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mathematics
precalculus 1st
Precalculus 1st Edition Jay Abramson - Solutions
For the following exercises, find the x- and y-intercepts of the given equation.7x + 9y = −63
For the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for 5 years.If the function P is graphed, find and interpret the x-and y-intercepts.
Given below are descriptions of two lines. Find the slopes of Line 1 and Line 2. Is the pair of lines parallel, perpendicular, or neither? Line 1: Passes through (-2,-6) and (3, 14) Line 2: Passes through (2, 6) and (4, 14)
For the following exercises, determine whether the equation of the curve can be written as a linear function.−x − 3/5 = 2y
For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular: у х-2 3 3x+y=-9
For the following exercises, find the x- and y-intercepts of each equation.h(x) = 3x − 5
For the following exercises, match each scatterplot with one of the four specified correlations in Figure 9 and Figure 10. r = 0.95 (a) Figure 9 Figure 10 (b)
For the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for 5 years.Find a reasonable domain and range for the function P.
For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular: Find the x- and y-intercepts of the equation 2x + 7y=-14.
For the following exercises, determine whether the equation of the curve can be written as a linear function.−2x2 + 3y2 = 6
For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular: 2x - 6y=12 -x+3y=1
For the following exercises, find the x- and y-intercepts of each equation.g(x) = 2x + 4
For the following data, draw a scatter plot. If we wanted to know when the temperature would reach 28°F, would the answer involve interpolation or extrapolation? Eyeball the line and estimate the answer. Temperature, F 16 Time, seconds 18 46 50 20 54 25 55 30 62
For the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for 5 years.Find the linear function that models the town’s population P as a function of the year, t, where t is the number of years since the model
For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular: −2x+y=3 3x + 2 у у=5
For the following exercises, determine whether the equation of the curve can be written as a linear function.3x + 5y2 = 15
For the following exercises, find the x- and y-intercepts of each equation.f(x) = −x + 2
For the following data, draw a scatter plot. If we wanted to know when the population would reach 15,000, would the answer involve interpolation or extrapolation? Eyeball the line, and estimate the answer. Year 1990 1995 2000 2005 2010 Population 11,500 12,100 12,700 13,000 13,750
On June 1st, a company has $4,000,000 profit. If the company then loses 150,000 dollars per day thereafter in the month of June, what is the company’s profit nth day after June 1st?
For the following exercises, consider this scenario: A town’s population has been increased at a constant rate. In 2010 the population was 46,020. By 2012 the population had increased to 52,070. Assume this trend continues.Identify the year in which the population will reach 75,000.
For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular: 314 y=-x x-9 -4x-3y=8
For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular: y= ²x+1 -3x + 4y = 1
For the following exercises, determine whether the equation of the curve can be written as a linear function.3x2 + 5y = 15
For the following exercises, consider this scenario: A town’s population has been increased at a constant rate. In 2010 the population was 46,020. By 2012 the population had increased to 52,070. Assume this trend continues.Predict the population in 2016.
Does the following table represent a linear function? If so, find the linear equation that models the data. 6 8 12 26 g(x) -8 -12 -18 -46 *
For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular: _y=x+1 3x + 2y = 1
For the following exercises, determine whether the equation of the curve can be written as a linear function.3x + 5y = 15
Does the following table represent a linear function? If so, find the linear equation that models the data. x -4 0 2 10 g(x) 18 -2 -12 -52
At 6 am, an online company has sold 120 items that day. If the company sells an average of 30 items per hour for the remainder of the day, write an expression to represent the number of items that were sold n after 6 am.
For the following exercises, draw a scatter plot for the data provided. Does the data appear to be linearly related? 100 250 300 450 600 12 12.6 13.1 14 14.5 750 15.2
Does Table 2 represent a linear function? If so, find a linear equation that models the data. x 1 3 g(x) 4 9 Table 2 نیا 7 19 11 12
For the following exercises, consider this scenario: A town’s population has been decreasing at a constant rate. In 2010 the population was 5,900. By 2012 the population had dropped 4,700. Assume this trend continues.Identify the year in which the population will reach 0.
