Step-by-step explanation:
y+4z=0
4x+y-2z=2
-3x-3z=-9
Answer:
common ratio: 1.155
rate of growth: 15.5 %
Step-by-step explanation:
The model for exponential growth of population P looks like: 
where 
is the population at time "t",
is the initial (starting) population
is the common ratio,
and 
is the rate of growth
Therefore, in our case we can replace specific values in this expression (including population after 12 years, and initial population), and solve for the unknown common ratio and its related rate of growth:
![P(t)=P_i(1+r)^t\\13000=2300*(1+r)^{12}\\\frac{13000}{2300} = (1+r)^12\\\frac{130}{23} = (1+r)^{12}\\1+r=\sqrt[12]{\frac{130}{23} } =1.155273\\](https://tex.z-dn.net/?f=P%28t%29%3DP_i%281%2Br%29%5Et%5C%5C13000%3D2300%2A%281%2Br%29%5E%7B12%7D%5C%5C%5Cfrac%7B13000%7D%7B2300%7D%20%3D%20%281%2Br%29%5E12%5C%5C%5Cfrac%7B130%7D%7B23%7D%20%3D%20%281%2Br%29%5E%7B12%7D%5C%5C1%2Br%3D%5Csqrt%5B12%5D%7B%5Cfrac%7B130%7D%7B23%7D%20%7D%20%3D1.155273%5C%5C)
This (1+r) is the common ratio, that we are asked to round to the nearest thousandth, so we use: 1.155
We are also asked to find the rate of increase (r), and to express it in percent form. Therefore we use the last equation shown above to solve for "r" and express tin percent form:
So, this number in percent form (and rounded to the nearest tenth as requested) is: 15.5 %
This is the concept algebra.
Volume of of paint that is required to paint large shipping crate is a liters.
suppose the volume of this crate is x cubic units.
The volume of the next crate to be painted will be 2x cubic units.
Hence the amount of paint required to paint the crate will be:
(volume of bigger crate)/(volume of smaller crate)×(volume of liters required to paint the first crate)
=(2x)/(x)×a
=2a liters
To paint the new crate 2a liters of oil is needed.
Answer:
Step-by-step explanation:
They are about 3 meters away from each other
and the correct area is 15.5-12 and the correct answer is 3.5 meters apart
The equation for the first option is Y=10x + 200
The equation for the second option is Y=30x + 100
X = one month
To find when they would be the same about you have to set the equations equal to each other
10x + 200 = 30x + 100
-10x -100 -10x -100
100= 20x
5 = x
After five months she would save the same amount. To find how much is saved you have to plug in 5 for x in one of the equations. You can always double-check 5 by plugging it in both equations and making sure you get the same answer
Y= 10(5) + 200 = 250
Y= 30(5) + 100 = 250
She would have saved $250 after five months by using either method
