<h3>PLEASE FIND THE ATTACHED PHOTOGRAPH FOR THE FIGURE.</h3><h2><u>SOLUTION:</u></h2>
- Given, BD bisects Angle ABC.
- So, Angle ABD = Angle CBD
- Measure of Angle ABD = 9x-7
- Measure of Angle CBD = 6x+2
- Therefore,
Angle ABD = Angle CBD
or, 9x-7 = 6x+2
or, 9x-6x = 2+7
or, 3x = 9
or, x = 9 ÷ 3
or, x = 3
- So, x = 3
- Measure of Angle ABC
= Measure of Angle ABD + Measure of Angle CBD
= [(9x-7)+(6x+2)]°
= [(9×3-7)+(6×3+2)]°
= [27-7+18+2]°
= 40°
<h2><u>ANSWER</u><u>:</u></h2>
x = 3
Measure of Angle ABC = 40°.
Hope it helps you.
B. Y= x+ 48 trust me bro.
Given:
Consider the function is:
![f(x)=\dfrac{x^2}{3}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7Bx%5E2%7D%7B3%7D)
To find:
The average rate of change over the interval 2 ≤ x ≤ 4.
Solution:
We have,
![f(x)=\dfrac{x^2}{3}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7Bx%5E2%7D%7B3%7D)
At
,
![f(2)=\dfrac{2^2}{3}](https://tex.z-dn.net/?f=f%282%29%3D%5Cdfrac%7B2%5E2%7D%7B3%7D)
![f(2)=\dfrac{4}{3}](https://tex.z-dn.net/?f=f%282%29%3D%5Cdfrac%7B4%7D%7B3%7D)
At
,
![f(4)=\dfrac{4^2}{3}](https://tex.z-dn.net/?f=f%284%29%3D%5Cdfrac%7B4%5E2%7D%7B3%7D)
![f(4)=\dfrac{16}{3}](https://tex.z-dn.net/?f=f%284%29%3D%5Cdfrac%7B16%7D%7B3%7D)
The average rate of change of a function f(x) over the interval [a,b] is:
![m=\dfrac{f(b)-f(a)}{b-a}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D)
So, the average rate of change over the interval 2 ≤ x ≤ 4 is:
![m=\dfrac{f(4)-f(2)}{4-2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7Bf%284%29-f%282%29%7D%7B4-2%7D)
![m=\dfrac{\dfrac{16}{3}-\dfrac{4}{3}}{2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B%5Cdfrac%7B16%7D%7B3%7D-%5Cdfrac%7B4%7D%7B3%7D%7D%7B2%7D)
![m=\dfrac{\dfrac{16-4}{3}}{2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B%5Cdfrac%7B16-4%7D%7B3%7D%7D%7B2%7D)
On further simplification, we get
![m=\dfrac{12}{3\times 2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B12%7D%7B3%5Ctimes%202%7D)
![m=\dfrac{12}{6}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B12%7D%7B6%7D)
![m=2](https://tex.z-dn.net/?f=m%3D2)
Therefore, the average rate of change over the interval 2 ≤ x ≤ 4 is 2.