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Nonlinear Equations

Math · Advanced Math · 95 questions · every one comes with a full explanation.

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  1. 1A system of equations consists of a quadratic equation and a linear equation. The equations in this system are graphed in the xy-plane above. How many solutions does this system haMedium · Advanced Math
  2. 2Which of the following inequalities is equivalent to the inequality above?Easy · Advanced Math
  3. 3If is a solution to the system of equations above, which of the following could be the value of x ?Medium · Advanced Math
  4. 4What values satisfy the equation above?Medium · Advanced Math
  5. 5x=49 y=x+9 The graphs of the given equations intersect at the point x,y in the xy-plane. What is the value of y ?Easy · Advanced Math
  6. 624-x+34-x=25 What is the positive solution to the given equation?Hard · Advanced Math
  7. 7x 2 - 2 x - 9 = 0 One solution to the given equation can be written as 1+k, where k is a constant. What is the value of k ?Hard · Advanced Math
  8. 8In the x y -plane, a line with equation 2 y = 4.5 intersects a parabola at exactly one point. If the parabola has equation y = - 4 x 2 + b x Hard · Advanced Math
  9. 9Which ordered pair is a solution to the system of equations above?Hard · Advanced Math
  10. 106r=7s+t The given equation relates the variables r , s , and t . Which equation correctly expresses s in terms of r and t ?Easy · Advanced Math
  11. 11If x is a solution to the given equation, which of the following is a possible value of ?Hard · Advanced Math
  12. 12During a 5-second time interval, the average acceleration a, in meters per second squared, of an object with an initial velocity of 12 meters per second is defined by the equation Hard · Advanced Math
  13. 13y = 76 y = x 2 - 5 The graphs of the given equations in the xy-plane intersect at the point (x,y). What is a possible value of x ?Easy · Advanced Math
  14. 147m=5n+p The given equation relates the positive numbers m , n , and p . Which equation correctly gives n in terms of m and p ?Medium · Advanced Math
  15. 15Which of the following is a solution to the equation above?Hard · Advanced Math
  16. 16In the xy-plane, a line with equation 2 y = c for some constant c intersects a parabola at exactly one point. If the parabola has equation y = - 2 x 2 Hard · Advanced Math
  17. 17For the curve in the system: Moving from left to right: The curve passes from quadrant 2 to quadrant 1. In quadrant 2, the curve trends up gradually to point (0 comma 3.25). In qEasy · Advanced Math
  18. 18What is the product of the solutions to the given equation?Medium · Advanced Math
  19. 19What is the solution to the equation above?Medium · Advanced Math
  20. 20x - 2 2 = 3 x + 34 What is the smallest solution to the given equation?Hard · Advanced Math
  21. 21If the ordered pair satisfies the system of equations above, what is one possible value of x ?Medium · Advanced Math
  22. 22An oceanographer uses the equation to model the speed s, in knots, of an ocean wave, where p represents the period of the wave, in seconds. Which of the following represents the peMedium · Advanced Math
  23. 23Which of the following is a solution to the equation ?Easy · Advanced Math
  24. 24q-29r=s The given equation relates the positive numbers q , r , and s . Which equation correctly expresses q in terms of r and s ?Easy · Advanced Math
  25. 2557x2+(57b+a)x+ab=0 In the given equation, a and b are positive constants. The product of the solutions to the given equation is kab, where k is a constant. What is the value ofHard · Advanced Math
  26. 26- x 2 + b x - 676 = 0 In the given equation, b is a positive integer. The equation has no real solution. What is the greatest possible value of b ?Hard · Advanced Math
  27. 27p = k 4 j + 9 The given equation relates the distinct positive numbers p , k , and j . Which equation correctly expresses 4 j + 9 in terms of p aMedium · Advanced Math
  28. 28If 3 x 2 - 18 x - 15 = 0 , what is the value of x 2 - 6 x ?Hard · Advanced Math
  29. 29In the xy-plane, what is the y-coordinate of the point of intersection of the graphs of and ?Medium · Advanced Math
