Dannika solved this equation: -2(x + 4) = 10. Below are her steps. Step 1: −2 (x+4)=10 Step 2: −2(x) + −2(4) =10 Step 3: −2x +−8 =10 Step 4: −8 −8 Step 5: −2x =2 Step 6: ÷−2 ÷−2 Step 7: x=1 Analyze Dannika's work. Dannika made 2 mistakes.

x = -9

Step-by-step explanation:

Given:

-2(x + 4) = 10.

Dannika's solution

-2(x + 4) = 10.

Step 1: −2 (x+4)=10

Step 2: −2(x) + −2(4) =10

Step 3: −2x +−8 =10

Step 4: −8 −8

Step 5: −2x =2

Step 6: ÷−2 ÷−2

Step 7: x=1

Correct calculation

-2(x + 4) = 10.

-2x - 8 = 10

Add 8 to both sides

-2x - 8 + 8 = 10 + 8

-2x = 18

Divide both sides by -2

x = 18 / -2

x = -9

Dannika made mistake in step 3 by saying + * - 8= +8 and step 4 by subtracting 8 from both sides of the equation

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.