20% of 57 is what number ? the proportion is ?

11.4

20/100 = x/57

Step-by-step explanation:

It is perhaps simplest just to translate the given English sentence into a mathematical sentence.

... 20% ... ... of ... 57 ... is ... what number

... 20/100 ... × ... 57 .... = ... what number . . . . . . . . translation to math sentence

... 11.4 = what number . . . . . . . . carry out the multiplication

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If you're asked to write this as a proportion, you can write it like this:

You can solve this proportion by multiplying by 57 (the denominator under "what number"). Doing so gives you the same arithmetic sentence as shown above.

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.

597

step-by-step explanation: