Arectangle with constant area has possible lengths and widths as shown in the table below. width vs. length of a rectangle width (w) length (l) 2 37.5 4 18.75 6 12.5 8 9.375 which equation can be used to find any corresponding length and width that fits the pattern in this table?

Given: A rectangle with constant area has possible lengths and width as shown in the given table.

Inverse variation states that a relationship between two variables in which the product is a constant.

If one variable increases,  the other decreases in proportion so that the product is unchanged.

i.e, if b is inversely proportional to a i.e, , the equation is of the form

 or ab = k , where k is constant of variation.

As, you can see from the table as width(w) increases, the length decreases so ,it is an inverse variation.

By area of rectangle formula: where l is the length and w is the width respectively;

Since, Area is constant i.e,

  ....

Therefore, the equation which is used to find any corresponding length and width that fits the pattern in this table is:    or lw = k ; where k is the constant area.

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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