Solve for e
d = 1/e + 1/f
Move 1/f to the left side of the = sign
d - 1/f = 1/e
Multiply each side by e
e(d - 1/f) = e(1/e)
e(d - 1/f) = 1
Divide out (d - 1/f)
e(d - 1/f) / (d - 1/f) = 1 / (d - 1/f)
e = 1 / (d - 1/f)
To expand two terms such as these, we can use the method called FOIL (stands for First, Outer, Inner, Last). Here is what I mean:
We have two terms: (x - 2)(x - 1)
We should first multiply the First two terms of each term in order to complete the F stage:
(x)*(x) =

So then, we take the two outer terms and multiply them together to complete the O stage:
(x)*(-1) = -x
So far we have two things that we have calculated; at the end of the FOIL process we will have four.
To keep going with the FOIL, we now multiply the two inner terms to complete the I stage:
(-2)*(x) = -2x
Last but not least, we need to complete the L stage - so we multiply the two last terms of each term:
(-2)*(-1) = 2
Now that we have our four terms, let us add them together and combine like terms:

Since -x and -2x both have the x portion in common and they are added together, we can add them to create one single term:
-x + (-2x) = -3x
So now that we have our terms completed, we can combine into one polynomial equation:

or
Step-by-step explanation:
here,,
a=3,b=10,C=120°
c^2=a^2+b^2-2ab cos120°
=(3)^2 +(10)^2 _2 (3)(10)(-1/2) [cos120°=-1/2]
=9+100-(-30)
=109+30
=139
c=(139 )1/2=11.79
c=12
Answer:
a) The graph shifted to the left by 3 units and up 1 unit.
b) Domain = x ∈ R Range = y ∈ R
(Domain (x) = All real numbers Range (y) = All real numbers)
c) (-4, 0)
d) (0, 2.442)
~Hope this helps! If you have any questions, please let me know!~