in selected years from 1954 to 2004. If the percentages continue to follow the linear models you found in Exercise 15, wh

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 1118 refer to the data in Table 1.6 below, showing the percentage of the female and male populations in the United States employed in the civilian work force in selected years from 1954 to 2004. Explain why the percentages cannot continue indefinitely to follow the linear models

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Doing Arithmetic with Lists Enter the data from the Total column of Table 1.2 of Example 2 into list \(L_1\) in your calculator. Enter the data from the Female column into list \(L_2\). Check a few computations to see that the procedures in (a) and (b) cause the calculator to divide each element

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Comparing Cakes A bakery sells a \(9^{\prime \prime}\) by \(13^{\prime \prime}\) cake for the same price as an \(8^{\prime \prime}\) diameter round cake. If the round cake is twice the height of the rectangular cake, which option gives the most cake for the money?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Stepping Stones A garden shop sells \(12^{\prime \prime}\) by \(12^{\prime \prime}\) square stepping stones for the same price as \(13^{\prime \prime}\) round stones. If all of the stepping stones are the same thickness, which option gives the most rock for the money?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Free Fall of a Smoke Bomb At the Oshkosh, WI, air show, Jake Trouper drops a smoke bomb to signal the official beginning of the show. Ignoring air resistance, an object in free fall will fall d feet in t seconds, where d and t are related by the algebraic model \(d=16 t^{2}\). (a) How long

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Physics Equipment A physics student obtains the following data involving a ball rolling down an inclined plane, where t is the elapsed time in seconds and y is the distance traveled in inches. Find an algebraic model that fits the data.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
U.S. Air Travel The number of revenue passengers enplaned in the United States over the 14-year period from 1994 to 2007 is shown in Table 1.7. (a) Graph a scatter plot of the data. Let x be the number of years since 1994. (b) From 1994 to 2000 the data seem to follow a linear model.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 2528 refer to the graph below, which shows the minimum salaries in major league baseball over a recent 18-year period and the average salaries in major league baseball over the same period. Salaries are measured in dollars and time is measured after the starting year (year 0).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 2528 refer to the graph below, which shows the minimum salaries in major league baseball over a recent 18-year period and the average salaries in major league baseball over the same period. Salaries are measured in dollars and time is measured after the starting year (year 0). A

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 2528 refer to the graph below, which shows the minimum salaries in major league baseball over a recent 18-year period and the average salaries in major league baseball over the same period. Salaries are measured in dollars and time is measured after the starting year (year 0). T

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 2528 refer to the graph below, which shows the minimum salaries in major league baseball over a recent 18-year period and the average salaries in major league baseball over the same period. Salaries are measured in dollars and time is measured after the starting year (year 0). A

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2938, solve the equation algebraically and confirm graphically. \(v^{2}-5=8-2 v^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2938, solve the equation algebraically and confirm graphically. \((x+11)^{2}=121\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2938, solve the equation algebraically and confirm graphically. \(2 x^{2}-5 x+2=(x-3)(x-2)+3 x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2938, solve the equation algebraically and confirm graphically. \(x^{2}-7 x-\frac{3}{4}=0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2938, solve the equation algebraically and confirm graphically. x(2x - 5) = 12

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2938, solve the equation algebraically and confirm graphically. x(2x - 1) = 10

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2938, solve the equation algebraically and confirm graphically. x(x + 7) = 14

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2938, solve the equation algebraically and confirm graphically. \(x^{2}-3 x+4=2 x^{2}-7 x-8\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2938, solve the equation algebraically and confirm graphically. \(x+1-2 \sqrt{x+4}=0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2938, solve the equation algebraically and confirm graphically. \(\sqrt{x}+x=1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3946, solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding the x-intercepts. \(2 x-5=\sqrt{x+4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3946, solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding the x-intercepts. \(|3 x-2|=2 \sqrt{x+8}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3946, solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding the x-intercepts. |2x - 5| = 4 - |x - 3|

