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mathematics
precalculus

Questions and Answers of Precalculus

In Problems 13–16,(a) Find the slope of the line(b) Interpret the slope. (-2,2) -2 YA 2 (1,1) -1 2 x
True or False The slope of the line 2y = 3x + 5 is 3.
For a circle, the_______ is the distance from the center to any point on the circle.
True or False The radius of the circle x2 + y2 = 9 is 3.
Choose the equation of a circle with radius 6 and center (3, −5).(a) (x − 3)2 + (y + 5)2 = 6(b) (x + 3)2 + (y − 5)2 = 36(c) (x + 3)2 + (y − 5)2 = 6(d) (x − 3)2 + (y + 5)2 = 36
In Problems 15–26, write the standard form of the equation and the general form of the equation of each circle of radius r and center (h, k). Graph each circle. =(hk)= k) = (0₁-1/2) -¹) 0, r=
In Problems 41 – 52, the graph of an equation is given.(a) Find the intercepts.(b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.
The equation of a circle can be changed from general form to standard from by doing which of the following?(a) Completing the squares(b) Solving for x(c) Solving for y(d) Squaring both sides
Given that the intercepts of a graph are (−4, 0) and (0, 5) , choose the statement that is true.(a) The y -intercept is − 4, and the x -intercept is 5.(b) The y -intercepts are − 4 and 5.(c)
Choose the point-slope equation of a nonvertical line with slope m that passes through the point (x1, y1).(a) y + y1 = mx + x1(b) y − y1 = mx − x1(c) y + y1 = m(x + x1)(d) y − y1 = m(x − x1)
In Problems 19 – 30, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.y = x + 2
In Problems 17–24, plot each pair of points and determine the slope of the line containing the points. Graph the line.(−2, 3); (2, 1)
In Problems 47–50, match each graph with the correct equation.(a) (x − 3)2 + (y + 3)2 = 9(b) (x + 1)2 + (y − 2)2 = 4(c) (x − 1)2 + (y + 2)2 = 4(d) (x + 3)2 + (y − 3)2 = 9 -6 -5 -4 -3
In Problems 47–50, match each graph with the correct equation.(a) (x − 3)2 + (y + 3)2 = 9(b) (x + 1)2 + (y − 2)2 = 4(c) (x − 1)2 + (y + 2)2 = 4(d) (x + 3)2 + (y − 3)2 = 9 -6 -5 -4
In Problems 45–52, find an equation of the line L. YA 2 (0,,0) -2 -1F (2,1) L 2 x X
In Problems 41 – 52, the graph of an equation is given.(a) Find the intercepts.(b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.
In Problems 41 – 52, the graph of an equation is given.(a) Find the intercepts.(b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.
In Problems 41 – 52, the graph of an equation is given.(a) Find the intercepts.(b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.
In Problems 41 – 52, the graph of an equation is given.(a) Find the intercepts.(b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.
In Problems 19 – 30, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.y = −x2 + 1
In Problems 25–32, graph the line that contains the point P and has slope m.P = (2, 1); m = 4
In Problems 41 – 52, the graph of an equation is given.(a) Find the intercepts.(b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.
In Problems 45–52, find an equation of the line L. YA 3 -1 y= 2xt (1, 2) 3 x L is perpendicular to y = 2x
In Problems 27–40,(a) Find the center (h, k) and radius r of each circle;(b) Graph each circle;(c) Find the intercepts, if any.x2 + (y − 1)2 = 1
In Problems 47–50, match each graph with the correct equation.(a) (x − 3)2 + (y + 3)2 = 9(b) (x + 1)2 + (y − 2)2 = 4(c) (x − 1)2 + (y + 2)2 = 4(d) (x + 3)2 + (y − 3)2 = 9 -6 -5 -4 -3 -2 6 G
In Problems 47–50, match each graph with the correct equation.(a) (x − 3)2 + (y + 3)2 = 9(b) (x + 1)2 + (y − 2)2 = 4(c) (x − 1)2 + (y + 2)2 = 4(d) (x + 3)2 + (y − 3)2 = 9 -4-3-2 -6 -5 -4
In Problems 39–44, the slope and a point on a line are given. Use this information to locate three additional points on the line.Slope −3/2; point (2, −4)
In Problems 41 – 52, the graph of an equation is given.(a) Find the intercepts.(b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.
