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Linear Equations in One Variable

Math · Algebra · 65 questions · every one comes with a full explanation.

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  1. 1Hector used a tool called an auger to remove corn from a storage bin at a constant rate. The bin contained 24,000 bushels of corn when Hector began to use the auger. After 5 hours Hard · Algebra
  2. 224-x+34-x=25 What is the positive solution to the given equation?Hard · Advanced Math
  3. 3x 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
  4. 4In 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
  5. 5Which ordered pair is a solution to the system of equations above?Hard · Advanced Math
  6. 6If x is a solution to the given equation, which of the following is a possible value of ?Hard · Advanced Math
  7. 7During 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
  8. 8Which of the following is a solution to the equation above?Hard · Advanced Math
  9. 9In 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
  10. 10Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5.Hard · Algebra
  11. 11x - 2 2 = 3 x + 34 What is the smallest solution to the given equation?Hard · Advanced Math
  12. 12How many solutions does the equation 1015x-9=-156-10x have?Hard · Algebra
  13. 1357x2+(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
  14. 14- 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
  15. 15If 3 x 2 - 18 x - 15 = 0 , what is the value of x 2 - 6 x ?Hard · Advanced Math
  16. 163(kx+13)= 48 17 x + 36 In the given equation, k is a constant. The equation has no solution. What is the value of k ?Hard · Algebra
  17. 17In 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
  18. 18x 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
  19. 1914x7y=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
  20. 20What is the solution set of the equation above?Hard · Advanced Math
  21. 21The 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
  22. 22x 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
  23. 23- 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
  24. 24x - 1 2 = -4 How many distinct real solutions does the given equation have?Hard · Advanced Math
  25. 25A certain product costs a company $65 to make. The product is sold by a salesperson who earns a commission that is equal to 20% of the sales price of the product. The profit the coHard · Algebra
  26. 265 x 2 + 10 x + 16 = 0 How many distinct real solutions does the given equation have?Hard · Advanced Math
  27. 27If and are the two solutions to the system of equations above, what is the value of ?Hard · Advanced Math
  28. 28If , what is t in terms of u ?Hard · Advanced Math
  29. 29- 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
  30. 302kx-n= - 28 15 x - 36 19 In the given equation, k and n are constants and n>1. The equation has no solution. What is the value of k ?Hard · Algebra
  31. 31x 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
  32. 328 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
  33. 335(t+3)-7(t+3)=38 What value of t is the solution to the given equation?Hard · Algebra
  34. 34x x + 1 - 56 = 4 x x - 7 What is the sum of the solutions to the given equation?Hard · Advanced Math
  35. 35The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the coHard · Algebra
  36. 36In 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
  37. 37Each side of a 30 -sided polygon has one of three lengths. The number of sides with length 8 centimeters cm is 5 times the number of sides n with length 3 cm. There are 6 sides Hard · Algebra
  38. 38The 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
  39. 39x-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
  40. 40-3x+21px=84 In the given equation, p is a constant. The equation has no solution. What is the value of p ?Hard · Algebra
  41. 41y = 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
  42. 42If x+63=x+613, the value of x+6 is between which of the following pairs of values?Hard · Algebra
  43. 43In the xy-plane, the graph of intersects the graph of at the points and . What is the value of a ?Hard · Advanced Math
  44. 4464x2-16a+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
  45. 45x 2 - 40 x - 10 = 0 What is the sum of the solutions to the given equation?Hard · Advanced Math
  46. 46How many solutions are there to the system of equations above?Hard · Advanced Math
  47. 47What value of x satisfies the equation above?Hard · Advanced Math
  48. 4864 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
  49. 49The equation , where a and b are constants, has no solutions. Which of the following must be true? I. II. III.Hard · Algebra
  50. 50y = -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
  51. 51A science teacher is preparing the 5 stations of a science laboratory. Each station will have either Experiment A materials or Experiment B materials, but not both. Experiment A reHard · Algebra
  52. 52In 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
  53. 53x 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