For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular: 6x-9y=10 3x+2y = 1
For the following exercises, determine whether the equation of the curve can be written as a linear function.y = 3x2 − 2
Write an equation in slope-intercept form for the line shown. g. fill y
For the following exercises, draw a scatter plot for the data provided. Does the data appear to be linearly related? 1 46 2 50 3 59 لیا 4 75 5 100 6 136
Does Table 1 represent a linear function? If so, find a linear equation that models the data. * -6 g(x) 14 32 Table 1 02 38 4 44
For the following exercises, consider this scenario: A town’s population has been decreasing at a constant rate. In 2010 the population was 5,900. By 2012 the population had dropped 4,700. Assume this trend continues.Predict the population in 2016.
Find the slope of the line shown in the graph. ITT *
For the following exercises, determine whether the equation of the curve can be written as a linear function.y = 3x − 5
For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular: 3y + 4x = 12 -6y=8x + 1
For the following exercises, draw a scatter plot for the data provided. Does the data appear to be linearly related? 0 2 -22 -19 4 -15 6 -11 8 -6 10 -2
Write an equation for line in Figure 2. --6-5-4-3 Figure 2 4 5 6 X
Find the area of a parallelogram bounded by the x-axis, the line g(x) = 2, the line f(x) = 3x, and the line parallel to f(x) passing through (6, 1).
Find the slope of the line shown in the graph. mai பரமபரனார்ம். mộn didmயபால் x
For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular: 3y + x = 12 -y = 8x + 1
For the following exercises, determine whether the equation of the curve can be written as a linear function. y = 1/4 x + 6
Find the area of a triangle bounded by the y-axis, the line f(x) = 9 – 6/7 x, and the line perpendicular to f(x) that passes through the origin.
Find the slope of the line in Figure 1. -6-5-4-3-2-1 Figure 1 3 4 5 X
A regression was run to determine whether there is a relationship between the diameter of a tree (x, in inches) and the tree’s age (y, in years). The results of the regression are given below. Use this to predict the age of a tree with diameter 10 inches.y = ax + ba = 6.301b = −1.044r = −0.970
Timmy goes to the fair with $40. Each ride costs $2. How much money will he have left after riding n rides?
For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular: 4x - 7y = 10 7x + 4y = 1
Given each set of information, find a linear equation that satisfies the given conditions, if possible. x-intercept at (6, 0) and y-intercept at (0, 10)
Find the area of a triangle bounded by the x-axis, the line f(x) = 12 –1/3 x, and the line perpendicular to f(x) that passes through the origin.
A regression was run to determine whether there is a relationship between hours of TV watched per day (x) and number of sit-ups a person can do (y). The results of the regression are given below. Use this to predict the number of situps a person who watches 11 hours of TV can do.y = ax + ba =
A boat is 100 miles away from the marina, sailing directly toward it at 10 miles per hour. Write an equation for the distance of the boat from the marina after t hours.
Given the following set of information, find a linear equation satisfying the conditions, if possible. x-intercept at (−4, 0) and y-intercept at (0, −6)
Given each set of information, find a linear equation that satisfies the given conditions, if possible. Passes through (7, 5) and (3, 17)
Explain how to find a line perpendicular to a linear function that passes through a given point.
Find the area of a parallelogram bounded by the y-axis, the line x = 3, the line f(x) = 1 + 2x, and the line parallel to f(x) passing through (2, 7).
Explain how to interpret the absolute value of a correlation coefficient.
Sonya is currently 10 miles from home and is walking farther away at 2 miles per hour. Write an equation for her distance from home t hours from now.
Given the following set of information, find a linear equation satisfying the conditions, if possible. Passes through (5, 1) and (3, −9)
Determine whether the function is increasing or decreasing. g(x) = −x + 2
Explain how to find a line perpendicular to a linear function that passes through a given point.
Explain how to determine the slope in a word problem that uses a linear function.
Explain the difference between a positive and a negative correlation coefficient.
Jessica is walking home from a friend’s house. After 2 minutes she is 1.4 miles from home. Twelve minutes after leaving, she is 0.9 miles from home. What is her rate in miles per hour?
Determine whether the following function is increasing or decreasing. f(x) = 7x + 9
Determine whether the function is increasing or decreasing. f(x) = 7x − 2
If a horizontal line has the equation f(x) = a and a vertical line has the equation x = a, what is the point of intersection? Explain why what you found is the point of intersection.
