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4 years ago

Quiz: Area of a Sector

Mathematics

1 answer:

bulgar [2K]4 years ago

3 0

Answer:

97 cm²

Step-by-step explanation:

The complete question is attached.

The circle has a diameter of 12 m. The radius of the circle = diameter/2 = 12/2 = 6 cm.

The area of the circle = πr² = π × 6² = 113 cm²

To find the area of the shaded portion we have to find the area of sector and subtract it from the circle area.

The angle of the sector (θ) = 360 - 310 = 50°

$Area\ of\ the\ sector=\frac{\theta}{360} *\pi r^2=\frac{50}{350}*\pi*6^2=16\ cm^2$

Area of shaded portion = Area of circle - Area of of sector = 113 - 16 = 97 cm²

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Is there enough information to prove each quadrilateral is a parallelogram? Explain.

omeli [17]

Answer:

1. yes

2, no

3. yes

4. yes

Step-by-step explanation:

1. yes

If both sets of opposite sides are congruent, the quadrilateral is a parallelogram.

2. no

We know two side lengths. We know nothing about the other 2 sides and also nothing about all 4 angles.

3. yes

The missing angle must be 102°. With both pairs of opposite angles congruent, it must be a parallelogram.

4. yes

With both pairs of opposite angles congruent, it must be a parallelogram.

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3 years ago

A hot tub that holds 300 gallons of water drains at a rate of 8 gallons write an equation that represents how many gallons of wa

Salsk061 [2.6K]

Answer:the number of gallons of water left in the tub after it has drained for x minutes is 300 - 8x

Step-by-step explanation:

A hot tub that holds 300 gallons of water drains at a rate of 8 gallons.

Let x represent the number of minutes for which the hot tub has drained water.

If the hot tub drains 8 gallons of water per minute, it means that in x minutes, the number of gallons of water that the hot tub would have drained is 8x

Therefore, the number of gallons of water left in the tub after it has drained for x minutes would be

300 - 8x

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3 years ago

Kaylee and Olivia go to the movie theater and purchase refreshments for their friends.

KatRina [158]

The price of one bag of popcorn is $3.75

Step-by-step explanation:

Let,

x represent the cost of a bag of popcorn

y represent the cost of a drink.

According to given statement;

4x+12y=30 Eqn 1

x+6y=11.25 Eqn 2

Multplying Eqn 2 by 2

$2(x+6y=11.25)\\2x+12y=22.50\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 1

$(4x+12y)-(2x+12y)=30-22.50\\4x+12y-2x-12y=7.50\\2x=7.50$

Dividing both sides by 2

$\frac{2x}{2}=\frac{7.50}{2}\\x=3.75$

4x+12y=30 and x+6y=11.25 can be used to find the price of one bag of popcorn and the price of one drink.

The price of one bag of popcorn is $3.75

Keywords: linear equation, elimination method

Learn more about elimination method at:

#LearnwithBrainly

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3 years ago

Significant figures in a measurement include all of the digits that are

bonufazy [111]

If you were to make your own measurements, your significant digits should include all of the measurable digits (the digits that correspond to the marks on the ruler) as well as one estimated position beyond the smallest measureable digit (the 5 in 3.5 cm, and the 2 in 3.52 cm).

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3 years ago

What is the justification for the step taken from line 2 to line 3?

stiv31 [10]

Step-by-step explanation:

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In the line 2, only variables were operated with a reduction of similar terms in each side of the equation, giving as result -4x at one side, and 2x at the other side.
In the line 3, terms with variables were joined together in one side of the equation, and then, they were operate it, given as result -6X.

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3 years ago

Read 2 more answers