Zack has two strings of equal length. one string is red the other is yellow. after cutting 2.5 meters of the red string and 3.8 m of the yellow string, the length of the red string is 1.5 times that of the yellow strain. find the original length of the yellow string.

6.4 m

Step-by-step explanation:

We have 2 expressions here.  The first one is the fact that r = y.  That's one of 2 equations.  The second one involves whats' left after cutting off certain lengths of each color string.  We cut 2.5 m from red, we cut 3.8 m from yellow.  We know that what's left of red is 1.5 times the length of what's left of yellow.  What's left of red is r - 2.5; what's left of yellow is y - 3.8.  We know that r = 1.5y, so filling that in with our corresponding expressions gives us

r - 2.5 = 1.5(y - 3.8)

Distribute to get

r - 25 = 1.5y - 3.2

Now from the first expression, r = y, so fill in y for r to get an equation in one variable:

y - 2.5 = 1.5y - 3.2

Combine like terms:

-.5y = -3.2 and divide to get

y = 6.4

Check it to make sure it works.  What's left of red should be 1.5 times the length of what's left of yellow and y = 6.4:

What's left of red: 6.4 - 2.5 = 3.9

What's left of yellow: 6.4 - 3.8 = 2.6

1.5 x 2.6 = 3.9, just like it should!

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1