Hello,
Question:
Jack popped some popcorn, but 3 of the 150 kernels did not pop.
Determine which popcorn snacks below has the same ratio of unpopped to total kernels as Jack's popcorn.
We Know:
3 out of 150 did not pop
Solution:
3/150 = 3 to 150
Find ratios similar to this one,
4/200
2/100
1/50
So now we know for every kernel that dosent pop there are 50 that did.
Answers:
4 unpopped out of 200 kernels
1 unpopped out of 50 kernels
We compute for the side lengths using the distance formula √[(x₂-x₁)²+(y₂-y₁)²].
AB = √[(-7--5)²+(4-7)²] = √13
A'B' = √[(-9--7)²+(0-3)²] = √13
BC = √[(-5--3)²+(7-4)²] = √13
B'C' = √[(-7--5)²+(3-0)²] =√13
CD = √[(-3--5)²+(4-1)²] = √13
C'D' = √[(-5--7)²+(0--3)²] = √13
DA = √[(-5--7)²+(1-4)²] = √13
D'A' = √[(-7--9)²+(-3-0)²] = √13
The two polygons are squares with the same side lengths.
But this is not enough information to support the argument that the two figures are congruent. In order for the two to be congruent, they must satisfy all conditions:
1. They have the same number of sides.
2. All the corresponding sides have equal length.
3. All the corresponding interior angles have the same measurements.
The third condition was not proven.
