We know, shortest distance between two points
and
is :

So, distance between house and library is :

Distance between library and post office :

Distance between post office and house :

Therefore, minimum distance that you can ride your bike is (5.39+7.07+7) km = 19.46 km.
Hence, this is the required solution.
You would have to solve for x by simplifying both sides of the equation, then isolating the variable.
So, x= -1/4
to find the radius of x^2+y^2-10x+6y+18=0, we must complete the square:
x^2 - 10x + y^2 + 6y = -18
Then:
x^2 - 10x + 5^2 - 5^2 + y^2 + 6y + 9 - 9 = -18
Collecting all three constants on the right-hand side, r^2 = -18 + 25 + 9 = 16
Then r = +sqrt(16) = +4 (answer)
X jumpers at <span>£15 each. Total = 15*x = </span><span>£15x
</span>
y shirts at £12 each. Total = 12*y = <span>£12y
Total cost = </span><span>£15x + </span><span>£12y
Total cost = </span><span><span>£(15x + 12y)</span></span>