  30. 30In the equation above, t is a constant. If the equation has no real solutions, which of the following could be the value of t ?Hard · Advanced Math
  31. 3114 j + 5 k = m The given equation relates the numbers j , k , and m . Which equation correctly expresses k in terms of j and m ?Medium · Advanced Math
  32. 32x k x - 56 = -16 In the given equation, k is an integer constant. If the equation has no real solution, what is the least possible value of k ?Hard · Advanced Math
  33. 33- 4 x 2 - 7 x = -36 What is the positive solution to the given equation?Medium · Advanced Math
  34. 3414x7y=2w+19 The given equation relates the distinct positive real numbers w , x , and y . Which equation correctly expresses w in terms of x and y ?Hard · Advanced Math
  35. 35Which of the following is a solution to the given equation?Medium · Advanced Math
  36. 36In the equation above, a is a constant and . If the equation has two integer solutions, what is a possible value of a ?Medium · Advanced Math
  37. 37What is the solution set of the equation above?Hard · Advanced Math
  38. 38The graph of the function f, defined by , is shown in the xy-plane above. If the function g (not shown) is defined by , what is one possible value of a such that ?Hard · Advanced Math
  39. 39x 2 - 34 x + c = 0 In the given equation, c is a constant. The equation has no real solutions if c>n. What is the least possible value of n ?Hard · Advanced Math
  40. 40x - 5 = 10 What is one possible solution to the given equation?Easy · Advanced Math
  41. 41- 16 x 2 - 8 x + c = 0 In the given equation, c is a constant. The equation has exactly one solution. What is the value of c ?Hard · Advanced Math
  42. 425 x 2 - 37 x - 24 = 0 What is the positive solution to the given equation?Medium · Advanced Math
  43. 43x - 1 2 = -4 How many distinct real solutions does the given equation have?Hard · Advanced Math
  44. 44z 2 + 10 z - 24 = 0 What is one of the solutions to the given equation?Medium · Advanced Math
  45. 455 x 2 + 10 x + 16 = 0 How many distinct real solutions does the given equation have?Hard · Advanced Math
  46. 46If and are the two solutions to the system of equations above, what is the value of ?Hard · Advanced Math
  47. 47If , what is t in terms of u ?Hard · Advanced Math
  48. 48- 9 x 2 + 30 x + c = 0 In the given equation, c is a constant. The equation has exactly one solution. What is the value of c ?Hard · Advanced Math
  49. 49x 2 x 2 - c 2 = c 2 x 2 - c 2 + 39 In the given equation, c is a positive constant. Which of the following iHard · Advanced Math
  50. 508j=k+15m The given equation relates the distinct positive numbers j , k , and m . Which equation correctly expresses j in terms of k and m ?Easy · Advanced Math
  51. 518 x + y = -11 2 x 2 = y + 341 The graphs of the equations in the given system of equations intersect at the point (x , y ) in the x y -plane. WhatHard · Advanced Math
  52. 52The speed of sound in dry air, v, can be modeled by the formula , where T is the temperature in degrees Celsius and v is measured in meters per second. Which of the following correMedium · Advanced Math
  53. 53x x + 1 - 56 = 4 x x - 7 What is the sum of the solutions to the given equation?Hard · Advanced Math
  54. 54If is a solution to the system of equations above, which of the following is a possible value of x?Easy · Advanced Math
  55. 55p = 20 + 16 n The given equation relates the numbers p and n , where n is not equal to 0 and p>20. Which equation correctly expresses n in terms of p ?Medium · Advanced Math
  56. 56y=x-2x+4 y=6x-12 Which ordered pair x,y is the solution to the given system of equations?Medium · Advanced Math
  57. 5717b=11xy The given equation relates the positive numbers b , x , and y . Which equation correctly expresses x in terms of b and y ?Medium · Advanced Math
  58. 58In the xy-plane, the graph of intersects line p at and , where a and b are constants. What is the slope of line p ?Hard · Advanced Math
  59. 59Blood volume,, in a human can be determined using the equation , where is the plasma volume and H is the hematocrit (the fraction of blood volume that is red blood cells). Which ofMedium · Advanced Math
  60. 60-54w=6 What is the solution to the given equation?Medium · Advanced Math