2(6x+y)=24. i hope this helps
We have the expression
![8 x^{2} + 10x](https://tex.z-dn.net/?f=8%20x%5E%7B2%7D%20%2B%2010x)
, note that both terms have the factor 2x, if we factor this out, we are left with:
2x(4x + 5)
If you redistribute it you can see that it equals
![8 x^{2} + 10x](https://tex.z-dn.net/?f=8%20x%5E%7B2%7D%20%2B%2010x)
Hope this helps! :)
Answer:
5/8, 3/8
Step-by-step explanation:
1/4 = 2/8
2/8 + 3/8 = 5/8
5/8
subtract 5/8 from 1
3/8
Answer:
The nth term of the geometric sequence is is 32805
Step-by-step explanation:
The nth term of a geometric sequence is given by
![$ a_n = a_1 \cdot r^{n - 1} $](https://tex.z-dn.net/?f=%24%20a_n%20%3D%20a_1%20%5Ccdot%20r%5E%7Bn%20-%201%7D%20%24)
Where
is the first term and
is the common ratio
We are given the fourth term of this sequence
The common ratio is
![r = -3](https://tex.z-dn.net/?f=r%20%3D%20-3)
Once we find the 1st term then we can find any other term.
![a_4 = a_1 \cdot r^{4 - 1} \\\\a_4 = a_1 \cdot r^{3} \\\\-135 = a_1 \cdot (-3)^{3} \\\\-135 = a_1 \cdot (-27) \\\\a_1 = \frac{-135}{-27} \\\\a_1 = 5](https://tex.z-dn.net/?f=a_4%20%3D%20a_1%20%5Ccdot%20r%5E%7B4%20-%201%7D%20%20%5C%5C%5C%5Ca_4%20%3D%20a_1%20%5Ccdot%20r%5E%7B3%7D%20%20%5C%5C%5C%5C-135%20%3D%20a_1%20%5Ccdot%20%28-3%29%5E%7B3%7D%20%20%5C%5C%5C%5C-135%20%3D%20a_1%20%5Ccdot%20%28-27%29%20%20%5C%5C%5C%5Ca_1%20%3D%20%5Cfrac%7B-135%7D%7B-27%7D%20%5C%5C%5C%5Ca_1%20%3D%205)
So the ninth term of this geometric sequence is
![a_n = a_1 \cdot r^{n - 1} \\\\a_9 = a_1 \cdot r^{9 - 1} \\\\a_9 = a_1 \cdot r^{8} \\\\a_9 = 5 \cdot (-3)^{8} \\\\a_9 = 5 \cdot (6561) \\\\a_9 = 32805](https://tex.z-dn.net/?f=a_n%20%3D%20a_1%20%5Ccdot%20r%5E%7Bn%20-%201%7D%20%20%5C%5C%5C%5Ca_9%20%3D%20a_1%20%5Ccdot%20r%5E%7B9%20-%201%7D%20%20%5C%5C%5C%5Ca_9%20%3D%20a_1%20%5Ccdot%20r%5E%7B8%7D%20%20%5C%5C%5C%5Ca_9%20%3D%205%20%5Ccdot%20%28-3%29%5E%7B8%7D%20%20%5C%5C%5C%5Ca_9%20%3D%205%20%5Ccdot%20%286561%29%20%20%5C%5C%5C%5Ca_9%20%3D%2032805)
Therefore, the nth term of the geometric sequence is is 32805
To find the value of x, isolate the x first,
5x + 6 = 2x +15
Subtract 6 to both sides because whatever you do on one side you would always to on the other side.
5x = 2x + 9
Subtract 2x from both sides
3x = 9
Divide to isolate the x
x = 3 is your answer