In Problems 41–46, find the standard form of the equation of each circle.Center at the origin and containing the point (−2, 3)
In Problems 39–44, the slope and a point on a line are given. Use this information to locate three additional points on the line.Slope 4/3; point (−3, 2)
In Problems 39–44, the slope and a point on a line are given. Use this information to locate three additional points on the line.Slope −2; point (−2, −3)
In Problems 45–52, find an equation of the line L. (-1, 1) -3, L YA 3 1 x y=-x
In Problems 57–72, list the intercepts and test for symmetry. y = X
If the equation of a circle is x2 + y2 = r2 and the equation of a tangent line is y = mx + b, show that:(a) r2 (1 + m2) = b2 .The quadratic equation x2 + (mx + b)2 = r2 has exactly one solution.(b)
Find an equation of the line containing the centers of the two circles (x − 4)2 + (y + 2)2 = 25 and (x + 1)2 + (y − 5)2 = 16
In Problems 53–78, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you
In Problems 57–72, list the intercepts and test for symmetry. y = √x
In Problems 53–78, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you
If a circle of radius 2 rolls along the x-axis in quadrants I and II, what is an equation for the path of the center of the circle?
In Problems 53–78, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you
A circle of radius 7 rolls along the y-axis in quadrants I and IV. Find an equation for the path of the center of the circle.
Refer to Problem 65. The line x − 2y + 4 = 0 is tangent to a circle at (0, 2). The line y = 2x − 7 is tangent to the same circle at (3, −1). Find the center of the circle.Data from problem 65If
In Problems 53–78, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you
In Problems 57–72, list the intercepts and test for symmetry.y2 = x + 16
In Problems 57–72, list the intercepts and test for symmetry.y2 = x + 9
In Problems 53–78, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you
If x2 + y2 + dx + ey + f = 0 is the equation of a circle, show thatis an equation of the tangent line to the circle at the point (x0, y0). y + yo xox + yox + dlxtaxo) + e() +5 2 2 + f = 0
Which of the following equations might have the graph shown? (a) (x - 2)² + (y + 3)² = 13 (b) (x - 2)² + (y-2)² = 8 (c) (x - 2)² + (y - 3)² (d) (x + 2)² + (y-2)² = 8 = 13 (e) x² + y² - 4x
In Problems 57–72, list the intercepts and test for symmetry. y = .x2 x² - 4 2x
In Problems 57–72, list the intercepts and test for symmetry.x2 + y − 9 = 0
In Problems 53–78, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you
In Problems 57–72, list the intercepts and test for symmetry. y = 4x x² + 16
In Problems 61–64, find the standard form of the equation of each circle. Center (−3, 1) and tangent to the y-axis
In Problems 57–72, list the intercepts and test for symmetry. y = -x3 x² 2 - 9 =
In Problems 61–64, find the standard form of the equation of each circle. Center (−1, 3) and tangent to the line y = 2
In Problems 61–64, find the standard form of the equation of each circle. (Refer to the preceding discussion).Center (4, −2) and tangent to the line x = 1
If (x1, y1) and (x2, y2) are the endpoints of a diameter of a circle, show that an equation of the circle is (x − x1)(x − x2) + (y − y1)(y − y2) = 0
In Problems 53–78, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you
Problems 61–68 require the following discussion.The Greek method for finding the equation of the tangent line to a circle uses the fact that at any point on a circle, the line containing the center
In Problems 57–72, list the intercepts and test for symmetry. y = x4 + 1 2x5
Problems 61–68 require the following discussion.Use the Greek method described in Problem 67 to find an equation of the tangent line to the circle x2 + y2 − 4x + 6y + 4 = 0 at the point (3, 2√2
In Problems 57–72, list the intercepts and test for symmetry.y = x2 + 4
In Problems 53–78, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you
In Problems 53–78, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you
The graph below shows the height y, in feet, of a shot (metal ball) thrown by a shot-putter after it has traveled x feet horizontally.(a) What is the height of the shot after it has traveled 10 feet
In Problems 79–86,(a) Find the intercepts of each equation,(b) Test each equation for symmetry with respect to the x-axis, the y-axis, and the origin,(c) Graph each equation by hand by plotting
