If you would like to solve the system of equations, you can do this using the following steps:
-3x + 4y = 12
x * 1/4 - 1/3 * y = 1 ... x * 1/4 = 1 + 1/3 * y ... x = 4 + 4/3 * y
_____________
<span>-3x + 4y = 12
</span>-3 * (4 + 4/3 * y) + 4y = 12
-12 - 4y + 4y = 12
-12 = 12
-12 - 12 = 0
-24 = 0
The correct result would be: <span>the system of the equations has no solution; the two lines are parallel.</span>
        
             
        
        
        
Answer:
1036 students
Step-by-step explanation:
Let the number of students at West High be "w" and the number of students at East High be "e"
West High population is 250 FEWER than TWICE of East High, we can write:
w = 2e - 250
Total students in both schools is 2858, so we can write 2nd equation as:
e + w = 2858
We can replace 1st equation in 2nd to get an equation in e, and find "e":
e + w = 2858
e + (2e - 250) = 2858
3e - 250 = 2858
3e = 2858 + 250
3e = 3108
e = 3108/3
e = 1036
Hence,
number of students attending East High School = 1036 students
 
        
             
        
        
        
Answer:
Using either method, we obtain:  
Step-by-step explanation:
a) By evaluating the integral:
  ![\frac{d}{dt} \int\limits^t_0 {\sqrt[8]{u^3} } \, du](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20%5Cint%5Climits%5Et_0%20%7B%5Csqrt%5B8%5D%7Bu%5E3%7D%20%7D%20%5C%2C%20du)
The integral itself can be evaluated by writing the root and exponent of the variable u as:   ![\sqrt[8]{u^3} =u^{\frac{3}{8}](https://tex.z-dn.net/?f=%5Csqrt%5B8%5D%7Bu%5E3%7D%20%3Du%5E%7B%5Cfrac%7B3%7D%7B8%7D)
Then, an antiderivative of this is: 
which evaluated between the limits of integration gives:

and now the derivative of this expression with respect to "t" is:

b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states: 
"If f is continuous on [a,b] then

is continuous on [a,b], differentiable on (a,b) and  
Since this this function  is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means:
 is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means:

 
        
             
        
        
        
Answer:
20 years apart.
Step-by-step explanation:
Daughter is 10 years old, and mother is 3 times older. This makes mother 30 years old.  There is a 20 year difference between them.
Ten years later, the daughter is 20 years old. Since the mother is 20 years older, she is now 40, which is 2 times older than the daughter. 
 
        
             
        
        
        
Answer:
$3,799.20
Step-by-step explanation:
We presume your formula is intended to be ...
M = Pm(1 + m)^(na)/((1 + m)^(na) - 1)
where M is the monthly payment, m is the monthly interest rate, n is 12, and a is the number of years.
This formula gives written below:
M = 3500·(.08/12)·(1 + (.08/12))^(12·2)/((1 + (.08/12))^(12·2) -1) ≈ 158.30
The total payback will be the sum of 24 of these payments is written below;
payback = 24×$158.30 = $3,799.20