7s + 20 = 4s -13
7s - 4s = -13 -20
3s = -33
s = -33/3
s = -11
Answer:
35.84
Step-by-step explanation:
You would take 19% of 30.12$ by doing 30.12x0.19 to get 5.72.
you then add 5.72 to 30.12 to get your total of 35.84$
Answer: 0.77
Step-by-step explanation:
-7(3x-1)
Let’s distribute that.
-7 x 3x = -21x
-7 x -1 = 7
Let’s rewrite, using the distributed numbers I just got.
91 = -21x + 7
Now, let’s solve for x.
91 -7 = -21x + 7 -7
(Remember, whatever you do on one side you do on the other)
84=-21x
84/-21=-21x/-21
-4=x
Solution : x=-4
It looks like you're given
![\displaystyle \sum_{i=1}^{10} 5 \left(\frac12\right)^i = \frac{x}{1024}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csum_%7Bi%3D1%7D%5E%7B10%7D%205%20%5Cleft%28%5Cfrac12%5Cright%29%5Ei%20%3D%20%5Cfrac%7Bx%7D%7B1024%7D)
Consider the geometric sum,
![\displaystyle S = \sum_{i=1}^{10} \left(\frac12\right)^i](https://tex.z-dn.net/?f=%5Cdisplaystyle%20S%20%3D%20%5Csum_%7Bi%3D1%7D%5E%7B10%7D%20%5Cleft%28%5Cfrac12%5Cright%29%5Ei)
![S = \dfrac12 + \dfrac1{2^2} + \dfrac1{2^3} + \cdots + \dfrac1{2^{10}}](https://tex.z-dn.net/?f=S%20%3D%20%5Cdfrac12%20%2B%20%5Cdfrac1%7B2%5E2%7D%20%2B%20%5Cdfrac1%7B2%5E3%7D%20%2B%20%5Ccdots%20%2B%20%5Cdfrac1%7B2%5E%7B10%7D%7D)
Multiply both sides by 1/2 :
![\dfrac12 S = \dfrac1{2^2} + \dfrac1{2^3} + \dfrac1{2^4} + \cdots + \dfrac1{2^{11}}](https://tex.z-dn.net/?f=%5Cdfrac12%20S%20%3D%20%5Cdfrac1%7B2%5E2%7D%20%2B%20%5Cdfrac1%7B2%5E3%7D%20%2B%20%5Cdfrac1%7B2%5E4%7D%20%2B%20%5Ccdots%20%2B%20%5Cdfrac1%7B2%5E%7B11%7D%7D)
Subtract this from S :
![S - \dfrac12 S = \dfrac12 - \dfrac1{2^{11}}](https://tex.z-dn.net/?f=S%20-%20%5Cdfrac12%20S%20%3D%20%5Cdfrac12%20-%20%5Cdfrac1%7B2%5E%7B11%7D%7D)
Solve for S :
![\dfrac12 S = \dfrac12 - \dfrac1{2^{11}}](https://tex.z-dn.net/?f=%5Cdfrac12%20S%20%3D%20%5Cdfrac12%20-%20%5Cdfrac1%7B2%5E%7B11%7D%7D)
![S = 1 - \dfrac1{2^{10}}](https://tex.z-dn.net/?f=S%20%3D%201%20-%20%5Cdfrac1%7B2%5E%7B10%7D%7D)
![S = \dfrac{2^{10} - 1}{2^{10}}](https://tex.z-dn.net/?f=S%20%3D%20%5Cdfrac%7B2%5E%7B10%7D%20-%201%7D%7B2%5E%7B10%7D%7D)
![S = \dfrac{1023}{1024}](https://tex.z-dn.net/?f=S%20%3D%20%5Cdfrac%7B1023%7D%7B1024%7D)
The given sum is just 5 times S, so x = 1023 × 5 = 5115.