Markus scared 85, 92, 82, and 94 on the first four tests of the semester. His teacher has not yet told him his score on his fifth test, but did tell him that his score on the fifth test is five points lower than the average (arithmetic mean) of all five tests. Which equation could Markus use to determine the score of the fifth test, x?

y — x = 5

5y — x = 353

Step-by-step explanation:

Let the fifth score be x

Let the average of all the scores be y.

But the fifth score is 5 points lower than the average ie

y — x = 5 (1)

The average of the scores is the sum of all the scores divided the number of scores. This is written as

y = (85 + 92 + 82 + 94 + x) /5

y = (353 + x) /5

Multiply through by 5

5y = 353 + x

Rearrange the equation

5y — x = 353 (2)

The equation Markus will use to determine the x is given as

y — x = 5

5y — x = 353

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

hope i could ! : )