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Romashka [77]
3 years ago
12

Which expression can be used to fine the slope of a line containing the points (-3,2) and (7,-1)

Mathematics
1 answer:
Charra [1.4K]3 years ago
7 0

Hello there! you can use the expression \frac{ y_{1}-y_{2}}{x_{1}-x_{2} }!

To find slope, subtract the y values over the x values.

In this case:

2 - - 1 / - 3 - 7

3 / -10

So, -3/10 would be the slope of these points.

Hope this helps, have a great day!

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Using properties of sets show that : a) A ∩ (A’ U B) = A ∩ B b) A ∩ (A U B )’ = Ф
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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)

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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;

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

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

Which gives;

A ∩ (A ∪ B)' = ∅.

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