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Nonlinear Equations

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

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  1. 124-x+34-x=25 What is the positive solution to the given equation?Hard · Advanced Math
  2. 2x 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
  3. 3In 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
  4. 4Which ordered pair is a solution to the system of equations above?Hard · Advanced Math
  5. 5If x is a solution to the given equation, which of the following is a possible value of ?Hard · Advanced Math
  6. 6During 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
  7. 7Which of the following is a solution to the equation above?Hard · Advanced Math
  8. 8In 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
  9. 9x - 2 2 = 3 x + 34 What is the smallest solution to the given equation?Hard · Advanced Math
  10. 1057x2+(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
  11. 11- 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
  12. 12If 3 x 2 - 18 x - 15 = 0 , what is the value of x 2 - 6 x ?Hard · Advanced Math
  13. 13In 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
  14. 14x 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
  15. 1514x7y=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
  16. 16What is the solution set of the equation above?Hard · Advanced Math
  17. 17The 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
  18. 18x 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
  19. 19- 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
  20. 20x - 1 2 = -4 How many distinct real solutions does the given equation have?Hard · Advanced Math
  21. 215 x 2 + 10 x + 16 = 0 How many distinct real solutions does the given equation have?Hard · Advanced Math
  22. 22If and are the two solutions to the system of equations above, what is the value of ?Hard · Advanced Math
  23. 23If , what is t in terms of u ?Hard · Advanced Math
  24. 24- 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
  25. 25x 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
  26. 268 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
  27. 27x x + 1 - 56 = 4 x x - 7 What is the sum of the solutions to the given equation?Hard · Advanced Math
  28. 28In 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
  29. 29The formula above can be used to approximate the dew point D, in degrees Fahrenheit, given the temperature T, in degrees Fahrenheit, and the relative humidity of H percent, where .Hard · Advanced Math
  30. 30x-29=x-ax-29 Which of the following are solutions to the given equation, where a is a constant and a>30? a a + 1 29Hard · Advanced Math
  31. 31y = 2 x 2 - 21 x + 64 y = 3 x + a In the given system of equations, a is a constant. The graphs of the equations in the given system interHard · Advanced Math
  32. 32In the xy-plane, the graph of intersects the graph of at the points and . What is the value of a ?Hard · Advanced Math
  33. 3364x2-16a+4bx+ab=0 In the given equation, a and b are positive constants. The sum of the solutions to the given equation is  k4a+b, where k is a constant. What is the value of kHard · Advanced Math
  34. 34x 2 - 40 x - 10 = 0 What is the sum of the solutions to the given equation?Hard · Advanced Math
  35. 35How many solutions are there to the system of equations above?Hard · Advanced Math
  36. 36What value of x satisfies the equation above?Hard · Advanced Math
  37. 3764 x 2 + b x + 25 = 0 In the given equation, b is a constant. For which of the following values of b will the equation have more than one real solution?Hard · Advanced Math
  38. 38y = -1.50 y = x 2 + 8 x + a In the given system of equations, a is a positive constant. The system has exactly one distinct real solution. What is the valHard · Advanced Math
  39. 39In the xy-plane, the graph of the equation y = - x 2 + 9 x - 100 intersects the line y = c at exactly one point. What is the value of c ?Hard · Advanced Math
  40. 40x 2 + y + 7 = 7 20x+100-y=0 The solution to the given system of equations is x,y. What is the value of x ?Hard · Advanced Math