A real estate office manages an apartment complex with 50 units. When the rent is $780 per month, all 50 units are occupied. However, when the rent is $825, the average number of occupied units drops to 47. Assume that the relationship between the monthly rent p and the demand x is linear. (Note: The term demand refers to the number of occupied units.) a. Write a linear equation giving the demand x in terms of the rent p. b. Linear extrapolation Use a graphing utility to graph the demand equation and use the trace feature to predict the number of units occupied when the rent is raised to $855. c. Linear interpolation Predict the number of units occupied when the rent is lowered to $795. Verify graphically.
> Determine the quadrant in which θ lies. a. sin θ < 0 and cos θ < 0 b. sec θ > 0 and cot θ < 0
> Evaluate the function at the given value(s) of the independent variable. Then find the domain and range. a. f (−2) b f (0) c. f (1) d. f (s2 + 2)
> Use a calculator to evaluate each trigonometric function. Round your answers to four decimal places. a. cot(1.35) b. tan(1.35)
> Use a calculator to evaluate each trigonometric function. Round your answers to four decimal places. a. tan π/9 b. tan 10π/9
> Use a calculator to evaluate each trigonometric function. Round your answers to four decimal places. a. sec 225° b. sec 135º
> Use a calculator to evaluate each trigonometric function. Round your answers to four decimal places. a. sin 10° b. csc 10º
> Evaluate the sine, cosine, and tangent of each angle. Do not use a calculator. a. 750º b. 510º c. 10π/3 d. 17π/3
> Sketch the graph of the equation by point plotting. y = √x + 2
> Evaluate the sine, cosine, and tangent of each angle. Do not use a calculator. a. 225º b. -225º c. 5π/3 d. 11π/6
> Evaluate the sine, cosine, and tangent of each angle. Do not use a calculator. a. -30º b. 150º c. -π/6 c. π/2
> Evaluate the sine, cosine, and tangent of each angle. Do not use a calculator. a. 60º b. 120º c. π/4 d. 5π/4
> Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Then evaluate the other five trigonometric functions of θ. sec θ = 13/5
> Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Then evaluate the other five trigonometric functions of θ. cos θ = 4/5
> Evaluate the function at the given value(s) of the independent variable. Then find the domain and range. a. f (−1) b. f (0) c. f (2) d. f (t2 + 1)
> Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Then evaluate the other five trigonometric functions of θ. sin θ = 1/3
> Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Then evaluate the other five trigonometric functions of θ. sin θ = 1/2
> Evaluate the six trigonometric functions of the angle θ. a. / b. /
> Evaluate the six trigonometric functions of the angle θ.
> Sketch the graph of the equation by point plotting. y = √x - 6
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If f is a function, then f(ax) = af(x).
> A car is moving at the rate of 50 miles per hour, and the diameter of its wheels is 2.5 feet. a. Find the number of revolutions per minute that the wheels are rotating. b. Find the angular speed of the wheels in radians per minute.
> Let r represent the radius of a circle, θ the central angle (measured in radians), and s the length of the arc subtended by the angle. Use the relationship s = rθ to complete the table.
> Convert the radian measure to degree measure. a. 7π / 3 b. –(11π / 30) c. 11π / 6 d. 0.438
> Convert the radian measure to degree measure. a. 3π / 2 b. 7π / 6 c. –(7π / 12) d. -2.367
> Convert the degree measure to radian measure as a multiple of π and as a decimal accurate to three decimal places. a. -20º b. -240º c. -270º d. 144º
> Convert the degree measure to radian measure as a multiple of π and as a decimal accurate to three decimal places. a. 30º b. 150º c. 315º d. 120º
> find the domain of the function. g(x) = 1 / │x2 - 4│
> Determine two co-terminal angles in radian measure (one positive and one negative) for each angle. a. / b. /
> Determine two co-terminal angles in radian measure (one positive and one negative) for each angle. a. / b. /
> Determine two co-terminal angles in degree measure (one positive and one negative) for each angle. a. / b. /
> Sketch the graph of the equation by point plotting. y = │x│ - 1
> Determine two co-terminal angles in degree measure (one positive and one negative) for each angle. a. / b. /
> In your own words, describe the meaning of amplitude and period.
> Find sin θ, cos θ, and tan θ.
> Explain how to convert from degrees to radians.
> Explain how to find co-terminal angles in degrees.
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If a line contains points in both the first and third quadrants, then its slope must be positive.
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The lines represented by ax + by = c1 and bx – ay = c2 are perpendicular. Assume a ≠ 0 and b ≠ 0.
> Find the domain of the function. f(x) = 1 / │x + 3│
> Prove that if the slopes of two non-vertical lines are negative reciprocals of each other, then the lines are perpendicular.
> Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x1∗, y1∗) and (x2∗, y2∗), then Assume x1 ≠x2 and x1∗ â‰
> Sketch the graph of the equation by point plotting. y = │x + 1│
> Prove that the figure formed by connecting consecutive midpoints of the sides of any quadrilateral is a parallelogram.
> Prove that the diagonals of a rhombus intersect at right angles. (A rhombus is a quadrilateral with sides of equal lengths.)
> Use the result below to find the distance between the point and line. Point: (2, 3) Line: 4x + 3y = 10
> Use the result below to find the distance between the point and line. Point: (−2, 1) Line: x − y − 2 = 0
> Write the distance d between the point (3, 1) and the line y = mx + 4 in terms of m. Use a graphing utility to graph the equation. When is the distance 0? Explain the result geometrically.
