5. divide and simplify if possible. √250x16√2x 6. what is the solution of the equation? √2x+13−5=x

5.  (5x^7)√(5x)

6.  x = -2

Step-by-step explanation:

5.

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6.

There is always the possibility of extraneous solutions for equations like this. We can check.

  √(2·(-6)+13) -5 = -6 . . . . substitute -6 for x

  √1 -5 = -6 . . . . . . . . . . . . not true; -6 is an extraneous solution

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  √2·(-2)+13) -5 = -2

  √9 -5 = -2 . . . . . . . . . . . true; x = -2 is the solution

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The attached graph has the equation rewritten so it is of the form

  f(x) = 0

where

  f(x) = √(2x+13) -5 -x

The x-intercept is highlighted on the graph. It is x=-2. You can see that if the negative branch of the square root function were included, it might make an x-intercept at x=-6. For our purposes, the square root function is the positive square root only, so that branch is not included and -6 is an extraneous solution.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.