Evaluate each of the following expression

|8|-|-4|

-|-4|-|-1-14|

-15

(Negative 15)

Step-by-step explanation:

The straight line symbols, bars  | |  around a number are absolute value symbols. When written around a number, it means the number between the symbols changes to positive. If the number is already positive, then it stays the same.

Similar to using brackets, solve the operations between the bars first before making the number positive.

When evaluating expressions, remember to use PEDMAS or BEDMAS from left to right.

(I put more spacing between each absolute value so you can see better.)

|8|  -  |-4|   -  |-4|  -  |-1-14|        First number: 8 is already positive.

= 8  -  |-4|   -  |-4|  -  |-1-14|         Second number: Change -4 to 4

= 8  -  4   -  |-4|  -  |-1-14|         Third number: Change -4 to 4

= 8  -  4   -  4  -  |-1-14|         Fourth: Solve between the bars -1-14 = -15

= 8  -  4   -  4  -  |-15|         Fourth: Change -15 to 15

= 8  -  4   -  4  -  15        Subtract from left to right. Simplify 8 - 4 = 4

= 4   -  4  -  15         Simplify 4 - 4 = 0

= 0 - 15         Subtract 15 from 0

= -15         Answer

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.