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horrorfan [7]
2 years ago
10

Which expression is equal to 9(6 - t)? How do you know?

Mathematics
2 answers:
Gnesinka [82]2 years ago
4 0

Answer:

54-9t

Step-by-step explanation:

multiply the 9 with 6 and multiply 9 with the t which has an invisible 1

labwork [276]2 years ago
3 0
The answer is 54-9t. good luck!
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Answer: D. Infinitely many solutions

Explanation:
1. Remove parentheses
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3. Calculate them
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The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².

The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines

b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°)   ⇒   b = 96√3 cm

Call b the base of this triangle.

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since the interior angles of any triangle sum to 180°. Solve for θ :

2θ = 60°

θ = 30°

Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find

tan(30°) = h / (b/2)   ⇒   h = 48 cm

Then the area of the triangle is

1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²

and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:

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7 0
2 years ago
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2 years ago
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To solve this problem we will start by calculating time needed for each of them to fill the pool.

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Betty:
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