Answer:
This is easy -- it's just a list of steps. At this level, the problems are pretty simple.
Let's just do one, then I'll write out the list of steps for you.
Find the inverse of f( x ) = -( 1 / 3 )x + 1
STEP 1: Stick a "y" in for the "f(x)" guy:
y = -( 1 / 3 )x + 1
STEP 2: Switch the x and y
( because every (x, y) has a (y, x) partner! ):
x = -( 1 / 3 )y + 1
STEP 3: Solve for y:
x = -( 1 / 3 )y + 1 ... multiply by 3 to ditch the fraction ... 3x = -y + 3 ... ditch the +3 ... subtract 3 from both sides ... 3x - 3 = -y ... multiply by -1 ... -3x + 3 = y ... y = -3x + 3
STEP 4: Stick in the inverse notation, f^( -1 )( x )
f^( -1 )( x ) = -3x + 3
Step-by-step explanation:
Hello, we need to see it as a difference of two squares as we know that for all a and b real numbers
![a^2-b^2=(a-b)(a+b)](https://tex.z-dn.net/?f=a%5E2-b%5E2%3D%28a-b%29%28a%2Bb%29)
So, here
![9x^2-4=(3x)^2-2^2=(3x-2)(3x+2)](https://tex.z-dn.net/?f=9x%5E2-4%3D%283x%29%5E2-2%5E2%3D%283x-2%29%283x%2B2%29)
Voila !
Thank you
Answer:
d = ![\frac{7}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B2%7D)
Step-by-step explanation:
The nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₉ = 16 , then
- 12 + 8d = 16 ( add 12 to both sides )
8d = 28 ( divide both sides by 8 )
d =
= ![\frac{7}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B2%7D)
slope is -1
![m=-1](https://tex.z-dn.net/?f=%20m%3D-1%20)
we have a point as (-4,3)
we can use slope intercept form of line
![y=mx+b](https://tex.z-dn.net/?f=%20y%3Dmx%2Bb%20)
we can plug m=-1
![y=-x+b](https://tex.z-dn.net/?f=%20y%3D-x%2Bb%20)
now, we can plug point (-4,3)
x=-4 and y=3 and then we can find b
![3=-1*-4+b](https://tex.z-dn.net/?f=%203%3D-1%2A-4%2Bb%20)
![b=-1](https://tex.z-dn.net/?f=%20b%3D-1%20)
now, we can plug back
and we get
............Answer