The average value of a continuous function f(x) over an interval [a, b] is
![\displaystyle f_{\mathrm{ave}[a,b]} = \frac1{b-a}\int_a^b f(x)\,dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f_%7B%5Cmathrm%7Bave%7D%5Ba%2Cb%5D%7D%20%3D%20%5Cfrac1%7Bb-a%7D%5Cint_a%5Eb%20f%28x%29%5C%2Cdx)
We're given that
![\displaystyle f_{\rm ave[-1,2]} = \frac13 \int_{-1}^2 f(x) \, dx = -4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f_%7B%5Crm%20ave%5B-1%2C2%5D%7D%20%3D%20%5Cfrac13%20%5Cint_%7B-1%7D%5E2%20f%28x%29%20%5C%2C%20dx%20%3D%20-4)
![\displaystyle f_{\rm ave[2,7]} = \frac15 \int_2^7 f(x) \, dx = 8](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f_%7B%5Crm%20ave%5B2%2C7%5D%7D%20%3D%20%5Cfrac15%20%5Cint_2%5E7%20f%28x%29%20%5C%2C%20dx%20%3D%208)
and we want to determine
![\displaystyle f_{\rm ave[-1,7]} = \frac18 \int_{-1}^7 f(x) \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f_%7B%5Crm%20ave%5B-1%2C7%5D%7D%20%3D%20%5Cfrac18%20%5Cint_%7B-1%7D%5E7%20f%28x%29%20%5C%2C%20dx)
By the additive property of definite integration, we have
so it follows that
![\displaystyle f_{\rm ave[-1,7]} = \frac18 \left(\int_{-1}^2 f(x)\,dx + \int_2^7 f(x)\,dx\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f_%7B%5Crm%20ave%5B-1%2C7%5D%7D%20%3D%20%5Cfrac18%20%5Cleft%28%5Cint_%7B-1%7D%5E2%20f%28x%29%5C%2Cdx%20%2B%20%5Cint_2%5E7%20f%28x%29%5C%2Cdx%5Cright%29)
![\displaystyle f_{\rm ave[-1,7]} = \frac18 \left(3\times(-4) + 5\times8\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f_%7B%5Crm%20ave%5B-1%2C7%5D%7D%20%3D%20%5Cfrac18%20%5Cleft%283%5Ctimes%28-4%29%20%2B%205%5Ctimes8%5Cright%29)
![\displaystyle f_{\rm ave[-1,7]} = \boxed{\frac72}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f_%7B%5Crm%20ave%5B-1%2C7%5D%7D%20%3D%20%5Cboxed%7B%5Cfrac72%7D)
Answer:
angle a is 116 degrees
Step-by-step explanation:
ok so first we have to make everything equal to 180 because every triangle is 180 degrees so it would be written like this:
(14x + 4) + (5x - 1) + (2x + 9) = 180
Then, we solve for x and x equals 8
After this we plug 8 back into the angle so it would be written like this:
14(8) + 4
This equals 116 degrees.
one of the properties of a cyclic quad (four sided shape in eucliean geometry) is that the opposite sides add up to 180°
So in this case to get x we= 180°-105°=285°
therefore x is 285°
Answer:
Step-by-step explanation:
As square root value is written with both + and - signs
In Given case:
A polynomial has root 
= ±3.316
Also
= ±3.316
Hence is also root of the polynomial!
Just subisute values that will work
one easy way is to make one sides equal to only one of the placeholders, like y, and then lug in values in for x exg
x+2y=3
subtract x from both sides
2y=3-x
divideb bith sides by 2
y=-1/2x+3
subsitute valudes for x and get values for y
if x=2 then
y=-1/2(2)+3
y==-1+3
y=2
when x=2, y=2
when y=0 then y=3
