Answer:
292,968
Step-by-step explanation:
As we know,
Sum of a geometric sequence (S) = ![\frac{a(1-r^{n}) }{(1-r)}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%281-r%5E%7Bn%7D%29%20%7D%7B%281-r%29%7D)
where,
a = first term of sequence,
r = the constant ratio,
n = number of terms in sequence.
So, according to the question,
a = 3,
r = 5,
n = 8.
by substituting the values in the above formula, we get;
⇒ ![S=\frac{3(1-5^{8}) }{(1-5)}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B3%281-5%5E%7B8%7D%29%20%7D%7B%281-5%29%7D)
⇒ ![292,968](https://tex.z-dn.net/?f=292%2C968)
Answer:
The side lengths are 30, 36 and 39.
Step-by-step explanation:
To find the missing side, write a proportion using side lengths from each similar shape. A proportion is an equation that sets equal two ratios.
![\frac{13}{39}=\frac{12}{y}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B39%7D%3D%5Cfrac%7B12%7D%7By%7D)
Find y by cross multiplying numerator and denominator of each fraction.
13y = 39(12)
13y = 468
y = 36
Find the other missing side by repeating the process.
![\frac{13}{39}=\frac{10}{y}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B39%7D%3D%5Cfrac%7B10%7D%7By%7D)
Find y by cross multiplying numerator and denominator of each fraction.
13y = 39(10)
13y = 390
y = 30
The side lengths are 30, 36 and 39.
To solve the function in terms of x:
![\log _{4^x}2^a=3](https://tex.z-dn.net/?f=%5Clog%20_%7B4%5Ex%7D2%5Ea%3D3)
find the power of the subscripts of the log
![\begin{gathered} \log _{4^x}2^a=3 \\ \log _{2^{2x}}2^a=3 \\ \frac{a}{2x}\log _22=3 \\ \text{where }\log _22=1 \\ \frac{a}{2x}=3 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Clog%20_%7B4%5Ex%7D2%5Ea%3D3%20%5C%5C%20%5Clog%20_%7B2%5E%7B2x%7D%7D2%5Ea%3D3%20%5C%5C%20%5Cfrac%7Ba%7D%7B2x%7D%5Clog%20_22%3D3%20%5C%5C%20%5Ctext%7Bwhere%20%7D%5Clog%20_22%3D1%20%5C%5C%20%5Cfrac%7Ba%7D%7B2x%7D%3D3%20%5Cend%7Bgathered%7D)
cross multiply the expression
![\begin{gathered} \frac{a}{2x}=3 \\ a=3(2x) \\ a=6x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7Ba%7D%7B2x%7D%3D3%20%5C%5C%20a%3D3%282x%29%20%5C%5C%20a%3D6x%20%5Cend%7Bgathered%7D)
Therefore the correct answer of a = 6x
Answer:
C
Step-by-step explanation:
start with factoring.
5x+15-9x+4
then solve
-4x+19
In linear change, the two variables keep increasing or decreasing at the same speed.