Using the information in the map, what is the distance between Camden and Lowell? Explain your reasoning using correct Geometry justification. For the ease of symbols used in your justification, let Morsetown be point o, Meridian be point M, Grenata be point G, Camden be point C, and Lowell be point L.

The map below shows five different towns. The town of Meridian wasgiven its name because it lies exactly halfway between two pairs of cities:
Camden and Grenata, and Lowell and Morsetown.

5 miles

Step-by-step explanation:

We are looking at triangles LCM and OGM.

Point M is the midpoint of segments LO and CG.

That makes segments CM and GM congruent (side).

Then angles CML and GMO are congruent since they are vertical angles (angle).

Finally, segments LM and OM are also congruent because of the midpoint (side).

By SAS, triangles LCM and OGM are congruent.

Then by CPCTC, segments LC and OG are congruent.

Since OG = 5 miles, then LC = 5 miles.

5 miles

y=−9/2x+10

step-by-step explanation:

let's solve for y.

0−9x−2y=−20

step 1: add 9x to both sides.

−9x−2y+9x=−20+9x

−2y=9x−20

step 2: divide both sides by -2.

−2y

−2

=

9x−20

−2

y=

−9

2

x+10

0 and 5 minutes

step-by-step explanation:

given that one morning eight buses arrive late by the number of minutes given below:

0 8 2 6 9 2 0 7 8

write these in ascending order

0   0 2 6 7 8 8 9

in the afternoon two more buses arrive at the bus stop say by x and y minutes late.

total number of buses = 10

median = average of 4th and 5th after arranging in ascending order

since 4th entry is 6, the values of x and y should be below 6

also given 0 is the mode so either x or y or both should be 0 because then only 0 gets the maximum frequency and hence mode

thus we have

0 0 0 2 6 7 8 8 9 and another unknown entry which is below 6.

since median is 3.5, we have the unknown entry to be 5 only because then only median =( 2+5)/2

thus the after noon buses were late by 0 and 5 minutes.