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mr_godi [17]
3 years ago
11

Please help! I'll give a lot of points!!!​

Mathematics
1 answer:
harina [27]3 years ago
4 0

Answer:

41 i think i hope this is right

Step-by-step explanation:

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Find the possible values of s in the inequality 12s-20 <3s-25
GaryK [48]

12s - 20 < 3s - 25 |+20

12s < 3s - 5 |-3s

9s < -5 |:9

s < -5/9

Answer: Any number from the set (-∞, -5/9).

7 0
3 years ago
Four lab rats stage a daring escape in broad daylight, eventually establishing a colony behind the
Andrei [34K]

Answer:

9 months.

Step-by-step explanation:

use a calculator

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3 years ago
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Let A, B, C and D be sets. Prove that A \ B and C \ D are disjoint if and only if A ∩ C ⊆ B ∪ D
ANEK [815]

Step-by-step explanation:

We have to prove both implications of the affirmation.

1) Let's assume that A \ B and C \ D are disjoint, we have to prove that A ∩ C ⊆ B ∪ D.

We'll prove it by reducing to absurd.

Let's suppose that A ∩ C ⊄ B ∪ D. That means that there is an element x that belongs to A ∩ C but not to B ∪ D.

As x belongs to A ∩ C, x ∈ A and x ∈ C.

As x doesn't belong to B ∪ D, x ∉ B and x ∉ D.

With this, we can say that x ∈ A \ B and x ∈ C \ D.

Therefore, x ∈ (A \ B) ∩ (C \ D), absurd!

It's absurd because we were assuming that A \ B and C \ D were disjoint, therefore their intersection must be empty.

The absurd came from assuming that A ∩ C ⊄ B ∪ D.

That proves that A ∩ C ⊆ B ∪ D.

2) Let's assume that A ∩ C ⊆ B ∪ D, we have to prove that A \ B and C \ D are disjoint (i.e.  A \ B ∩ C \ D is empty)

We'll prove it again by reducing to absurd.

Let's suppose that  A \ B ∩ C \ D is not empty. That means there is an element x that belongs to  A \ B ∩ C \ D. Therefore, x ∈ A \ B and x ∈ C \ D.

As x ∈ A \ B, x belongs to A but x doesn't belong to B.  

As x ∈ C \ D, x belongs to C but x doesn't belong to D.

With this, we can say that x ∈ A ∩ C and x ∉ B ∪ D.

So, there is an element that belongs to A ∩ C but not to B∪D, absurd!

It's absurd because we were assuming that A ∩ C ⊆ B ∪ D, therefore every element of A ∩ C must belong to B ∪ D.

The absurd came from assuming that A \ B ∩ C \ D is not empty.

That proves that A \ B ∩ C \ D is empty, i.e. A \ B and C \ D are disjoint.

7 0
3 years ago
Evaluate the expression when x=-2 and y=3 3x-4y​
Illusion [34]

The expression re-written: 3(2) - 4(3)

First, we multiply (PEMDAS)

3 * 2 = 6

4 * 3 = 12

6 - 12 = -6

Answer: - 6

7 0
3 years ago
Solve the inequality​
Olegator [25]

Answer:

2 ≤ x

Step-by-step explanation:

6 0
2 years ago
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