Find the length of side x in the simplest radical form with a rational denominator

Step-by-step explanation:

Recognize that this is a 30-60-90 triangle.  

Write and solve an equation of ratios:

 x         1

= (which is the tangent of 30°)

√2       √3  

Then √3*x = √2, and so:

       √2

x =

        √3

Rationalize this as follows:  

      √2*√3        √6

x = =

            3-            3

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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step-by-step explanation:

both graphs increase on their domain

neither graph has a y-intercept

step-by-step explanation:

the following points can be visualized easily from the graph