What two numbers multiply to negative 12 and add up to negative 13

  −13.8654599313 and 0.8654599313

Step-by-step explanation:

The two numbers of interest will be the solutions to ...

  xy = -12

  x +y = -13

Substituting for y, this becomes the quadratic ...

  x(-13 -x) = -12

  x^2 +13x = 12 . . . . . multiply by -1

  x^2 +13x +6.5^2 = 12 +6.5^2 . . . . . complete the square

  (x +6.5)^2 = 54.25

  x = -6.5 ± √54.25 . . . . . . take the square root, subtract 6.5

  x ≈ -13.865499313 or 0.8654599313

The value of y is the other of these two numbers. So, the two numbers of interest are {-13.865499313, 0.8654599313}.

answer: 177/8

step-by-step explanation:

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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