3/4 x -18 = 1/4 x -4
subtract 1/4 x from each side
3/4 x -1/4 x -18 = 1/4 x- 1/4 x -4
2/4 x - 18 = -4
add 18 to each side
1/2 x -18 + 18 = -4 + 18
1/2 x =14
multiply by 2 on each side
2* 1/2 x = 14 * 2
x =28
Answer:
Option C
Step-by-step explanation:
- Initial balance= $11
- Interest rate = 1.9% PA simple
<u>It will be graphed as function:</u>
Since is has a very small slope of 0.019 it will be shown almost parallel to x axis.
<u>Some points on the graph:</u>
- Amount in 1 year= 11*(1+0.019) = $11.21
- Amount in 2 years = 11*(1+2*0.019) = $11.42
- Amount in 6 years = 11*(1+6*0.019) = $12.25
- Amount in 10 years = 11*(1 + 10*0.019) = $13.09
Correct graph is option C
Hello there.
First, assume the numbers
such that they satisties both affirmations:
- The sum of the squares of two numbers is
. - The product of the two numbers is
.
With these informations, we can set the following equations:
![\begin{center}\align x^2+y^2=8\\ x\cdot y=4\\\end{center}](https://tex.z-dn.net/?f=%5Cbegin%7Bcenter%7D%5Calign%20x%5E2%2By%5E2%3D8%5C%5C%20x%5Ccdot%20y%3D4%5C%5C%5Cend%7Bcenter%7D)
Multiply both sides of the second equation by a factor of
:
![2\cdot x\cdot y = 2\cdot 4\\\\\\ 2xy=8~~~~~(2)^{\ast}](https://tex.z-dn.net/?f=2%5Ccdot%20x%5Ccdot%20y%20%3D%202%5Ccdot%204%5C%5C%5C%5C%5C%5C%202xy%3D8~~~~~%282%29%5E%7B%5Cast%7D)
Make ![(1)-(2)^{\ast}](https://tex.z-dn.net/?f=%281%29-%282%29%5E%7B%5Cast%7D)
![x^2+y^2-2xy=8-8\\\\\\ x^2-2xy+y^2=0](https://tex.z-dn.net/?f=x%5E2%2By%5E2-2xy%3D8-8%5C%5C%5C%5C%5C%5C%20x%5E2-2xy%2By%5E2%3D0)
We can rewrite the expression on the left hand side using the binomial expansion in reverse:
, such that:
![(x-y)^2=0](https://tex.z-dn.net/?f=%28x-y%29%5E2%3D0)
The square of a number is equal to
if and only if such number is equal to
, thus:
![x-y=0\\\\\\ x=y~~~~~~(3)](https://tex.z-dn.net/?f=x-y%3D0%5C%5C%5C%5C%5C%5C%20x%3Dy~~~~~~%283%29)
Substituting that information from
in
, we get:
![x\cdot x = 4\\\\\\ x^2=4](https://tex.z-dn.net/?f=x%5Ccdot%20x%20%3D%204%5C%5C%5C%5C%5C%5C%20x%5E2%3D4)
Calculate the square root on both sides of the equation:
![\sqrt{x^2}=\sqrt{4}\\\\\\ |x|=2\\\\\\ x=\pm~2](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2%7D%3D%5Csqrt%7B4%7D%5C%5C%5C%5C%5C%5C%20%7Cx%7C%3D2%5C%5C%5C%5C%5C%5C%20x%3D%5Cpm~2)
Once again with the information in
, we have that:
![y=\pm~2](https://tex.z-dn.net/?f=y%3D%5Cpm~2)
The set of solutions of that satisfies both affirmations is:
![S=\{(x,~y)\in\mathbb{R}^2~|~(x,~y)=(-2,\,-2),~(2,~2)\}](https://tex.z-dn.net/?f=S%3D%5C%7B%28x%2C~y%29%5Cin%5Cmathbb%7BR%7D%5E2~%7C~%28x%2C~y%29%3D%28-2%2C%5C%2C-2%29%2C~%282%2C~2%29%5C%7D)
This is the set we were looking for.
<span>16407.
An integer is a whole number that doesn't need to be written using a fraction or decimals. (Some examples of integers are 4, 50, and -3; on the other hand, fractions or decimals like 1/2 or .3 are not).
Because we round up a number when the decimal is greater than or equal to .5 (which in this case it is), we round 16406.5 to the next biggest integer, 16407.</span><span />
I think it’s 8 ( I’m not sure )