Jane wants to determine the shortest route from her home to her workplace. She walks only on the sidewalks indicated by dotted lines on the map. What is
the distance of the shortest route from home to work to the nearest block?
(IMPORTANT NOTE - 1) Turn radicals into decimals. 2) Do not round decimals
until the very end of the problem).
HELP PLEASE I have no idea how to do this

The distance between two points on a plane can be found by Pythagoras's theorem.

The shortest route from her home to her workplace is the route that passes along the block in the middle of the graph ,which is approximately 2.5 blocks shorter, than the apparently next shortest route.

Reason:

The shortest distance between two points is a straight line.

The shortest route to her workplace are the routes that approximate a straight line the most.

Following the dotted lines, there are two routes, that are approximately direct and therefore short routes to her workplace which are;

Taking the route that passes close to the center of the map to her workplace ,gives;

Path 1 = √(2² + 4²) = 2·√5 (by Pythagoras's theorem)

Path 2 = √(1² + 2²) = √5

Path 3 = 1 + 1 = 2

Path 4 = √(2² + 3²) = √13

Path 5 = 3

Cumulative distance = 2·√5 + √5 + 2 + √13 + 3 ≈ 15.3

Taking the route to the left of the above route, gives;

Path 1 = √(2² + 4²) = 2·√5

Path 2 = 7 + 6 = 13

Cumulative distance = 2·√5 + 13 ≈ 17.5

Therefore, the shortest route is the route that heads to her workplace, through, close to the center of the map, which approximately 17.5 blocks - 15.3 blocks  = 2.5 blocks shorter

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there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1