Apiece of yellow yarn was 230 inches long. after 90 inches had een cut from the piece of yellow yarn was twice as longas a piece of blue yarn. how much longer  than the blue yarn was the yellow yarn at first?  

160 inches longer.

Step-by-step explanation:

Let x represent the length of the blue yarn.

We have been given that a piece of yellow yarn was 230 inches long. After 90 inches had been cut from it, the piece of yellow yarn was twice as long as a piece of blue yarn.

Twice the length of blue yarn would be .

We can represent this information in an equation as:  

Therefore, the length of blue yarn is 70 inches long.

Now, we will subtract 70 from 230 as:

Therefore, the yellow yarn was 160 inches longer than the blue yarn.

b or 2, just plug these equations into your graphing calculator then check the graph to see the image. if it matches up then that's your answer!

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this