Renan found the sum (4.2x + 3) + (5.7x – 2) + (5 – 2.6x), as shown. 4.2x + 3 + 5.7x – 2 + 5 – 2.6x

4.2x + 5.7x + 2.6x + 3 – 2 + 5

(4.2 + 5.7 + 2.6)x + 3 – 2 + 5

12.5x + 6

What was Renan’s error in adding the expressions?
He used the commutative property incorrectly.
He used the distributive property incorrectly.
He added incorrectly.
He multiplied incorrectly.

He added incorrectly.

in his second step, he should have subtracted 2.6x instead of adding 2.6x

A

Step-by-step explanation:

He used the commutative property incorrectly

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.

7

step-by-step explanation: