Answer:
A). 101 inches
B). 110 years
Step-by-step explanation:
Years since planting Circumference Difference
1 3 -
2 5 (5 - 3) = 2
3 7 (7 - 5) = 2
4 9 (9 - 7) = 2
5 11 (11 - 9) = 2
6 13 (13 - 11) = 2
There is a difference of 2 in every successive term of the circumference.
Therefore, the given sequence is an arithmetic sequence.
Explicit formula of an arithmetic sequence is given by,
![A_n=a+(n-1)d](https://tex.z-dn.net/?f=A_n%3Da%2B%28n-1%29d)
Here a = first term
n = number of terms
d = common difference
From the given table,
![A_n=3+(n-1)2](https://tex.z-dn.net/?f=A_n%3D3%2B%28n-1%292)
![A_n=2n+1](https://tex.z-dn.net/?f=A_n%3D2n%2B1)
Here
= circumference after 'n' years
n = Age of the plant
By this formula,
Circumference of a tree after 50 years,
![A_{50}=2(50)+1](https://tex.z-dn.net/?f=A_%7B50%7D%3D2%2850%29%2B1)
= 101 inches
Age of tree with the circumference = 221 inches,
221 = 2n + 1
2n = 220
n = 110 years
Answer:
![y=-3x+4](https://tex.z-dn.net/?f=y%3D-3x%2B4)
Step-by-step explanation:
Hi there!
<u>What we need to know:</u>
- Slope-intercept form:
where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis) - Parallel lines have the same slope (m) and different y-intercepts (b)
<u>1) Determine the slope (m)</u>
![6x+2y=2](https://tex.z-dn.net/?f=6x%2B2y%3D2)
Rearrange this equation in slope-intercept form (so it's easier for us to identify the slope)
Subtract 6x from both sides to isolate 2y
![6x+2y-6x=-6x+2\\2y=-6x+2](https://tex.z-dn.net/?f=6x%2B2y-6x%3D-6x%2B2%5C%5C2y%3D-6x%2B2)
Divide both sides by 2 to isolate y
![y=-3x+1](https://tex.z-dn.net/?f=y%3D-3x%2B1)
Now, we can tell clearly that -3 is in the place of m. Therefore, because parallel lines have the same slope, we know that the line we're solving for will also have a slope of -3. Plug this into
:
![y=-3x+b](https://tex.z-dn.net/?f=y%3D-3x%2Bb)
<u>2) Determine the y-intercept</u>
![y=-3x+b](https://tex.z-dn.net/?f=y%3D-3x%2Bb)
Plug in the given point (-1,7)
![7=-3(-1)+b\\7=3+b](https://tex.z-dn.net/?f=7%3D-3%28-1%29%2Bb%5C%5C7%3D3%2Bb)
Subtract 3 from both sides
![7-3=3+b-3\\4=b](https://tex.z-dn.net/?f=7-3%3D3%2Bb-3%5C%5C4%3Db)
Therefore, the y-intercept of the line is 4. Plug this back into
:
![y=-3x+4](https://tex.z-dn.net/?f=y%3D-3x%2B4)
I hope this helps!
Answer:
Step-by-step explanation:
7(x-5)²=63
(x-5)²=63/7
(x-5) = +/- 3
x = 5 + 3
or
x = 5- 3
x = 8 or 2