Let "c" be the original number of classrooms.
The 1200/c was the original number of students per classroom.
1200/(c-4) = (1200/c)+10
Multiply thru by c(c-4)
1200c = 1200(c-4)+10c(c-4)
1200c = 1200c-4800 + 10c^2-40c
10c^2-40c-4800 = 0
c^2-4c-480 = 0
(c-24)(c+20) = 0
c = 24 (# of classrooms originaly planned)
An irrational number is a number that can not be written as the quotient of two integer numbers.
Then if we have:
A = a rational number
B = a irrational number.
Then we can write:
A = x/y
Then the product of A and B can be written as:
A*B = (x/y)*B
Now, let's assume that this product is a rational number, then the product can be written as the quotient between two integer numbers.
(x/y)*B = (m/n)
If we isolate B, we get:
B = (m/n)*(y/x)
We can rewrite this as:
B = (m*y)/(n*x)
Where m, n, y, and x are integer numbers, then:
m*y is an integer
n*x is an integer.
Then B can be written as the quotient of two integer numbers, but this contradicts the initial hypothesis where we assumed that B was an irrational number.
Then the product of an irrational number and a rational number different than zero is always an irrational number.
We need to add the fact that the rational number is different than zero because if:
B is an irrational number
And we multiply it by zero, we get:
B*0 = 0
Then the product of an irrational number and zero is zero, which is a rational number.
This would be neither as they're passing through points that are across from each other by a large distance.
5x + 4y = - 8
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
4x - 5y = 20 ( subtract 4x from both sides )
- 5y = - 4x + 20 ( divide all terms by - 5 )
y = x - 4 ← in slope- intercept form
with slope m =
Given a line with slope m then the slope of a line perpendicular to it is
= - = - = - , thus
y = - x + c ← is the partial equation
To find c substitute (- 4, 3) into the partial equation
3 = 5 + c ⇒ c = 3 - 5 = - 2
y = - x - 2 ← in slope- intercept form
Multiply through by 4
4y = - 5x - 8 ( add 5x to both sides )
5x + 4y = - 8 ← equation in standard form