> Show that the distance between the point (x1, y1) and the line Ax + By + C = 0 is Distance = /
> An instructor gives regular 20-point quizzes and 100-point exams in a mathematics course. Average scores for six students, given as ordered pairs (x, y), where x is the average quiz score and y is the average exam score, are (18, 87), (10, 55), (19, 96),
> Find the domain of the function. f(x) = √x2 − 3x + 2
> As a salesperson, you receive a monthly salary of $2000, plus a commission of 7% of sales. You are offered a new job at $2300 per month, plus a commission of 5% of sales. Write linear equations for your monthly wage W in terms of your monthly sales s for
> Sketch the graph of the equation by point plotting. y = (x − 3)2
> Find a linear equation that expresses the relationship between the temperature in degrees Celsius C and degrees Fahrenheit F. Use the fact that water freezes at 0°C (32°F) and boils at 100°C (212°F). Use the equation to convert 72°F to degrees Celsius.
> Several lines are shown in the figure below. (The lines are labeled a–f.) a. Which lines have a positive slope? b. Which lines have a negative slope? c. Which lines appear parallel? d. Which lines appear perpendicular?
> Find the coordinates of the point of intersection of the given segments. Explain your reasoning. a. Perpendicular bisectors b. Medians
> Find an equation of the line tangent to the circle (x − 1)2 + (y − 1)2 = 25 at the point (4, −3).
> Find an equation of the line tangent to the circle x2 + y2 = 169 at the point (5, 12).
> A line is represented by the equation ax + by = 4. When is the line parallel to the x-axis? When is the line parallel to the y-axis? Give values for a and b such that the line has a slope of 5/8. Give values for a and b such that the line is perpendicula
> Show that the points (−1, 0), (3, 0), (1, 2), and (1, −2) are vertices of a square.
> Determine whether the points are collinear. (Three points are collinear if they lie on the same line.) (0, 4), (7, -6), (-5, 11)
> Determine whether the points are collinear. (Three points are collinear if they lie on the same line.) (-2, 1), (-1, 0), (2, -2)
> Find the domain of the function. f(x) = √x + √1 − x
> You are given the dollar value of a product in 2016 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 0 repr
> You are given the dollar value of a product in 2016 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 0 repr
> Write the general forms of the equations of the lines that pass through the point and are a. parallel to the given line and b. perpendicular to the given line. Point: (5/6, - (1/2)) Line: 7x + 4y = 8
> Write the general forms of the equations of the lines that pass through the point and are a. parallel to the given line and b. perpendicular to the given line. Point: (3/4, 7/8) Line: 5x - 3y = 0
> Write the general forms of the equations of the lines that pass through the point and are a. parallel to the given line and b. perpendicular to the given line. Point: (2, 5) Line: x - y = -2
> Write the general forms of the equations of the lines that pass through the point and are a. parallel to the given line and b. perpendicular to the given line. Point: (-3, 2) Line: x + y = 7
> Write the general forms of the equations of the lines that pass through the point and are parallel to the given line and perpendicular to the given line. Point: (-1, 0) Line: y = -3
> Write the general forms of the equations of the lines that pass through the point and are parallel to the given line and perpendicular to the given line. Point: (-7, -2) Line: x = 1
> Use the below result to write an equation of the line with the given characteristics in general form. Point on line: (-(2/3), -2) x-intercept: (a, 0) y-intercept: (0, a) (a ≠0)
> Use the below result to write an equation of the line with the given characteristics in general form. Point on line: (9, -2) x-intercept: (2a, 0) y-intercept: (0, a) (a ≠0)
> Sketch the graph of the equation by point plotting. y = 4 − x2
> Find the domain and range of the function. f(x) = x – 2 / x+4
> Use the below result to write an equation of the line with the given characteristics in general form. x-intercept: (-2/3, 0) y-intercept: (0, -2)
> Use the below result to write an equation of the line with the given characteristics in general form. x-intercept: (2, 0) y-intercept: (0, 3)
> Show that the line with intercepts (a, 0) and (0, b) has the following equation. x/a + y/b = 1, a ≠ 0, b ≠ 0
> Write an equation for the line that passes through the points (0, b) and (3, 1).
> Find an equation of the line that passes through the points. Then sketch the line. (2, 5), (2, 7)
> Find an equation of the line that passes through the points. Then sketch the line. (3, 1), (5, 1)
> Find an equation of the line that passes through the points. Then sketch the line. (1, -2), (3, -2)
> Find an equation of the line that passes through the points. Then sketch the line. (6, 3), (6, 8)
> Find an equation of the line that passes through the points. Then sketch the line. (-3, 6), (1, 2)
> Sketch the graph of the equation by point plotting. y = 5 − 2x
> Find an equation of the line that passes through the points. Then sketch the line. (2, 8), (5, 0)
> Find the domain and range of the function. f(x) = 3/x
> Find an equation of the line that passes through the points. Then sketch the line. (-2, -2), (1, 7)
> Find an equation of the line that passes through the points. Then sketch the line. (4, 3), (0, -5)
> Sketch the graph of the equation. x + 2y + 6 = 0
> Sketch the graph of the equation. 3x – 3y + 1 = 0
> Sketch the graph of the equation. y – 1 = 3(x + 4)
> Sketch the graph of the equation. y – 2 = 3/2 (x – 1)
> Sketch the graph of the equation. y = 1 / 3 x - 1
> Sketch the graph of the equation. y = -2x + 1
> Sketch the graph of the equation by point plotting. y = (1/2)x + 2
> Sketch the graph of the equation. x = 4
> Sketch the graph of the equation. y = -3
> Find the domain and range of the function. f(x) = │x − 3│
> Find the slope and the y-intercept (if possible) of the line. y = -1
> Find the slope and the y-intercept (if possible) of the line. x = 4
