Answer:
Hope this helps you.
The answer is 61, x+40+5x+14=180, so x equals 21. 5(21)+14 ends up equaling 119, so 180-119 equals 1
Answer:
x=8
Step-by-step explanation:
Cause 8+1 =9
Answer:
The equation is:
![S=\frac{a_n*r-a_1}{r-1}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7Ba_n%2Ar-a_1%7D%7Br-1%7D)
![S=\frac{\frac{16}{243}*\frac{2}{3}-\frac{1}{3}}{\frac{2}{3}-1}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B%5Cfrac%7B16%7D%7B243%7D%2A%5Cfrac%7B2%7D%7B3%7D-%5Cfrac%7B1%7D%7B3%7D%7D%7B%5Cfrac%7B2%7D%7B3%7D-1%7D)
The sum is:
![S=\frac{211}{243}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B211%7D%7B243%7D)
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If the sequence is infinite, the formula is:
![S = \frac{a_1}{1-r}](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7Ba_1%7D%7B1-r%7D)
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Step-by-step explanation:
We must calculate the radius of the geometric series
![r =\frac{a_{n+1}}{a_n}\\\\r=\frac{\frac{2}{9}}{\frac{1}{3}}\\\\r=\frac{2}{3}](https://tex.z-dn.net/?f=r%20%3D%5Cfrac%7Ba_%7Bn%2B1%7D%7D%7Ba_n%7D%5C%5C%5C%5Cr%3D%5Cfrac%7B%5Cfrac%7B2%7D%7B9%7D%7D%7B%5Cfrac%7B1%7D%7B3%7D%7D%5C%5C%5C%5Cr%3D%5Cfrac%7B2%7D%7B3%7D)
The first term of the series is: ![a_1=\frac{1}{3}](https://tex.z-dn.net/?f=a_1%3D%5Cfrac%7B1%7D%7B3%7D)
The last term of the series is: ![a_n=\frac{16}{243}](https://tex.z-dn.net/?f=a_n%3D%5Cfrac%7B16%7D%7B243%7D)
If the sequence is finite then the formula is:
![S=\frac{a_n*r-a_1}{r-1}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7Ba_n%2Ar-a_1%7D%7Br-1%7D)
![S=\frac{\frac{16}{243}*\frac{2}{3}-\frac{1}{3}}{\frac{2}{3}-1}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B%5Cfrac%7B16%7D%7B243%7D%2A%5Cfrac%7B2%7D%7B3%7D-%5Cfrac%7B1%7D%7B3%7D%7D%7B%5Cfrac%7B2%7D%7B3%7D-1%7D)
![S=\frac{211}{243}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B211%7D%7B243%7D)
If the sequence is infinite then by definition as the radius are
then the formula for the sum of the geometric sequence is:
![S = \frac{a_1}{1-r}\\\\S = \frac{\frac{1}{3}}{1-\frac{2}{3}}\\\\S =1](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7Ba_1%7D%7B1-r%7D%5C%5C%5C%5CS%20%3D%20%5Cfrac%7B%5Cfrac%7B1%7D%7B3%7D%7D%7B1-%5Cfrac%7B2%7D%7B3%7D%7D%5C%5C%5C%5CS%20%3D1)
Answer:
A: 540
Step-by-step explanation:
The scale factor makes each side length 6 times longer. Area = width * length, these are both multiplied by 6 so the area actually is 36 times bigger.
15 * 36 = 540
Answer:
4.4
Step-by-step explanation:
4.4