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Svetach [21]
3 years ago
9

37. Rectangle ABCD is graphed on a coordinate

Mathematics
1 answer:
Firlakuza [10]3 years ago
6 0

AC # A'B'

Step-by-step explanation:

While solving the above problem one must keep in mind that

  • Reflection along Y-axis would just make the rectangle upside down at the same distance from X-axis in the down direction.

Thus, from the figure it becomes clear that

  • AB ∦ B’D’
  • CD║A’B’
  • BD ∦ C’D’

Only statement that comes out true is the third statement which states that AC is not parallel to A’B’

Since the diagonal of a rectangle can not be parallel to one of its side (though the side in question is side of the same rectangle reflected in y axis)

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-7.5 - (8.5 + 5)

Step-by-step explanation:

We just add together the values of how much it dropped at different parts of the day, and subtract them from what we started with. The parenthesis are important cause we want to know what the total temperature drop for the day was before we subtract it to get the actual temperature we end up with.

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In the image, point A marks the center of the circle. Which two lengths must form a ratio of 2:1?
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Using properties of sets show that : a) A ∩ (A’ U B) = A ∩ B b) A ∩ (A U B )’ = Ф
asambeis [7]

Answer:

a) From A ∩ A' = ∅, we have;

A ∩ (A' ∪ B) = A ∩ B

b) From A ∩ (A' ∩ B') = (A ∩ A') ∩ B' and A ∩ A' = ∅, we have;

A ∩ (A ∪ B)' = ∅

Step-by-step explanation:

a) By distributive law of sets, we have;

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

From the complementary law of sets, we have;

A ∩ A' = ∅

Therefore, for A ∩ (A' ∪ B) = A ∩ B, we have

A ∩ (A' ∪ B) = (A ∩ A') ∪ (A ∩ B) (distributive law of sets)

A ∩ A' = ∅ (complementary law of sets)

Therefore;

(A ∩ A') ∪ (A ∩ B) = ∅ ∪ (A ∩ B)  = (A ∩ B) (Addition to zero identity property)

∴  A ∩ (A' ∪ B) = A ∩ B

b) By De Morgan's law

(A ∪ B)' = A' ∩ B'

Therefore, A ∩ (A ∪ B)' = A ∩ (A' ∩ B')

By associative law of sets, we have;

A ∩ (A' ∩ B') = (A ∩ A') ∩ B'

A ∩ A' = ∅ (complementary law of sets)

Therefore, (A ∩ A') ∩ B' = ∅  ∩ B' = ∅

Which gives;

A ∩ (A ∪ B)' = ∅.

4 0
3 years ago
How do solve this problem
Tanzania [10]
Multiply the first equation by 3
21x+15y=-6

Add this to the second equation
21x+15y=-6
-21x-15y=6
0+0=0

True

Final answer: Infinitely Many Solutions (they are coinciding lines)
8 0
3 years ago
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