Answer:
x=3
Step-by-step explanation:
Set equations equal to each other:

Subtract two from both sides

Factor out x^2 from the left side

Factor the right side, look for two factors of 9, which add to -6, which is just -3 and-3

So as you can see here, we have both sides in factored form, and both have a factor of (x-3) on both sides, and if one of the factors is zero, then the entire thing becomes zero, since 0 * anything= zero.
this means a solution would be at x=3, since it makes the right side 0 * 0 = 0, and the left side (3)^2 * 0 = 0
It's important to notice this, since had we divided by x-3 to make the equation a quadratic, we would've excluded this real solution, because when dividing by x-3 the solution x=3 makes it 0, so we would've been dividing by zero.
So one of the real solutions is at x=3
Answer:
(-2 , 2)
Step-by-step explanation:
A(-8 , 2) = (x1 , y1)
B(4 , -2) = (x2 , y2)
midpoint = (x1 + x2/2 , y1 + y2/2)
=(-8 + 4/2 , 2-(-2)/2)
=(-4/2 , 2+2/2)
(-2 , 2)
(3 , 7) = (x1 , y1)
(9 , 2) = (x2 , y2)
distance of PQ = 
=
=
=
=
=7.8 unit
Answer:
The speed of wind is 75 miles / hour
Step-by-step explanation:
Let's assume
speed of airplane is x miles /hour
speed of wind is y miles /hour
Against wind:
An airplane travels 600 miles against the wind in 4 hours
against wind means resultant speed will be less
so, speed =x-y
total distance traveled in 4 hour is

and this has to be equal to 600

Divide both sides by 4
and we get

With wind:
makes the return trip with then same wind in 2 hours
with wind means resultant speed will be more
so, speed =x+y
total distance traveled in 2 hour is

and this has to be equal to 600

Divide both sides by 2
and we get

So, we get system of equations


now, we can solve it by adding both equations


now, we can solve for x

now, we can find y by plugging x into any one equation


So,
The speed of wind is 75 miles / hour
Answer-63/18
Step-by-step explanation: