Answer:
x = 19.
Step-by-step explanation:
By the tangent - secant theorem:
BD^2 = AB * EB
so:
8^2 = (x - 7 + 4) * 4
4(x - 3) = 64
4x - 12 = 64
4x = 64 + 12 = 76
x = 76/4
= 19.
Answer:
Step-by-step explanation:
The final value of the given log expression is -28
<h3>Logarithm functions</h3>
Logarithm functions are inverse of exponential functions. Given the log expression below;
![log\frac{c^5}{\sqrt{b^3}}](https://tex.z-dn.net/?f=log%5Cfrac%7Bc%5E5%7D%7B%5Csqrt%7Bb%5E3%7D%7D)
Given the following parameters
log a = 6
log b = -10
log c = -8
The log expression can be expressed as:
![log\frac{c^5}{\sqrt{b^3}}=logc^5-log(\sqrt{ab^3})\\log\frac{c^5}{\sqrt{b^3}}=5logc-(1/2loga +3/2logb)\\log\frac{c^5}{\sqrt{b^3}}=5(-8)-(1/2(6)+3/2(-10))\\log\frac{c^5}{\sqrt{b^3}}=-40-(3-15)\\log\frac{c^5}{\sqrt{b^3}}=-40+12\\log\frac{c^5}{\sqrt{b^3}}=-28](https://tex.z-dn.net/?f=log%5Cfrac%7Bc%5E5%7D%7B%5Csqrt%7Bb%5E3%7D%7D%3Dlogc%5E5-log%28%5Csqrt%7Bab%5E3%7D%29%5C%5Clog%5Cfrac%7Bc%5E5%7D%7B%5Csqrt%7Bb%5E3%7D%7D%3D5logc-%281%2F2loga%20%2B3%2F2logb%29%5C%5Clog%5Cfrac%7Bc%5E5%7D%7B%5Csqrt%7Bb%5E3%7D%7D%3D5%28-8%29-%281%2F2%286%29%2B3%2F2%28-10%29%29%5C%5Clog%5Cfrac%7Bc%5E5%7D%7B%5Csqrt%7Bb%5E3%7D%7D%3D-40-%283-15%29%5C%5Clog%5Cfrac%7Bc%5E5%7D%7B%5Csqrt%7Bb%5E3%7D%7D%3D-40%2B12%5C%5Clog%5Cfrac%7Bc%5E5%7D%7B%5Csqrt%7Bb%5E3%7D%7D%3D-28)
Hence the final value of the given log expression is -28
Learn more on log function here: brainly.com/question/13473114
#SPJ1
There really is no single "obvious" choice here...
Possibly the sequence is periodic, with seven copies of -1 followed by six copies of 0, or perhaps seven -1s and seven 0s. Or maybe seven -1s, followed by six 0s, then five 1s, and so on, but after a certain point it would seem we have to have negative copies of a number, which is meaningless.
Or maybe it's not periodic, and every seventh value in the sequence is incremented by 1? Who knows?
I'll go ahead and assume the latter case, that the sequence is not periodic, since that's technically somewhat easier to manage. We can assign the following rule to the
![n](https://tex.z-dn.net/?f=n)
-th term in the sequence:
![\{a_n\}=\{-1,\ldots,-1,0,\ldots,0,1,\ldots,1,2,\ldots,2,3,\ldots\}](https://tex.z-dn.net/?f=%5C%7Ba_n%5C%7D%3D%5C%7B-1%2C%5Cldots%2C-1%2C0%2C%5Cldots%2C0%2C1%2C%5Cldots%2C1%2C2%2C%5Cldots%2C2%2C3%2C%5Cldots%5C%7D)
![\implies a_n=\left\lfloor\dfrac n7\right\rfloor-1](https://tex.z-dn.net/?f=%5Cimplies%20a_n%3D%5Cleft%5Clfloor%5Cdfrac%20n7%5Cright%5Crfloor-1)
for
![n\ge0](https://tex.z-dn.net/?f=n%5Cge0)
.
So the generating function for this sequence might be
![G(a_n;x)=\displaystyle\sum_{n\ge0}\left(\left\lfloor\frac n7\right\rfloor-1\right)x^n](https://tex.z-dn.net/?f=G%28a_n%3Bx%29%3D%5Cdisplaystyle%5Csum_%7Bn%5Cge0%7D%5Cleft%28%5Cleft%5Clfloor%5Cfrac%20n7%5Cright%5Crfloor-1%5Cright%29x%5En)
As to what is meant by "closed form", I'm not sure. Would this answer be acceptable? Or do you need to find a possibly more tractable form for the coefficient not in terms of the floor function?
Step-by-step explanation:
y = x - 2
x + y = 12
Substitute the first expression for y into the second equation.
x + (x - 2) = 12
2x - 2 = 12
2x = 14
x = 7
Now plug into either equation to find y.
y = 7 - 2
y = 5
So the solution is (7, 5).