To the nearest tenth, what is the perimeter of the triangle with vertices at (−2, 3), (3, 6), and (2, −2)?

9514 1404 393

  20.3

Step-by-step explanation:

The distance formula can be used to find the side lengths.

  d = √((x2 -x1)^2 +(y2 -y1)^2)

For the first two points, ...

  d = √((3 -(-2))^2 +(6 -3)^2) = √(5^2 +3^2) = √34 ≈ 5.83

For the next two points, ...

  d = √((2 -3)^2 +(-2-6)^2) = √(1 +64) = √65 ≈ 8.06

For the last and first points, ...

  d = √((-2-2)^2 +(3-(-2)^2) = √(16 +25) = √41 ≈ 6.40

Then the sum of the side lengths is ...

  5.83 +8.06 +6.40 = 20.29 ≈ 20.3

The perimeter of the triangle is about 20.3 units.

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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