fredric leads a team of hikers for a full-day hike. the total elevation gain during the hike is 2,100 feet. all of the hikers have to pass two checkpoints before they reach the peak. the elevation gain from the starting point to checkpoint 1 is 100 feet less than double the elevation gain from checkpoint 2 to the peak. the elevation gain from checkpoint 1 to checkpoint 2 is the mean of the elevation gain from the start to checkpoint 1 and the elevation gain from checkpoint 2 to the peak. let x represent the elevation gain from the starting point to checkpoint 1, y represent the elevation gain from checkpoint 1 to checkpoint 2, and z represent the elevation gain from checkpoint 2 to the peak. which augmented matrices represent the context of this scenario?

  see below

Step-by-step explanation:

It's a matter of carefully reading the problem statement, formulating expressions that match the words, then rearranging those to matrix form.

Useful initial expressions might be ...

  x + y + z = 2100 . . . . . . the total elevation gain is 2100 ft

  x = 2z -100 . . . . . . . . . . the first leg is 100 ft less than twice the last

  y = (x +z)/2 . . . . . . . . . . the middle leg is the mean of the other two

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The second of these equations can be rewritten as ...

  -x + 2z = 100

The last of these equation can be rewritten as ...

  0.5x - y + 0.5z = 0

These forms together with the first of the equations above can be written as the augmented matrix below.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1