Answer:

Step-by-step explanation:
we know that
The absolute value function has two solutions
Observing the graph
the solutions are
and 
First solution (case positive)
assume the symbol of the first solution and then compare the results




Second solution (case negative)

Multiply by -1 both sides

substitute the value of b and compare the results


-------> is correct
The fencing line x is the height of a rectangle triangle of base = y, hypothenuse of 9 m, so we use Pythagoras theorem to solve:
hyp^2 = height^2 + base^2
9^2 = x^2 + y^2
x^2 = 81 - y^2
we can see that x is also the height of another rectangle triangle of base = 15 - y, hypothenuse of 12 m, so we use Pythagoras theorem to solve:
hyp^2 = height^2 + base^2
12^2 = x^2 + (15 - y)^2
lets expand:
144 = x^2 + 225 - 30y + y^2
substitute x^2 from the first equation in the last:
144 = 81 - y^2 + 225 - 30y + y^2
144 = 81 + 225 - 30y
30y = -144 + 81 + 225
y = 5.4 m
substitute in the fence equation:
x^2 = 81 - y^2
x^2 = 81 - 5.4^2
x = 7.2 m that is the length of the fence
Y=600000(1+1.8%)^(x-2000)
So the population in 2012
Y=600,000×(1+0.018)^(2,012−2,000)
Y=743,232
Answer:

Step-by-step explanation:
Let consider that door has a height of 5 feet and a width of 3 feet. The scale factor is:


The height of the cabinet is:



Given:
The system of inequalities is


To find:
The values of a for which the system has no solution.
Solution:
We have,
...(1)
It means the value of x is less than or equal to 5.
...(2)
It means the value of x is greater than or equal to a
Using (1) and (2), we get

But if a is great than 5, then there is no value of which satisfies this inequality.
Therefore, the system has no solution for a>5.