A) I would make the positive integer x and then form an equation.
x + 30 = x^2 - 12
x + 42 = x^2
0 = x^2 - x - 42 this can be factorised
(x - 7) ( x + 6) Therefore x = 7 or x = -6
Since the question asks for a positive integer the answer is 7.
B) two positive numbers x and y.
X - y = 3
x^2 + y^2 = 117
Use these simultaneous equations to figure out each number.
Rearrange the first equation
x = y + 3
Then substitute it into the second equation.
(y+3)^2 + y^2 = 117
y^2 + 6y + 9 + y^2 = 117
2y^2 + 6y - 108 = 0
then factorise this.
(2y - 12) (y + 9)
This means that y = 6 or y = -9 but it’s 6 because that’s the only positive number.
Use y to find x
x = y + 3
x = 6 + 3
x = 9
So the answers are x = 9 and y = 6.
For this case, the first thing we must do is define variables:
p: plane speed
w: wind speed
With the wind in favor, the speed is:

With the wind against the speed is:

Rewriting both equations, we have the following system of equations:

Then, solving the system of equations (graphically for example), we have the solution is:

Therefore, jet stream's speed:
Answer:
A) p + w = 960; p - w = 600; jet stream's speed = 180 km / h
Answer:
The slope equation of the line AB is 
Step-by-step explanation:
Here, the given points are A (2, 3) and B (7,4).
Now, slope of any line is given as :

or, 
Hence, the slope of the line AB is (1/5)
Now , A POINT SLOPE FORM of an equation is
(y - y0) = m (x - x0) ; (x0, y0) is any arbitrary point on line.
Hence, the equation of line AB with slope (1/5 ) and point (7,4) is given as:

or, 5y - 20 = x -7
⇒ x - 57 + 13 = 0 ( SIMPLIFIED FORM of equation)
Hence, the slope equation of the line AB is 
Answer:
sin(a)=20/29
cos(a)=21/29
1. x^2 + x - 90
2. (x+10)(x-1)
3. x= -10 and 1