Eli runs 2 miles on his first day of training for a road race. the next day, he increases his distance run by 0.25 miles. the day after that, he increases his distance run by another 0.25 miles, and so on.
what is the total number of miles eli runs over the course of 12 days?
39.5 mi
40.25 mi
40.5 mi
42.75 mi

Total number of miles Eli runs over the course of 12 days is 40.5 mi .

Step-by-step explanation:

The sum formula for airthmetic series is given by

Where is the nth term , is the first term and d is the common difference .

As given

Eli runs 2 miles on his first day of training for a road race.

The next day, he increases his distance run by 0.25 miles. The day after that, he increases his distance run by another 0.25 miles, and so on.

d = 0.25 miles

n = 12

Put all the values in the sum formula

Therefore the total number of miles Eli runs over the course of 12 days is 40.5 mi .

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

step-by-step explanation:

de-gf

hj=3x+20

ji=15x-64