1. What length is the shortest path from A to C in the graph below?
A) 3
B) 4
C) 5 <
D) 9

2. What length is the shortest path from A to D in the graph below?
A) 6
B) 7
C) 8
D) 9

3. What length is the shortest path from A to G in the graph below?
A) 6
B) 7
C) 8
D) 9

Problem 1

This is through point B. We have AB+BC = 2+3 = 5

Another path is AE+EB+BC = 4+1+3 = 8, which is longer than 5 found earlier.

Another path is AE+ED+DC = 4+3+2 = 9, which is longer as well.

Another path is AE+ED+DB+BC = 4+3+5+3 = 19, which is longer as well.

Problem 2

This route is

AC+CF+FE+ED = 1+2+1+2 = 6

which is the shortest route

A longer route would be

AC+CF+FD = 1+2+4 = 7

Another longer route is

AB+BE+ED = 3+4+2 = 9

There are other longer routes as well.

Problem 3

Start at point A. There are two paths to take. Take the shortest one AE = 1

Then from there repeat the last step: take the shortest path

Keep this up until you reach point G

AE+ED+DF+FG = 1+2+1+3 = 7

Let's go back to point A. If we go to E, then we travel 1 unit so far. If we go for EH =8 instead of ED = 2, then we have 1+8 = 9 units traveled so far, but that exceeds 7 we found earlier. So we can rule this path out. This is one way you can use process of elimination to find the shortest path.

Similarly, go from A to B to C and we travel 2+5 = 7 units, which is equal to the answer, but we haven't reached G yet. So we can rule out any path that has ABC as the start.

The path ABDFG is not the shortest because AB+BD+DF+FG = 2+3+1+3 = 9, which is not shorter than 7.

45.3592

step-by-step explanation:

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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