Answer:
2 additional premium channels
Step-by-step explanation:
Using the given function, we substitute c(x) = 114 and solve for x:
114 =90 + 12x
Subtract 90 from both sides:
24=12x
Divide both sides by 12:
2=x
So you have ordered 2 additional premium channels.
Answer:
6
Step-by-step explanation:
Answer: 
Step-by-step explanation:
The equation of the line is Slope-intercept form is:

Where "m" is the slope and "b" the y-intercept.
The slopes of perpendicular lines are negative reciprocal.
Then, if the slope of the first line is -3, the slope of the other line must be:

Substitute the point (3,4) into the equation and solve for b:

Then the equation of this line is:

Answer:

Step-by-step explanation:
We are given:

![interval = [a,b] = [0,2]](https://tex.z-dn.net/?f=interval%20%3D%20%5Ba%2Cb%5D%20%3D%20%5B0%2C2%5D)
Since
⇒ 
Riemann sum is area under the function given. And it is asked to find Riemann sum for the left endpoint.

Note:
If it will be asked to find right endpoint too,

The average of left and right endpoint Riemann sums will give approximate result of the area under
and it can be compared with the result of integral of the same function in the interval given.
So, 

Result are close but not same, since one is approximate and one is exact; however, by increasing sample rates (subintervals), closer result to the exact value can be found.
Distance between points

and

is

Distance from H to B:
![[tex]d=\sqrt{(10-(-3))^2+(1-(-9))^2}=\sqrt{169+100}=\sqrt{269}](https://tex.z-dn.net/?f=%5Btex%5Dd%3D%5Csqrt%7B%2810-%28-3%29%29%5E2%2B%281-%28-9%29%29%5E2%7D%3D%5Csqrt%7B169%2B100%7D%3D%5Csqrt%7B269%7D)
d=\sqrt{(1-(-3))^2+(10-(-9))^2}=\sqrt{16+361}=\sqrt{376}[/tex] units.
Distance from Z to B:

units.
Horse Z is closer to the barn.
(The conversion to meters is not required; the question does not ask for actual distances, so "units" is OK.)