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jok3333 [9.3K]
3 years ago
6

An angle has a measure of (5x + 7)º, and another angle has a measure of (2x + 54)°.

Mathematics
1 answer:
nadezda [96]3 years ago
3 0

Answer:

17

Step-by-step explanation:

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Pretty Pavers company is installing a driveway. Below is a diagram of the driveway they are
prohojiy [21]

Answer:

The most correct option is;

(B) 958.2 ft.²

Step-by-step explanation:

From the question, the dimension of each square = 3 ft.²

Therefore, the length of the sides of the square = √3 ft.

Based on the above dimensions, the dimension of the small semicircle is found by counting the number of square sides ti subtends as follows;

The dimension of the diameter of the small semicircle = 10·√3

Radius of the small semicircle = Diameter/2 = 10·√3/2 = 5·√3

Area of the small semicircle = (π·r²)/2 = (π×(5·√3)²)/2 = 117.81 ft.²

Similarly;

The dimension of the diameter of the large semicircle = 10·√3 + 2 × 6 × √3

∴ The dimension of the diameter of the large semicircle = 22·√3

Radius of the large semicircle = Diameter/2 = 22·√3/2 = 11·√3

Area of the large semicircle = (π·r²)/2 = (π×(11·√3)²)/2 = 570.2 ft.²

Area of rectangle = 11·√3 × 17·√3 = 561

Area, A of large semicircle cutting into the rectangle is found as follows;

A_{(segment \, of \, semicircle)} = \frac{1}{4} \times (\theta - sin\theta) \times r^2

Where:

\theta = 2\times tan^{-1}( \frac{The \, number \, of  \, vertical  \, squrare  \, sides  \ cut  \,  by  \  the  \  large  \,  semicircle}{The \, number \, of  \, horizontal \, squrare  \, sides  \ cut  \,  by  \  the  \  large  \,  semicircle} )

\therefore \theta = 2\times tan^{-1}( \frac{10\cdot \sqrt{3} }{5\cdot \sqrt{3}} ) = 2.214

Hence;

A_{(segment \, of \, semicircle)} = \frac{1}{4} \times (2.214 - sin2.214) \times (11\cdot\sqrt{3} )^2 = 128.3 \, ft^2

Therefore; t

The area covered by the pavers = 561 - 128.3 + 570.2 - 117.81 = 885.19 ft²

Therefor, the most correct option is (B) 958.2 ft.².

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3 years ago
A mathematical sentence which contains an inequality symbol and one variable raised to the first power is called a ____ inequali
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The answer to fill in the blank should be ''Linear''.
5 0
3 years ago
Choose the problem that has the same answer as 6 × 2 × 3.
11Alexandr11 [23.1K]

Answer:

6x3x2

Step-by-step explanation:

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3 years ago
A new drug claims to reduce the number of migraines an individual suffers. In a study on the effectiveness of the new drug, 50 s
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Answer:

I got A on edg

Step-by-step explanation:

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3 years ago
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he graph of f(x) = |x| is stretched by a factor of 0.3 and translated down 4 units. Which statement about the domain and range o
vampirchik [111]

Answer:

Out of the four, the only statement true about the parent and the transformed function is:

"The domain of the transformed function and the parent function are all real numbers."

Step-by-step explanation:

Parent function:

f(x) = |x|

Applying transformations:

1. Stretched by a factor of 0.3:

f(x) = 3|x|

2. Translated down 4 units:

f(x) = 3|x| - 4

Transformed function:

f(x) = 3|x| - 4

We can see that:

Range of the parent function = All real numbers greater than or equal to 0.

Range of the transformed function = All real numbers greater than or equal to -4.

Domain of the parent and the transformed function is same and equal to all real numbers.

Hence, the first three statements are wrong and the fourth one is true.

6 0
3 years ago
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