Answer:
Step-by-step explanation:
The given system is:
4x-3y=8
5x-2y=-11
We make x the subject in the top equation to get:
Plug this expression for x in the bottom equation to get
We expand to obtain
Multiply through by 4
Group similar terms
This means
Look up the law of sines, I suggest Khan Academy. It is better if you know how to do it, it is very useful.
Answer:
They started at 4:45 pm
Step-by-step explanation:
Time spend at the mall:
15 minutes in the shoe store
1 hour shopping for a dress
30 minutes eating
Total 1 hour 45 minutes
x + 1 hour 45 minutes = 6:30
Subtract 1 hours
5 : 30 pm
Subtract 45 minutes
4 :45 pm
They started at 4:45 pm
Answer:
The volume of the tumor experimented a decrease of 54.34 percent.
Step-by-step explanation:
Let suppose that tumor has an spherical geometry, whose volume (
) is calculated by:
Where 
is the radius of the tumor.
The percentage decrease in the volume of the tumor (
) is expressed by:
Where:
- Absolute decrease in the volume of the tumor.
- Initial volume of the tumor.
The absolute decrease in the volume of the tumor is:
The percentage decrease is finally simplified:
![\%V = \left[1-\left(\frac{R_{f}}{R_{o}}\right)^{3} \right]\times 100\,\%](https://tex.z-dn.net/?f=%5C%25V%20%3D%20%5Cleft%5B1-%5Cleft%28%5Cfrac%7BR_%7Bf%7D%7D%7BR_%7Bo%7D%7D%5Cright%29%5E%7B3%7D%20%5Cright%5D%5Ctimes%20100%5C%2C%5C%25)
Given that 
and 
, the percentage decrease in the volume of tumor is:
![\%V = \left[1-\left(\frac{0.77\cdot R}{R}\right)^{3} \right]\times 100\,\%](https://tex.z-dn.net/?f=%5C%25V%20%3D%20%5Cleft%5B1-%5Cleft%28%5Cfrac%7B0.77%5Ccdot%20R%7D%7BR%7D%5Cright%29%5E%7B3%7D%20%5Cright%5D%5Ctimes%20100%5C%2C%5C%25)
The volume of the tumor experimented a decrease of 54.34 percent.
Answer:
Step-by-step explanation:
1. Express each quadratic function f in the form f (x) -yo = p (x - xo) x ϵ R, where xo, i, p ϵ R are appropriately chosen. Indicate the coordinates
of the vertex of the parabola, the minimum or maximum of the function f, especially R. Draw the graph of f.
a) f (x) = 2x2 + 3x -5, ϵ R,
b) f (x) = -3x2 + 7x +9, ϵ R,
c) f (x) = - x +1, ϵ R,
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