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3 years ago

Find the radius of the circle of the shaded sector has an area of 5pi and a central angle of 2pi/5 rads Please include steps !!!

Mathematics

2 answers:

miskamm [114]3 years ago

7 0

Answer:

5 units

Step-by-step explanation:

Area of sector = ½ × r² × theta

5pi = ½ × r² × 2pi/5

r² = 5pi × 2 × 5/2pi

r² = 25

r = 5

Lerok [7]3 years ago

5 0

Answer:

r=5

Step-by-step explanation:

The area of a sector is found by

A = 1/2 r^2 theta where theta is in radians

We know the area and we know theta

5pi = 1/2 r^2 (2 pi/5)

5pi = r^2 pi/5

Multiply each side by 5/pi to isolate r^2

5/pi * 5pi = r^2 pi/5 * 5/pi

25 = r^2

Take the square root of each side

sqrt(25) = sqrt(r^2)

5 =r

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Factor Completely.<br> 12k^2-16k-60

faltersainse [42]

Answer:

4(k - 3)(3k + 5)

Step-by-step explanation:

Given

12k² - 16k - 60 ← factor out 4 from each term

= 4(3k² - 4k - 15) ← factor the quadratic

Consider the factors of the product of the coefficient of the k² term and the constant term which sum to give the coefficient of the k term

product = 3 × - 15 = - 45 , sum = - 4

Factors are - 9 and + 5

Use these factors to split the middle term

3k² - 9k + 5k - 15 → ( factor the first/second and third/fourth terms

= 3k(k - 3) + 5(k - 3) ← factor out (k - 3)

= (k - 3)(3k + 5)

Hence

12k² - 16k - 60 = 4(k - 3)(3k + 5) ← in factored form

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3 years ago

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Units of Capacity

marysya [2.9K]

Answer:

$\large\boxed{\large\boxed{0.2deciliter}}$

Explanation:

Build your conversion factors using the conversion table:

$1 cup = 0.237 liters\implies 1=0.237liters/1cup$

From the prefixes used in the metric system, you know that 1 deciliter = 0.100 liters. Then:

$1 deciliter = 0.100 liters\implies 1=1deciliter/0.100liters$

Arrange the expression to simplify the units and convert from cups to deciliters:

$9cups\times 0.237liters/cup\times 1deciliter/0.100liters=0.2133deciliter$

Round to the nearest tenth: 0.2 deciliter.

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3 years ago

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Does (1,-2) (2,1) (3,0) (4,2) represent a function Yes or No?

Artemon [7]

Answer:

Step-by-step explanation:

x= 1, 2, 3, 4

y= -2, 1, 0, 2

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2 years ago

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Anyone answering the coordinates subtraction can get there 100 points here.

Sholpan [36]

Answer:

c = -6

d = 2

Step-by-step explanation:

After reflection about the x-axis:

A --> A'

(x,y) --> (x,-y)

(2,3) --> (2,-3)

(4,3) --> (4,-3)

(2,6) --> (2,-6)

After translation:

(2 + c, -6 + d) --> (-4, -4)

2+c = -4

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If the basic measuring unit in base-7 is 49 circles, what does the measuring unit of size .001seven look like

Serjik [45]

The measuring unit is the standard unit of a quantity

The measuring unit of size 0.001 is represented by one millionth circle

<h3>How to determine the unit of base 0.001</h3>

The basic measuring unit in base 7 is given as:

49 circles

The above can be represented as:

Base 7 = 49 circles

Represent the base with n.

So, we have the following rule

$Circle = n^2$

For measuring unit 0.001, we have:

$Circle = 0.001^2$

Evaluate the square

$Circle = 0.000001$

This means that,

The measuring unit of size 0.001 is represented by one millionth circle