Answer:
It would take 75.8 minutes for the element to decay to 2 grams.
Step-by-step explanation:
The number of grams of element x, after t minutes, is given by the following equation:
In which X(0) is the initial amount and r is the decay rate.
There are 160 grams of Element X
This means that X(0) = 160.
So
Half life of 12 minutes.
This means that X(12) = 0.5*X(0) = 0.5*160 = 80. So
![\sqrt[12]{(1 - r)^{12}} = \sqrt[12]{0.5}](https://tex.z-dn.net/?f=%5Csqrt%5B12%5D%7B%281%20-%20r%29%5E%7B12%7D%7D%20%3D%20%5Csqrt%5B12%5D%7B0.5%7D)
So
How long would it take for the element to decay to 2 grams?
This is t for which X(t) = 2. So
It would take 75.8 minutes for the element to decay to 2 grams.
The example for an inconsistent system of equations:
x + 2 y = 10 and x + 2 y = 20. If we try to solve it algebraically:
x = 10 - 2 y; 10 - 2 y + 2 y = 20; 10 = 20 ( not true ). We will with something that is not true. Graph of those equations shows 2 parallel lines. Therefore the system is inconsistent.
The system is dependent when we have equivalent equations. For example:
2 x + y = 5 and 4 x + 2 y = 10. If we try to solve this system, we will end up with: 0 = 0 ( true ). The graph of this system shows the same line. This system is dependent.
Finally, if we have just one solution for the system of equations then the system is independent. For example: x + y = 5 and - x + 2 y = 10. When we add those equations: 3 y = 15; y = 15 : 3; y = 5; x + 5 = 5; x = 0. So we have just one solution ( x , y ) = ( 0, 5 ). The system of equations is independent.
Things to remember the sum of the measures of the interior and exterior angles at each vertex is 180 (supplementary angles)
add and equal to 180
3x-5+5x+17= 180
8x+12=180
8x= 168
x=21
substitute in the algebraic expression for exterior angle
3(21) -5=
63-5=58
58 degrees is the exterior angle
hope this helps
$236.25 is how much money carrie got
$78.75 is how much juanita got
Answer:
5
Step-by-step explanation:
