Answer:
$ 14.00
Step-by-step explanation:
10 · 1.75 = 17.50
17.50 · .20 = 3.5
17.50 - 3.50 = 14.00
good luck, i hope this helps :)
Recall the definition of absolute value.
![|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}](https://tex.z-dn.net/?f=%7Cx%7C%20%3D%20%5Cbegin%7Bcases%7D%20x%20%26%20%5Ctext%7Bif%20%7D%20x%20%5Cge%200%20%5C%5C%20-x%20%26%20%5Ctext%7Bif%20%7D%20x%20%3C%200%20%5Cend%7Bcases%7D)
When
,
![|x| = x \implies \dfrac{d|x|}{dx} = 1](https://tex.z-dn.net/?f=%7Cx%7C%20%3D%20x%20%5Cimplies%20%5Cdfrac%7Bd%7Cx%7C%7D%7Bdx%7D%20%3D%201)
When
,
![|x| = -x \implies \dfrac{d|x|}{dx} = -1](https://tex.z-dn.net/?f=%7Cx%7C%20%3D%20-x%20%5Cimplies%20%5Cdfrac%7Bd%7Cx%7C%7D%7Bdx%7D%20%3D%20-1)
The derivative does not exist at
, since the one-sided limits
![\displaystyle \lim_{x\to0^-} f'(x) = -1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%5Cto0%5E-%7D%20f%27%28x%29%20%3D%20-1)
and
![\displaystyle \lim_{x\to0^+} f'(x) = +1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%5Cto0%5E%2B%7D%20f%27%28x%29%20%3D%20%2B1)
do not match.
So the derivative of
is
![\dfrac{d|x|}{dx} = \begin{cases} 1 & \text{if } x > 0 \\ -1 & \text{if } x < 0 \\ \text{undefined} & \text{if } x = 0\end{cases}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7Cx%7C%7D%7Bdx%7D%20%3D%20%5Cbegin%7Bcases%7D%201%20%26%20%5Ctext%7Bif%20%7D%20x%20%3E%200%20%5C%5C%20-1%20%26%20%5Ctext%7Bif%20%7D%20x%20%3C%200%20%5C%5C%20%5Ctext%7Bundefined%7D%20%26%20%5Ctext%7Bif%20%7D%20x%20%3D%200%5Cend%7Bcases%7D)
Now we can write this as
![\dfrac{d|x|}{dx} = \dfrac x{|x|} = \dfrac{|x|}x](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7Cx%7C%7D%7Bdx%7D%20%3D%20%5Cdfrac%20x%7B%7Cx%7C%7D%20%3D%20%5Cdfrac%7B%7Cx%7C%7Dx)
since
![x > 0 \implies |x| = x \implies \dfrac{|x|}x = \dfrac xx = 1](https://tex.z-dn.net/?f=x%20%3E%200%20%5Cimplies%20%7Cx%7C%20%3D%20x%20%5Cimplies%20%5Cdfrac%7B%7Cx%7C%7Dx%20%3D%20%5Cdfrac%20xx%20%3D%201)
and
![x < 0 \implies |x| = -x \implies \dfrac{|x|}x = -\dfrac xx = -1](https://tex.z-dn.net/?f=x%20%3C%200%20%5Cimplies%20%7Cx%7C%20%3D%20-x%20%5Cimplies%20%5Cdfrac%7B%7Cx%7C%7Dx%20%3D%20-%5Cdfrac%20xx%20%3D%20-1)
Do you mean the hypotenuse of the triangle?
If so, you can use pythagorean theorem:
a^2 + b^2 = c^2
11^2 + 8^2 = c^2
121 + 64 = 185 = c^2
c = sqrt(185) = 13.6
Answer:
(a)They were treated like slaves.
Answer:
n < -11
Step-by-step explanation:
n + 7 < -4
n < -11 (subract 7 from both sides)