Danielle’s text messaging plan costs 7$ for the first 700 messages and 30 cents for each additional text message. If she owes 18.40$ for text messaging in the month of October, how many text messages did she send that month?

738 messages

Step-by-step explanation:

Use the given information to set up an equation. 7 is constant and 0.3 per message, with a total of 18.40.

0.3x + 7 = 18.4

Now solve for x

0.3x = 11.4

x = 38

She sent 38 messages over the standard 700, meaning she sent a total of 738 messages in the month of October

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.