In Problems 53–78, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you
In Problems 79–86,(a) Find the intercepts of each equation,(b) Test each equation for symmetry with respect to the x-axis, the y-axis, and the origin,(c) Graph each equation by hand by plotting
In Problems 73–76, graph each equation.x = y2
In Problems 53–78, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you
Caleb rides home from his friend’s house on his bicycle. The graph below shows his distance d from his house after m minutes.(a) How far was Caleb from home after 10 minutes?(b) How far was Caleb
In Problems 53–78, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you
A movie theater offers a monthly membership for avid movie lovers. The graph below shows the relation between the monthly cost C and the number of movies seen m.(a) What is the cost of watching 5
The graph below shows the height h, in meters, of a discus t seconds after it is thrown.(a) What is the height of the discus after 6 seconds?(b) When does the discus reach its maximum height? What is
In Problems 53–78, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you
In Problems 53–78, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you
In Problems 79–86,(a) Find the intercepts of each equation,(b) Test each equation for symmetry with respect to the x-axis, the y-axis, and the origin,(c) Graph each equation by hand by plotting
In Problems 79–86,(a) Find the intercepts of each equation,(b) Test each equation for symmetry with respect to the x-axis, the y-axis, and the origin,(c) Graph each equation by hand by plotting
In Problems 115–118, write an equation of each line. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. -3 34 0 -3 3
In Problems 115–118, write an equation of each line. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. -3 34 0 -3 3
In Problems 115–118, write an equation of each line. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. -3 34 0 -3 3
In Problems 79–86,(a) Find the intercepts of each equation,(b) Test each equation for symmetry with respect to the x-axis, the y-axis, and the origin,(c) Graph each equation by hand by plotting
In Problems 115–118, write an equation of each line. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. -3 34 -3 3
In Problems 79–98, find the slope and y-intercept of each line. Graph the line.3x + 2y = 0
(a) Graph y = √x2, y = x, y = |x|, and y = (√x)2, noting which graphs are the same.(b) Explain why the graphs of y = √x2 and y = |x| are the same.(c) Explain why the graphs of y = x and y =
Find the equation of the x-axis.
Find the equation of the y-axis.
Use slopes to show that the quadrilateral whose vertices are (1, −1), (4, 1), (2, 2), and (5, 4) is a parallelogram.
Form a triangle using the points (0, 0), (a, 0), and (b, c), where a > 0, b > 0, and c > 0. Find the point of intersection of the three lines joining the midpoint of a side of the triangle
The annual fixed costs of owning a small sedan are $4880, assuming the car is completely paid for. The cost to drive the car is approximately $0.16 per mile. Write a linear equation that relates the
Wages of a Car Salesperson Dontrell receives $525 per week for selling new and used cars. He also receives 5% of the profit on any sales. Write a linear equation that represents Dontrell’s weekly
Ameren Illinois supplies natural gas to residential customers for a monthly customer charge of $18.76 plus 31.935 cents per therm of heat energy.(a) Write a linear equation that relates the monthly
Find three numbers a for which the lines x + 2y = 5, 2x − 3y + 4 = 0, and ax + y = 0 do not form a triangle.
Which of the following equations might have the graph shown? (a) 2x + 3y = 6 (c) 3x - 4y = -12 (e) x - y = -1 (g) y = = 2x + 3 (b) 2x + 3y = 6 (d) x - y = 1 (f) y = 3x - 5 (h) y=-3x + 3
In Problems 39–62, identify and graph each polar equation. r = 1 cos
In Problems 39–62, identify and graph each polar equation. r = 4 cos (30)
In Problems 43–58, polar coordinates of a point are given. Find the rectangular coordinates of each point.(8.1, 5.2)
If v, w, u and a, b, c are vectors for whichandshow that a. v = b.w = c.u = 1
In Problems 39–62, identify and graph each polar equation. r² 2 sin (20)
In Problems 39–62, identify and graph each polar equation. r² = 9 cos(20)

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