Step-by-step explanation:
The question is not clear to me
Answer:
c. ![\frac{1}{12n} = {[12n]}^{-1}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B12n%7D%20%3D%20%7B%5B12n%5D%7D%5E%7B-1%7D)
Step-by-step explanation:
![[\frac{1}{4}][\frac{2}{5}][\frac{1}{2}][\frac{4}{7}][\frac{5}{8}][\frac{2}{3}][\frac{7}{n}] = \frac{560}{6720n} = [12n]^{-1} = \frac{1}{12n}](https://tex.z-dn.net/?f=%5B%5Cfrac%7B1%7D%7B4%7D%5D%5B%5Cfrac%7B2%7D%7B5%7D%5D%5B%5Cfrac%7B1%7D%7B2%7D%5D%5B%5Cfrac%7B4%7D%7B7%7D%5D%5B%5Cfrac%7B5%7D%7B8%7D%5D%5B%5Cfrac%7B2%7D%7B3%7D%5D%5B%5Cfrac%7B7%7D%7Bn%7D%5D%20%3D%20%5Cfrac%7B560%7D%7B6720n%7D%20%3D%20%5B12n%5D%5E%7B-1%7D%20%3D%20%5Cfrac%7B1%7D%7B12n%7D)
![\frac{2}{3} = \frac{6}{9}\\ \\ \frac{1}{2} = \frac{3}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%20%3D%20%5Cfrac%7B6%7D%7B9%7D%5C%5C%20%5C%5C%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Cfrac%7B3%7D%7B6%7D)
* To make this simpler, reduce these two fractions in lowest terms.
I am joyous to assist you anytime.
Answer:
131 in²
Step-by-step explanation:
Let x represent the length of the painting. Given that The width of a painting is 4 inches less than the length. Hence:
Width = x - 4
The area of painting = length * width = x(x - 4) = x² - 4x
The frame that surrounds the painting is 2 inches wide (at the top and bottom, left and right). Hence the total width of the frame = (x - 4) + 2 + 2 = x, the length of the frame = x + 2 + 2 = x + 4
The area of the frame = length * breath = x(x + 4) = x² + 4x
Given that the area of the frame = 240 in², hence:
x² + 4x = 240
x² + 4x - 240 = 0
x = -17.62 and x = 13.62
Since the length cannot be negative, hence length = x = 13.62 inches
Area of painting = x(x - 4) = 13.62(13.62 - 4) = 131 in²
Answer:
The 10th term of the sequence is:
Step-by-step explanation:
Given the number
729, 243, 81, 27...
A geometric sequence has a constant ratio 'r' and is defined by
![a_n=a_0\cdot r^{n-1}](https://tex.z-dn.net/?f=a_n%3Da_0%5Ccdot%20r%5E%7Bn-1%7D)
Computing the ratio of all the adjacent terms
![\frac{243}{729}=\frac{1}{3},\:\quad \frac{81}{243}=\frac{1}{3},\:\quad \frac{27}{81}=\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B243%7D%7B729%7D%3D%5Cfrac%7B1%7D%7B3%7D%2C%5C%3A%5Cquad%20%5Cfrac%7B81%7D%7B243%7D%3D%5Cfrac%7B1%7D%7B3%7D%2C%5C%3A%5Cquad%20%5Cfrac%7B27%7D%7B81%7D%3D%5Cfrac%7B1%7D%7B3%7D)
The ratio of all the adjacent terms is the same and equal to
![r=\frac{1}{3}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B1%7D%7B3%7D)
also
![a_1=729](https://tex.z-dn.net/?f=a_1%3D729)
Therefore, the nth term is computed by:
![a_n=729\left(\frac{1}{3}\right)^{n-1}](https://tex.z-dn.net/?f=a_n%3D729%5Cleft%28%5Cfrac%7B1%7D%7B3%7D%5Cright%29%5E%7Bn-1%7D)
Putting n = 10 to find the 10th term
![a_{10}=729\left(\frac{1}{3}\right)^{10-1}](https://tex.z-dn.net/?f=a_%7B10%7D%3D729%5Cleft%28%5Cfrac%7B1%7D%7B3%7D%5Cright%29%5E%7B10-1%7D)
![=729\cdot \frac{1}{3^9}](https://tex.z-dn.net/?f=%3D729%5Ccdot%20%5Cfrac%7B1%7D%7B3%5E9%7D)
![=\frac{1\cdot \:729}{3^9}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%5Ccdot%20%5C%3A729%7D%7B3%5E9%7D)
![=\frac{729}{3^9}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B729%7D%7B3%5E9%7D)
![=\frac{3^6}{3^9}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3%5E6%7D%7B3%5E9%7D)
![=\frac{1}{3^3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B3%5E3%7D)
![a_{10}=\frac{1}{27}](https://tex.z-dn.net/?f=a_%7B10%7D%3D%5Cfrac%7B1%7D%7B27%7D)
Therefore, the 10th term of the sequence is:
Answer:
the answer is 10
Step-by-step explanation:
because 5+5=10 or 5x2=10