27-30 - Finding Inequalities from a Graph An equation and its graph are given. Find an inequality whose solution is the shaded region. 27. y = x – 1 28. y = x* + 2 y. y. 29. x² + y = 4 30. y = x' – 4x
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- To solve the nonlinear inequality x+1x20 , we first observe that the number, ____ and ____ are zeros of the numerator and denominator. These numbers divide the real line into three intervals. Complete the table. Do any of the endpoints fail to satisfy the inequality> If so, which one(s)? ____________.The solution of the inequality is __________________.Sketch the region that corresponds to the given inequalities. 2x + 4y ≥ 4 2x − 4y ≤ 4 x ≥ 0 The x y-coordinate plane is given. There are 3 lines and a region labeled "solution set" on the graph. The first line enters the window in the second quadrant, goes down and right, passes through the point (−4, 3), crosses the y-axis at y = 1 crossing the vertical line, crosses the x-axis at x = 2 crossing the second line, passes through the point (4, −1), and exits the window in the fourth quadrant. The second line enters the window in the third quadrant, goes up and right, passes through the point (−4, −3), crosses the y-axis at y = −1 crossing the vertical line, crosses the x-axis at x = 2 crossing the first line, passes through the point (4, 1), and exits the window in the first quadrant. The vertical line crosses the x-axis at the origin. The solution set is below the first line, below the second line, and to the right of the vertical line. The regions…1. Draw the lines associated with the two inequalities x+y≤6, y>2x (I) Shade on the a graph the region which represents the solution set for the three inequalities; x+y≤6, y>2 and y≤2x.
- Sketch the region that corresponds to the given inequalities. 3x − y ≤ 3 x + 2y ≤ 8 The x y-coordinate plane is given. There are 2 lines and a region labeled "solution set" on the graph. The first line enters the window in the third quadrant, goes up and right, passes through the point (−1, −6), crosses the y-axis at y = −3, crosses the x-axis at x = 1, passes through the point (2, 3) crossing the second line, and exits the window in the first quadrant. The second line enters the window in the second quadrant, goes down and right, passes through the point (−1, 4.5), crosses the y-axis at y = 4, passes through the point (1, 3.5), passes through the point (2, 3) crossing the first line, crosses the x-axis at x = 8, and exits the window in the fourth quadrant. The solution set is above the first line and below the second line. The regions outside the solution set are shaded. The x y-coordinate plane is given. There are 2 lines and a region labeled "solution…express answer as both a linear inequality of y as a function x and as a graph in the real plane. For problems 9 and 10, graph the solution in the real plane. Be sure to shade regions and use solid or dashed curves as appropriate. Label at least two points along graph's boundary. 8. Find the solution set to the inequality 3x+5y>30 9. Find the solution set to the pair of inequalities y<2x−3 and y<9−3x 10. Find the solution set to the pair of inequalities 5x−2y>10 and x2+(y−1)2≤25express answer as both a linear inequality of y as a function x and as a graph in the real plane. For problems 9 and 10, graph the solution in the real plane. Be sure to shade regions and use solid or dashed curves as appropriate. Label at least two points along graph's boundary. 7. Find the solution set to the inequality 2y≤6x−8 8. Find the solution set to the inequality 3x+5y>30 9. Find the solution set to the pair of inequalities y<2x−3 and y<9−3x 10. Find the solution set to the pair of inequalities 5x−2y>10 and x2+(y−1)2≤25
- 2) We need to maximize ▭, which is the price per seminar ticket times the number of seminar tickets sold. 3) Since price cannot be negative, we have x ≤___________ 4) A negative value of x would result in a price increase. Since the problem is stated in terms of price reductions, we must restrict x so that x ≥ _____.3) The average cost per item for a product is given by: AC(x)=x^3/3-7x^2/2+12x+10 Where x is the number of items produced ( in hundreds) and AC(x) is the average cost per item.The company can produce between 300 and 600 items per day. How many should be produced soThat the average cost per item is a minimum?The region bounded by the graph y = 3x - x3, the y axis, and the line y = 2 is revolved about y axis. the point of intersection is ______. Show solution. (-2,2) (1,2) (2,1) None of these Show
- A doctor sees between 7 and 12 patients each day. On Mondays and Tuesdays, the appointment times are 15 minutes. On Wednesdays and Thursdays, they are 30 minutes. On Fridays, they are one hour long. The doctor works for no more than 8 hours a day. Here are some inequalities that represent this situation. - .25 is less than or equal to y is less than or equal to 1 - 7 is less than or equal to x is less than or equal to 12 - What does each variable represent? What does the expression in the last inequality mean in this situation?Consider the inequality. −y 20 > 1 4 Solve the inequality for y. When graphing the inequality, the corresponding line will be a line with a at the point (x, y) = . Use (0, 0) as a test point to determine whether the shaded half-plane includes the test point. The shaded region . Graph the inequality.how to solve this problem nbr. 33 you need to find the maximum, minimum and inflexion point if there is one