Answer:
maybe it's D ( not sure tho)
<span>The
sales tax in New Jersey is 6%. For a $16 book, what will the total cost be,
including sales tax?
Solutions:
=> 16 dollars is the amount of book
=> 6% is the sales tax which is equals to (6% / 100% = 0.06)
Let’s follow the formula to get the total amount to be paid.
=> 16 dollars * .06 = .96 dollars
Now, let’s add this together:
=> .96 + 16 dollars = 16.96 dollars.</span>
Given:
Consider the given function:
![f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot(x-b)}{a-b}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7Bb%5Ccdot%28x-a%29%7D%7Bb-a%7D%2B%5Cdfrac%7Ba%5Ccdot%28x-b%29%7D%7Ba-b%7D)
To prove:
![f(a)+f(b)=f(a+b)](https://tex.z-dn.net/?f=f%28a%29%2Bf%28b%29%3Df%28a%2Bb%29)
Solution:
We have,
![f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot (x-b)}{a-b}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7Bb%5Ccdot%28x-a%29%7D%7Bb-a%7D%2B%5Cdfrac%7Ba%5Ccdot%20%28x-b%29%7D%7Ba-b%7D)
Substituting
, we get
![f(a)=\dfrac{b\cdot(a-a)}{b-a}+\dfrac{a\cdot (a-b)}{a-b}](https://tex.z-dn.net/?f=f%28a%29%3D%5Cdfrac%7Bb%5Ccdot%28a-a%29%7D%7Bb-a%7D%2B%5Cdfrac%7Ba%5Ccdot%20%28a-b%29%7D%7Ba-b%7D)
![f(a)=\dfrac{b\cdot 0}{b-a}+\dfrac{a}{1}](https://tex.z-dn.net/?f=f%28a%29%3D%5Cdfrac%7Bb%5Ccdot%200%7D%7Bb-a%7D%2B%5Cdfrac%7Ba%7D%7B1%7D)
![f(a)=0+a](https://tex.z-dn.net/?f=f%28a%29%3D0%2Ba)
![f(a)=a](https://tex.z-dn.net/?f=f%28a%29%3Da)
Substituting
, we get
![f(b)=\dfrac{b\cdot(b-a)}{b-a}+\dfrac{a\cdot (b-b)}{a-b}](https://tex.z-dn.net/?f=f%28b%29%3D%5Cdfrac%7Bb%5Ccdot%28b-a%29%7D%7Bb-a%7D%2B%5Cdfrac%7Ba%5Ccdot%20%28b-b%29%7D%7Ba-b%7D)
![f(b)=\dfrac{b}{1}+\dfrac{a\cdot 0}{a-b}](https://tex.z-dn.net/?f=f%28b%29%3D%5Cdfrac%7Bb%7D%7B1%7D%2B%5Cdfrac%7Ba%5Ccdot%200%7D%7Ba-b%7D)
![f(b)=b+0](https://tex.z-dn.net/?f=f%28b%29%3Db%2B0)
![f(b)=b](https://tex.z-dn.net/?f=f%28b%29%3Db)
Substituting
, we get
![f(a+b)=\dfrac{b\cdot(a+b-a)}{b-a}+\dfrac{a\cdot (a+b-b)}{a-b}](https://tex.z-dn.net/?f=f%28a%2Bb%29%3D%5Cdfrac%7Bb%5Ccdot%28a%2Bb-a%29%7D%7Bb-a%7D%2B%5Cdfrac%7Ba%5Ccdot%20%28a%2Bb-b%29%7D%7Ba-b%7D)
![f(a+b)=\dfrac{b\cdot (b)}{b-a}+\dfrac{a\cdot (a)}{-(b-a)}](https://tex.z-dn.net/?f=f%28a%2Bb%29%3D%5Cdfrac%7Bb%5Ccdot%20%28b%29%7D%7Bb-a%7D%2B%5Cdfrac%7Ba%5Ccdot%20%28a%29%7D%7B-%28b-a%29%7D)
![f(a+b)=\dfrac{b^2}{b-a}-\dfrac{a^2}{b-a}](https://tex.z-dn.net/?f=f%28a%2Bb%29%3D%5Cdfrac%7Bb%5E2%7D%7Bb-a%7D-%5Cdfrac%7Ba%5E2%7D%7Bb-a%7D)
![f(a+b)=\dfrac{b^2-a^2}{b-a}](https://tex.z-dn.net/?f=f%28a%2Bb%29%3D%5Cdfrac%7Bb%5E2-a%5E2%7D%7Bb-a%7D)
Using the algebraic formula, we get
![[\because b^2-a^2=(b-a)(b+a)]](https://tex.z-dn.net/?f=%5B%5Cbecause%20b%5E2-a%5E2%3D%28b-a%29%28b%2Ba%29%5D)
![f(a+b)=b+a](https://tex.z-dn.net/?f=f%28a%2Bb%29%3Db%2Ba)
[Commutative property of addition]
Now,
![LHS=f(a)+f(b)](https://tex.z-dn.net/?f=LHS%3Df%28a%29%2Bf%28b%29)
![LHS=a+b](https://tex.z-dn.net/?f=LHS%3Da%2Bb)
![LHS=f(a+b)](https://tex.z-dn.net/?f=LHS%3Df%28a%2Bb%29)
![LHS=RHS](https://tex.z-dn.net/?f=LHS%3DRHS)
Hence proved.
Answer:
I think the answer is y = 3x + 12.
Step-by-step explanation:
y = 3 (x - 1) (x - 4)
y = 3x -3 (x - 4)
y = 3x + 12
Answer:
x=6 2/5
Step-by-step explanation:
I don't know how to explain other than doing the math of (x*5)/2=16