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3 years ago

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Simplify 5 x times the fraction 1 over x to the power of negative 7 times x to the power of negative 2.

1 answer:

loris [4]3 years ago

3 0

Answer:

$5\ x^6$

Step-by-step explanation:

Given expression:

$5x\ .\ \frac{1}{x^{-7}}\ .\ x^{-2}$

Rules of exponents to be used:

$a^{-b}=\frac{1}{a^b}$ [Rule of negative exponent]

$a^b\ .\ a^c=a^{b+c}$ [Product Rule]

Using the above rules to simplify the given expression.

⇒ $5x\ .\frac{1}{\frac{1}{x^7}}\ .\ x^{-2}$ [By rule of negative exponent]

⇒ $5x\ .\ x^7\ .\ x^{-2}$ [Simplifying fractions]

⇒ $5\ x^{1+7-2}$ [By product rule]

⇒ $5\ x^6$ (Answer)

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Harry's parrot is 11 years older than his cat.

Sav [38]

Answer:

The answer to your question is: P = 17 years

Step-by-step explanation:

Data

Parrot = 11 years older than the cat

C = cat age

P = parrot age

P = ? when C = 6

Process

P = C + 11

P = 6 + 11

P = 17 years

8 0

3 years ago

When the members of a family discussed where their annual reunion should take place, they found that out of all the family mem

Doss [256]

Answer:

The total number of family members is 21.

Step-by-step explanation:

To solve this problem, we must build the Venn's Diagram of these sets.

I am going to say that:

-The set A represents those that would not go to a park.

-The set B represents those who would not go to a beach.

-The set C represents those who would not go to the family cottage.

The value d represents those who would go to all three places.

We have that:

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

In which a are those that would only not go to a park, $A \cap B$ are those who would not got to a park or to the beach, $A \cap C$ are those who would not go to a park or to the famili cottage. And $A \cap B \cap C$ are those that would not go to any of these places.

By the same logic, we have:

$B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)$

$C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

This diagram has the following values:

$a,b,c,d,(A \cap B), (A \cap C), (B \cap C), (A \cap B \cap C)$

The total number of family members is the sum of all these values:

$T = a + b + c + d + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

We start finding the values from the intersection of the three sets

5 would not go to a park or a beach or to the family cottage.

This means that $A \cap B \cap C = 5$

1 would go to all three places. This means that $d = 1$ .

8 would go to neither a park nor the family cottage

This means that:

$A \cap C + (A \cap B \cap C) = 8$

$A \cap C = 3$

8 would go to neither a beach nor the family cottage

$B \cap C + (A \cap B \cap C) = 8$

$B \cap C = 3$

7 would go to neither a park nor a beach

$A \cap B + (A \cap B \cap C) = 7$

$A \cap B = 2$

15 would not go to the family cottage

$C = 15$

$C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

$15 = c + 3 + 3 + 5$

$c = 4$

12 would not go to a beach

$B = 12$

$B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)$

$12 = b + 3 + 2 + 5$

$b = 2$

11 would not go to a park

$A = 11$

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

$11 = a + 2 + 3 + 5$

$a = 1$

Now, we can find the total number of family members.

$T = a + b + c + d + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

$T = 1 + 2 + 4 + 1 + 2 + 3 + 3 + 5$

$T = 21$

The total number of family members is 21.

5 0

2 years ago

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mars1129 [50]

Answer:

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Step-by-step explanation:

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Answer:

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2 years ago

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umka21 [38]

Answer:

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