![\huge\text{$m\angle O=\boxed{11^{\circ}}$}](https://tex.z-dn.net/?f=%5Chuge%5Ctext%7B%24m%5Cangle%20O%3D%5Cboxed%7B11%5E%7B%5Ccirc%7D%7D%24%7D)
Since we know that all angles in a triangle add up to
, we can solve for
and substitute it back into
to find
.
![\begin{aligned}m\angle N+m\angle O+m\angle P&=180\\(5x-8)+(x-5)+(6x+1)&=180\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%5Cangle%20N%2Bm%5Cangle%20O%2Bm%5Cangle%20P%26%3D180%5C%5C%285x-8%29%2B%28x-5%29%2B%286x%2B1%29%26%3D180%5Cend%7Baligned%7D)
Remove the parentheses and combine like terms.
![\begin{aligned}5x-8+x-5+6x+1&=180\\(5x+x+6x)+(-8-5+1)&=180\\12x-12&=180\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D5x-8%2Bx-5%2B6x%2B1%26%3D180%5C%5C%285x%2Bx%2B6x%29%2B%28-8-5%2B1%29%26%3D180%5C%5C12x-12%26%3D180%5Cend%7Baligned%7D)
Add
to both sides of the equation.
![\begin{aligned}12x-12&=180\\12x&=192\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D12x-12%26%3D180%5C%5C12x%26%3D192%5Cend%7Baligned%7D)
Divide both sides of the equation by
.
![\begin{aligned}x=16\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dx%3D16%5Cend%7Baligned%7D)
Now that we have the value of
, we can substitute it back into
to find
.
![\begin{aligned}m\angle O&=(x-5)\\&=16-5\\&=\boxed{11}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%5Cangle%20O%26%3D%28x-5%29%5C%5C%26%3D16-5%5C%5C%26%3D%5Cboxed%7B11%7D%5Cend%7Baligned%7D)
That's the derivative at 2 so is going to be 2(2)+1=5, second choice, but let's do it the hard way.
![\displaystyle \lim_{h \to 0} \dfrac{f(2+h)-f(2)}{h} = \lim_{h \to 0} \dfrac{(2+h)^2 + (2+h) + 1 -(2^2 + 2 + 1)}{h}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cdfrac%7Bf%282%2Bh%29-f%282%29%7D%7Bh%7D%20%3D%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cdfrac%7B%282%2Bh%29%5E2%20%2B%20%282%2Bh%29%20%2B%201%20-%282%5E2%20%2B%202%20%2B%201%29%7D%7Bh%7D)
![\displaystyle =\lim_{h \to 0} \dfrac{4 + 4h +h^2 +h-4}{h}=\lim_{h \to 0} \dfrac{h^2 +5h}{h} = \lim_{h \to 0} h+5 = 5](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%3D%5Clim_%7Bh%20%5Cto%200%7D%20%5Cdfrac%7B4%20%2B%204h%20%2Bh%5E2%20%2Bh-4%7D%7Bh%7D%3D%5Clim_%7Bh%20%5Cto%200%7D%20%5Cdfrac%7Bh%5E2%20%2B5h%7D%7Bh%7D%20%3D%20%5Clim_%7Bh%20%5Cto%200%7D%20h%2B5%20%3D%205)
Answer: 5, second choice
$65 I believe because 6 times 15 is 90 and 90 divided by 36 (inches=yard) is 2.5 and 2.5 time $26 is $60
Answer:
a) ![\frac{d-5.50}{0.45}](https://tex.z-dn.net/?f=%5Cfrac%7Bd-5.50%7D%7B0.45%7D)
b) The inverse function is a reflection of the original function across the line
y = x. For example, if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x. So you would use it to find the x-value at a y just like you use the original to find the y value at an x.
Step-by-step explanation:
To do an inverse of a function you first switch the independent variable (d) and the dependent variable (c).
d = 0.45c + 5.50
Then you solve for c
d - 5.50 = 0.45 c
c = (d-5.50)/0.45
The asymptotes are in the picture