The denominator of a fraction is three more than twice the numerator. if both the numerator and denominator are decreased by one, the simplified result is 7/16. find the original fraction

15/33

Step-by-step explanation:

Let x represent the numerator of the original fraction. Then that fraction is ...

... x/(2x+3)

Decreasing numerator and denominator by 1 gives ...

... (x-1)/(2x +3 -1) = 7/16

Multiplying by the product of the denominators, we get ...

... 16(x -1) = 7(2x +2)

... 16x -16 = 14x +14 . . . . eliminate parentheses

... 2x = 30 . . . . . . . . . . . add 16-14x

... x = 15 . . . . . . . . . . . . divide by 2

And the original fraction is

... 15/(2·15+3) = 15/33

54 km / hours

step-by-step explanation:

we need to convert seconds to hours

60 seconds = 1 minutes

60 minutes = 1hour

15 m         60 second   60 minutes

  * *         = 54000 meters/ hour

second     1 minute             1 hour

now we need to convert meters to km

1000 m = 1 km

54000 m       1 km

*   = 54 km / hours

hour               1000m

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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rauschg

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