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algol [13]
3 years ago
12

Solve the equation of e^x-2=(1/e^6)^x+3.

Mathematics
1 answer:
Aliun [14]3 years ago
5 0

Answer:

x = -16/7

Step-by-step explanation:

The equation as written reduces to finding the solution to a 7th-degree polynomial. The one real solution, found using a graphing calculator, is ...

x ≈ 1.60945071137

_____

Since this is beyond the scope of most algebra courses, we suspect you want the solution to ...

e^(x-2) = (1/e^6)^(x+3)

x -2 = -6(x +3) . . . . . . . . take the natural log of both sides

x -2 = -6x -18 . . . . . . . . . eliminate parentheses

7x -2 = -18 . . . . . . . . . . . add 6x

7x = -16 . . . . . . . . . . . . . add 2

x = -16/7

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Answer:

  1. first distribute the 5 to the d and 4
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  3. then subtract 20 from both sides of the equation
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  5. lastly divide 5 from both sides
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What is the distance from -12 to 88?
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100

Step-by-step explanation:

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Answer:

48.

Step-by-step explanation:

33 + 15 = 48.

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Which of these supporting details BEST fits after sentence 2?
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A survey of 1,107 tourists visiting Orlando was taken. Of those surveyed:
Ira Lisetskai [31]

Answer:

602 tourists visited only the LEGOLAND.

Step-by-step explanation:

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

I am going to say that:

-The set A represents the tourists that visited LEGOLAND

-The set B represents the tourists that visited Universal Studios

-The set C represents the tourists that visited Magic Kingdown.

-The value d is the number of tourists that did not visit any of these parks, so: d = 58

We have that:

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

In which a is the number of tourists that only visited LEGOLAND, A \cap B is the number of tourists that visited both LEGOLAND and Universal Studies, A \cap C is the number of tourists that visited both LEGOLAND and the Magic Kingdom. and A \cap B \cap C is the number of students that visited all these parks.

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 subsets:

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

There were 1,107 tourists suveyed. This means that:

a + b + c + d + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 1,107

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

The problem states that:

36 tourists had visited all three theme parks. So:

(A \cap B \cap C) = 36

72 tourists had visited both LEGOLAND and Universal Studios. So:

(A \cap B) + (A \cap B \cap C) = 72

(A \cap B) = 72 - 36

(A \cap B) = 36

79 tourists had visited both the Magic Kingdom and Universal Studios

(B \cap C) + (A \cap B \cap C) = 79

(B \cap C) = 79 - 36

(B \cap C) = 43

68 tourists had visited both the Magic Kingdom and LEGOLAND

(A \cap C) + (A \cap B \cap C) = 68

(A \cap C) = 68 - 36

(A \cap C) = 32

258 tourists had visited Universal Studios:

B = 258

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

258 = b + 43 + 36 + 36

b = 143

268 tourists had visited the Magic Kingdom:

C = 268

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

268 = c + 32 + 43 + 36

c = 157

How many tourists only visited the LEGOLAND (of these three)?

We have to find the value of a, and we can do this by the following equation:

a + b + c + d + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 1,107

a + 143 + 157 + 58 + 36 + 32 + 43 + 36 = 1,107

a = 602

602 tourists visited only the LEGOLAND.

6 0
3 years ago
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