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storchak [24]
3 years ago
11

Carpenter A charges $50 an hour. Carpenter B charges $20 to visit your home plus $45 for each hour. For how many hours will the

total cost for each carpenter be the same? How much will that cost be? If a customer thinks they need a carpenter for 3 hours, which carpenter should be hired?
Mathematics
1 answer:
umka2103 [35]3 years ago
8 0

Answer:

4 hours to pay the same amount

and aif you want a 3 hours work you should get carpenter A

Step-by-step explanation:

50x = 20 + 45x \\ 5x = 20 \\ x = 4hours \\

carpenter A for 3 hours:

50 \times 3 = 150dollars \\

carpenter B for 3 hours:

20 + 45 \times 3 = 155dollars

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AP^2=BP^2\implies AP=BP

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This means triangles APO and BPO are congruent, which means angles APO and BPO are congruent, so angle APB is bisected by PO.

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a botanist was measuring how tall her plant grew. after two weeks it had grown 9.62 inches. the second week alone it had grown 3
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Answer:

6.5 inches

Step-by-step explanation:

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3 years ago
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
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