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Degger [83]
3 years ago
9

The Cheer Club is making a banner for your school using the design shown. The area of the yellow portion is 1 ft2. The expressio

n 8z−1 represents the area in square feet of the blue material in the banner. Evaluate the expression for z=9 to find the area of the blue material. When the length z is 9 ​feet, the blue area is ft2?
Mathematics
1 answer:
olga nikolaevna [1]3 years ago
3 0

Answer:

Blue = \frac{8}{9}

Step-by-step explanation:

Given

Yellow = 1ft^2

Blue = 8z^{-1

Required

Evaluate Blue when z = 9

To do this, we simply substitute 9 for z in Blue = 8z^{-1

Blue = 8 * 9^{-1

Convert indices to fraction

Blue = 8 * \frac{1}{9}

Blue = \frac{8}{9}

<em>Hence, the blue section has an area of </em>\frac{8}{9}ft^2<em></em>

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I believe it is -14 :)
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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
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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.

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3 years ago
The measures of two complementary angles have a ratio of 3:2 what is the meusure of the larger angle
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Answer:

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Step-by-step explanation:

The two angles add to 90 degrees since they are complementary

the ratio is 3:2

Multiply by x

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Add them together and set equal to 90

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5x=90

Divide each side by 5

5x/5 = 90/5

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The first angle is 3*18 = 54

The second angle is 2*18 = 36

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