Plz im really in trouble with thisfind the equation of another tangent to which is parallel to the tangent at (1,2)

I'm just going to take a dab at this.  I haven't done calculus in years.

So you found the equation of the tangent line for your equation at the point (1,2) which is:
y = 5 - 3x

Which is correct and all, but the question seems to be asking for "another tangent", so we are looking for another tangent line that is parallel to:
y = 5 - 3x

So we know that the equation of this line must also have a slope of "-3".

So if it must have a slope of "-3", then it must follow that:

-3 = -3 + 24x - 24x²

I got the above from setting our derivative equation equal to -3.

So if we solve the above equation we get:

24x - 24x² = 0
24x(1 - x) = 0

So "x" must be equal to 0 or 1. (These are the two points that have a slope of -3)
And since we already know about the point x = 1, we are interested in the point x = 0.  So from our original equation the point x = 0 has a y-value of 1, therefore we have the point (0,1).  Finally, we just need to find the equation of the line that has a slope of -3 and contains the point (0,1).

I'm sure you can do this part on your own.  The equation of that line is:

y = -3x +1
or
y = 1 - 3x (as you pointed out)

Whew, that was a nice refresher.  :)

I hope that was easy to follow!

Do the math. she originally had 50 dollars on her gift card and she had 12 dollars left on her gift card after she finished her shopping spree. if you subtract 50 minus 12 you get thirty eight dollars as your answer. so therefore, ciara spent 38 dollars total o