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3946, solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding the x-intercepts. \(\sqrt{x+6}=6-2 \sqrt{5-x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3946, solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding the x-intercepts. \(2 x-3=x^{3}-5\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3946, solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding the x-intercepts. \(x+1=x^{3}-2 x-5\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 39-46, solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding the x-intercepts. (x + 1)-1 = x-1 + x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 39-46, solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding the x-intercepts. x2 = |x|

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Swan Auto Rental charges $32 per day plus $0.18 per mile for an automobile rental. (a) Elaine rented a car for one day and she drove 83 miles. How much did she pay? (b) Ramon paid $69.80 to rent a car for one day. How far did he drive?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Connecting Graphs and Equations The curves on the graph below are the graphs of the three curves given by y1 = 4x + 5 y2 = x3 + 2x2 - x + 3 y3 = -x3 - 2x2 + 5x + 2. (a) Write an equation that can be solved to find the points of intersection of the graphs of y1 and y2 .

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exploring Grapher Failure Let y = (x200)1/200. (a) Explain algebraically why y= x for all x \(\geq\) 0 (b) Graph the equation y = (x200)1/200 in the window [0, 1] by [0, 1]. (c) Is the graph different from the graph of y=x? (d) Can you explain why the grapher failed?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Connecting Algebra and Geometry Explain how the algebraic equation (x + b)2 = x2 + 2bx + b2 models the areas of the regions in the geometric figure shown below on the left:

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exploring Hidden Behavior Solving graphically, find all real solutions to the following equations. Watch out for hidden behavior. (a) y = 10x3 + 7.5x2 - 54.85x + 37.95 (b) y = x3 + x2 - 4.99x + 3.03

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Connecting Algebra and Geometry The geometric figure shown on the right above is a large square with a small square missing. (a) Find the area of the figure. (b) What area must be added to complete the large square? (c) Explain how the algebraic formula for completing the square models

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Proving a Theorem Prove that if n is a positive integer, then n2 + 2n is either odd or a multiple of 4. Compare your proof with those of your classmates.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn The graph below shows the distance from home against time for a jogger. Using information from the graph, write a paragraph describing the joggers workout.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False A product of real numbers is zero if and only if every factor in the product is zero. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False An algebraic model can always be used to make accurate predictions.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5760, you may use a graphing calculator to decide which algebraic model corresponds to the given graphical or numerical model. (A) y = 2x + 3 (B) y= x2+5 (C) y = 12 - 3x (D) y =4x + 3 (E) \(y=\sqrt{8-x}\

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5760, you may use a graphing calculator to decide which algebraic model corresponds to the given graphical or numerical model. (A) y = 2x + 3 (B) y= x2+5 (C) y = 12 - 3x (D) y =4x + 3 (E) \(y=\sqrt{8

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5760, you may use a graphing calculator to decide which algebraic model corresponds to the given graphical or numerical model. (A) y = 2x + 3 (B) y= x2+5 (C) y = 12 - 3x (D) y =4x + 3 (E) \(y=\sqrt{8

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5760, you may use a graphing calculator to decide which algebraic model corresponds to the given graphical or numerical model. (A) y = 2x + 3 (B) y= x2+5 (C) y = 12 - 3x (D) y =4x + 3 (E) \(y=\sqrt{8

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Analyzing the Market Both Ahmad and LaToya watch the stock market throughout the year for stocks that make significant jumps from one month to another. When they spot one, each buys 100 shares. Ahmads rule is to sell the stock if it fails to perform well for three months in a row. LaToyas rule is to

Precalculus: Graphical, Numerical, Algebraic 8th Edition
You can create your own graphs with hidden behavior. Working in groups of two or three, try this exploration. (a) Graph the equation \(y=(x+2)\left(x^{2}-4 x+4\right)\) in the window [-4, 4] by [-10, 10]. (b) Confirm algebraically that this function has zeros only at x = -2 and x = 2 (c

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The Proliferation of Cell Phones Table 1.8 shows the number of cellular phone subscribers in the United States and their average monthly bill in the years from 1998 to 2007. (a) Graph the scatter plots of the number of subscribers and the average local monthly bill as functions of time, l

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activity (Continuation of Exercise 63) Discuss the economic forces suggested by the two models in Exercise 63 and speculate about the future by analyzing the graphs.