E^2x -2e^x -8=0 => e<span>^(2x) -2e^x -8=0
Temporarily replace e^x with y.
Then (y)^2 - 2y - 8 = 0. Factors are (y-4) and (y+2).
Roots are y = 4 and y= -2.
Now remembering that we temporarily replaced e^x with y, we let
y=4 = e^x. We need to solve for x. Taking the natural log of both sides, we get:
ln 4 = x (answer)
We have to discard the other root (y= -2), because we cannot take the ln of a negative number.
</span>
Answer:
(4x+1)-(3x-4)=
4x-3x+1-4=
x-3
Step-by-step explanation:
Find the GCF (Greatest Common Factor)
GCF = 3
Factor out the GCF ( Write the GCF first. Then, in parentheses, divide each term by the GCF)
3(3x^2/3 + -12x/3 - 15/3)
Simplify each term in parentheses
3(x^2 - 4x - 5)
Factor x^2 - 4x - 5
<u>3(x - 5)(x + 1)</u>
Small triangle: <span>The side // x axis has a length of 4
Large triangle: The side // x axis has a length of 12
So Small/Large = 4/12 = 1/3
Small triangle: <span>The side // y axis has a length of 3
Large triangle: The side // y axis has a length of 9
</span><span>So Small/Large = 3/9 = 1/3
So the scale factor to obtain this dilatation is 1/3</span>
</span>