Explain how to interpret the initial value in a word problem that uses a linear function.
What is extrapolation when using a linear model?
Maria is climbing a mountain. Maria’s elevation, E(t), in feet after t minutes is given by E(t) = 1200 + 40t. Write a complete sentence describing Maria’s starting elevation and how it is changing over time.
Determine whether the following function is increasing or decreasing. f(x) = −2x + 5
Determine whether the algebraic equation is linear. 6x2 − y = 5
If the graphs of two linear functions are perpendicular, describe the relationship between the slopes and the y-intercepts.
What is interpolation when using a linear model?
Terry is skiing down a steep hill. Terry’s elevation, E(t), in feet after t seconds is given by E(t) = 3000 − 70t. Write a complete sentence describing Terry’s starting elevation and how it is changing over time.
Determine whether the following algebraic equation can be written as a linear function. 2x + 3y = 7
Determine whether the algebraic equation is linear. 2x + 3y = 7
If the graphs of two linear functions are parallel, describe the relationship between the slopes and the y-intercepts.
Explain how to find the input variable in a word problem that uses a linear function.
Describe what it means if there is a model breakdown when using a linear model.
The number of bacteria in a refrigerated food product is given byN(T) = 23T2 − 56T+ 1, 3 < T < 33,Where T is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by T(t) = 5t + 1.5, where t is the time in hours.a. Find the composite function
The radius r, in inches, of a spherical balloon is related to the volume, V, by r(V) = 3√3V/4π. Air is pumped into the balloon, so the volume after t seconds is given by V(t) = 10 + 20t.a. Find the composite function r(V(t)).b. Find the exact time when the radius reaches 10 inches.
Use the function you found in the previous exercise to find the total area burned after 5 minutes.
A forest fire leaves behind an area of grass burned in an expanding circular pattern. If the radius of the circle of burning grass is increasing with time according to the formula r(t) = 2t + 1, express the area burned as a function of time, t (minutes).
A rain drop hitting a lake makes a circular ripple. If the radius, in inches, grows as a function of time in minutes according to r(t) = 25 √t + 2, find the area of the ripple as a function of time. Find the area of the ripple at t = 2.
Show that the function f(x) = 3(x − 5)2 + 7 is not one-to-one.
A store offers customers a 30% discount on the price x of selected items. Then, the store takes off an additional 15% at the cash register. Write a price function P(x) that computes the final price of the item in terms of the original price x.
The function A(d) gives the pain level on a scale of 0 to 10 experienced by a patient with d milligrams of a pain- reducing drug in her system. The milligrams of the drug in the patient’s system after t minutes is modeled by m(t). Which of the following would you do in order to determine when the
Let f(t) be the number of ducks in a lake t years after 1990. Explain the meaning of each statement:a. f(5) = 30 b. f(10) = 40
The function D(p) gives the number of items that will be demanded when the price is p. The production cost C(x) is the cost of producing x items. To determine the cost of production when the price is $6, you would do which of the following ?a. Evaluate D(C(6)).b. Evaluate C(D(6)).c. Solve D(C(x)) =
The number of cubic yards of dirt, D, needed to cover a garden with area a square feet is given by D = g(a).a. A garden with area 5,000 ft2 requires 50 yd3 of dirt. Express this information in terms of the function g. b. Explain the meaning of the statement g(100) = 1.
For the following exercises, let F(x) = (x + 1)5, f(x) = x5, and g(x) = x + 1. (f ∘ g )(11); (g ∘ f)(11)
The amount of garbage, G, produced by a city with population p is given by G = f(p). G is measured in tons per week, and p is measured in thousands of people. A. The town of Tola has a population of 40,000 and produces 13 tons of garbage each week. Express this information in terms of the
For the following exercises, let F(x) = (x + 1)5, f(x) = x5, and g(x) = x + 1. (g ∘ f)(a); (f ∘ g)(a)
For the following exercises, graph y = 3 √— x on the given viewing window. Determine the corresponding range for each viewing window. Show each graph. [−1,000,000, 1,000,000]
For the following exercises, let F(x) = (x + 1)5 , f(x) = x5 , and g(x) = x + 1. (f ∘ g)(6); ( g ∘ f)(6)
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