Please Help M, Amanda's house is due west of Stamford and due south of Newport. Stamford is 12 kilometers from Amanda's house and 13 kilometers from Newport. How far is Newport from Amanda's house, measured in a straight line? kilometers

  5 km

Step-by-step explanation:

It helps to draw a diagram.

The triangle between Stamford, Newport, and Amanda's house is a right triangle with one leg of length 12 and hypotenuse 13. The Pythagorean theorem can be used to find the remaining leg:

  13² = 12² + (distance to Newport)²

  169 -144 = (distance to Newport)²

  √25 = 5 = distance to Newport

Newport is 5 km from Amanda's house.

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It can be useful to remember this right triangle. 5-12-13 right triangles show up in a number of algebra and geometry problems.

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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