<span>Clear out any fractions by Multiplying every term by the bottom parts.Add or Subtract the same value from both sides.Divide every term by the same nonzero value.Combine Like Terms.Factoring.<span>Expanding (the opposite of factoring) may also help.
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The angles are vertically opposite,
therefore,
9x + 22 + 130 = 180
9x + 152 = 180
9x = 180 - 152
9x = 28
![x = \frac{28}{9}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B28%7D%7B9%7D%20)
![x = 3 \frac{1}{9}](https://tex.z-dn.net/?f=x%20%3D%203%20%5Cfrac%7B1%7D%7B9%7D%20)
To find x, replace y as 0 and solve. To find y, replace x with 0 and solve.
Data:
x: number of months
y: tree's height
Tipical grow: 0.22
Fifteen months into the observation, the tree was 20.5 feet tall: x=15 y=20.5ft (15,20.5)
In this case the slope (m) or rate of change is the tipical grow.
m=0.22
To find the line's slope-intercep equation you use the slope (m) and the given values of x and y (15 , 20.5) in the next formula to find the y-intercept (b):
![\begin{gathered} y=mx+b \\ 20.5=0.22(15)+b \\ 20.5=3.3+b \\ 20.5-3.3=b \\ 17.2=b \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3Dmx%2Bb%20%5C%5C%2020.5%3D0.22%2815%29%2Bb%20%5C%5C%2020.5%3D3.3%2Bb%20%5C%5C%2020.5-3.3%3Db%20%5C%5C%2017.2%3Db%20%5Cend%7Bgathered%7D)
Use the slope(m) and y-intercept (b) to write the equation:
![\begin{gathered} y=mx+b \\ \\ y=0.22x+17.2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3Dmx%2Bb%20%5C%5C%20%20%5C%5C%20y%3D0.22x%2B17.2%20%5Cend%7Bgathered%7D)
A) This line's slope-intercept equation is: y=0.22x+17.2
B) To find the height of the tree after 29 months you substitute in the equation the x for 29 and evaluate to find the y:
![\begin{gathered} y=0.22(29)+17.2 \\ y=6.38+17.2 \\ \\ y=23.58 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D0.22%2829%29%2B17.2%20%5C%5C%20y%3D6.38%2B17.2%20%5C%5C%20%20%5C%5C%20y%3D23.58%20%5Cend%7Bgathered%7D)
Then, after 29 months the tree would be 23.58 feet in height
C) In this case as you have the height and need to find the number of moths you substitute the y for 29.96feet and solve the equation for x, as follow:
![\begin{gathered} 29.96=0.22x+17.2 \\ 29.96-17.2=0.22x \\ 12.76=0.22x \\ \frac{12.76}{0.22}=x \\ \\ 58=x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%2029.96%3D0.22x%2B17.2%20%5C%5C%2029.96-17.2%3D0.22x%20%5C%5C%2012.76%3D0.22x%20%5C%5C%20%5Cfrac%7B12.76%7D%7B0.22%7D%3Dx%20%5C%5C%20%20%5C%5C%2058%3Dx%20%5Cend%7Bgathered%7D)
Then, after 58 months the tree would be 29.96feet tall
Circumference of a circle = pi * diameter, or 2(pi) * radius.
The first circle with circumference of 12pi means that the diameter is equal to 12. Since radius is just half of diameter 12/2=6. Same goes for the second circle. Half of 32 is 16. The ratio is then equal to 6:16 or 3:8