It would be: 5x - 8 = 75
5x = 75 + 8
5x = 83
x = 83 / 5
x = 16.6
So, the number & your final answer is 16.6
Hope this helps!
$7881.18
Step-by-step explanation:
Let the initial Investment be
. The Interest is compounded on a monthly basis at 12% annual interest rate. After 17 years, the Investment amounts to $60,000.
As the annual interest rate is 12%, the monthly interest rate is 1%.
Since this is a compound interest problem, the total amount can be modeled as follows: ![P(t)=P_{0}(1+\frac{i}{100})^{t}](https://tex.z-dn.net/?f=P%28t%29%3DP_%7B0%7D%281%2B%5Cfrac%7Bi%7D%7B100%7D%29%5E%7Bt%7D)
Here
is the interest rate, i.e
, and t is the number of time periods, i.e
= ![204\textrm{ months}](https://tex.z-dn.net/?f=204%5Ctextrm%7B%20months%7D)
![60,000=P_{0}\textrm{ x }(\frac{101}{100})^{204}](https://tex.z-dn.net/?f=60%2C000%3DP_%7B0%7D%5Ctextrm%7B%20x%20%7D%28%5Cfrac%7B101%7D%7B100%7D%29%5E%7B204%7D)
![P_{0}=7881.18](https://tex.z-dn.net/?f=P_%7B0%7D%3D7881.18)
∴ Initial Investment = $7881.18
Answer:
<h2>x = 2, y = 4</h2>
Step-by-step explanation:
![\left\{\begin{array}{ccc}x+\frac{3}{4}y=5&\text{multiply both sides by 4}\\x-\frac{1}{2}y=0&\text{multiply both sides by 6}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}4x+3y=20\\6x-3y=0\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad10x=20\qquad\text{divide both sides by 10}\\.\qquad\dfrac{10x}{10}=\dfrac{20}{10}\\.\qquad\boxed{x=2}\\\\\\\text{Put it to the first equation:}\\\\4(2)+3y=20\\8+3y=20\qquad\text{subtract 8 from both sides}\\8-8+3y=20-8\\3y=12\qquad\text{divide both sides by 3}\\\boxed{y=4}](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dx%2B%5Cfrac%7B3%7D%7B4%7Dy%3D5%26%5Ctext%7Bmultiply%20both%20sides%20by%204%7D%5C%5Cx-%5Cfrac%7B1%7D%7B2%7Dy%3D0%26%5Ctext%7Bmultiply%20both%20sides%20by%206%7D%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Cunderline%7B%2B%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D4x%2B3y%3D20%5C%5C6x-3y%3D0%5Cend%7Barray%7D%5Cright%7D%5Cqquad%5Ctext%7Badd%20both%20sides%20of%20the%20equations%7D%5C%5C.%5Cqquad10x%3D20%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%2010%7D%5C%5C.%5Cqquad%5Cdfrac%7B10x%7D%7B10%7D%3D%5Cdfrac%7B20%7D%7B10%7D%5C%5C.%5Cqquad%5Cboxed%7Bx%3D2%7D%5C%5C%5C%5C%5C%5C%5Ctext%7BPut%20it%20to%20the%20first%20equation%3A%7D%5C%5C%5C%5C4%282%29%2B3y%3D20%5C%5C8%2B3y%3D20%5Cqquad%5Ctext%7Bsubtract%208%20from%20both%20sides%7D%5C%5C8-8%2B3y%3D20-8%5C%5C3y%3D12%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%203%7D%5C%5C%5Cboxed%7By%3D4%7D)
Varies inversely :
f(x) = k/x
There is always a constant of variation , k to solve for using the given information. when x = 0.4 ; f(x) = 0.2
0.2 = k/0.4
0.2(0.4) = k
0.08 = k
final equation : f(x) = 0.08/x
when x = 1.6
f(x) = 0.08/1.6
f(x) = 0.05