On a town map, each unit of the coordinate plane represents 1 mile. three branches of a bank are located at a(-3,1), b(2,3), and c(4,-1). a bank employee drives from branch a to branch b and then drives halfway to branch c before getting stuck in traffic. what is the minimum total distance the employee may have driven before getting stuck in traffic? round to the nearest tenth of a mile.

we have

A(-3,1), B(2,3), and C(4,-1)  

we know that

the distance between two points is equal to the formula

so

Step 1

Find the distance AB

convert units to miles

Step 2

find the distance BC

convert unit to miles

Step 3

Find the minimum total distance the employee may have driven before getting stuck in traffic

Sum the distance AB and the half distance BC

therefore

the answer is

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204