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3 years ago

Find the perimeter and area of this figure

Mathematics

1 answer:

Sonja [21]3 years ago

8 0

Answer:

A = (16π -32) in²

P = (4π +8√2) in

Step-by-step explanation:

The area is that of a quarter-circle of radius 8 inches less half the area of a square with side length 8 inches. Two formulas are useful:

area of a circle = πr² . . . . .r = radius

area of a square = s² . . . . s = side length

Then your area is ...

A = (1/4)π(8 in)² - (1/2)(8 in)² = (64 in²)(π/4 -1/2)

A = (16π -32) in²

____

The applicable formulas for the side lengths of your figure are ...

arc BD = (1/4)(2πr) = π(r/2) = π(8 in)/2 = 4π in

segment BD = (8 in)√2

The perimeter is the sum of these lengths, so is ...

P = (4π +8√2) in

_____

Of course, you are very familiar with the fact that an isosceles right triangle with side lengths 1 has a hypotenuse of length √(1²+1²) = √2. Scaling the triangle by a factor of 8 inches means the segment AB will be 8√2 inches long.

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A=-2 b=3 -1/3<br> 7b-2/-a+1

SVETLANKA909090 [29]

The answer is 22.666666667

5 0

3 years ago

Write a polynomial expression, in simplified form, that represents the AREA of the blanket and use the expression to evaluate th

pochemuha

Answer:

Polynomial expression that represents the area of blanket:

$A(x)=(6x^2+5x-21)cm^2$

If $x=2$ : $A(2)=13cm^2$

Step-by-step explanation:

The area of the rectangle can be calculated with the formula:

$A=lw$

Being l the lenght of the rectangle and w the width of the rectangle.

In this case, the lenght and the width are represented with:

$l=(3x+7)cm$

$w=(2x-3)cm$

Substitute them into $A=lw$ :

$A(x)=(3x+7)(2x-3)$

Then:

Use Distributive property (Remember the Product of powers property: $b^a*b^c=b^{(a+c)}$ ):

$A(x)=(3x+7)(2x-3)\\A(x)=6x^2-9x+14x-21$

Add like terms:

$A(x)=(6x^2+5x-21)cm^2$ (Simplied form)

Evaluate $x=2$ :

$A(2)=(6(2)^2+5(2)-21)cm^2\\A(2)=(6(4)+10-21)cm^2\\A(2)=(24-11)cm^2\\A(2)=13cm^2$

6 0

4 years ago

What is 150 % of 32 ?

Mnenie [13.5K]

Answer: 48

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Explanation:

The keyword "of" means multiply

150% converts to the decimal form 1.5; you move the decimal point two spots to the left to go from percent form to decimal form

Putting those two facts together lead to...

150% of 32 = 1.5*32 = 48

----------------

Another approach:

x% = x/100

150% = 150/100 = 1.5

150% of 32 = 1.5*32 = 48

The last step is identical as before, but the conversion of 150% is slightly different this time.

------------------

Yet another approach:

100% of anything is itself

So 100% of 32 is 32

The extra 50% means we take half of 32 to get 16. Then we add that onto the 32 to get 16+32 = 48

5 0

3 years ago

Multiply.<br> (7c+6)(-5c-4)<br> Simplify your answer.<br> Х

Semenov [28]

Answer:

120c

Step-by-step explanation:

7c(-5c)*(-4+6)

7c+5c*4+6

12c*10

120c

7 0

3 years ago

Read 2 more answers

Is the number of members of Club X greater than the number of members of Club Y ? (1) Of the members of Club X, 20 percent are a

Oliga [24]

Answer:

Yes

Step-by-step explanation:

The 20% of members of club X that are also members of club Y can be written as: P(Y/X) = 20% (that is, the probability of belonging to Y given that it belongs to X)

The 30% of members of club Y that are also members of club X can be written as: P(X/Y) = 30% (that is, the probability of belonging to X given that it belongs to Y)

The formula of conditional probability of A given B is

P(A/B) = (A∩B) / P(A)

Where (A∩B) is the probability that both events A and B occur and P(A) is the probability of A.

Based on that, we can write,

P(Y/X) = P(Y∩X) / P(X) = 20 % = 0.2

P(X/Y) = P(Y∩X) / P(Y) = 30 % = 0.3

Clearing P(Y∩X) of both equations and equalizing,

P(Y/X).P(X) = P(X/Y).P(Y)

Moving terms ,

P(X) / P(Y) = P(X/Y) / P(Y/X) = 0.3 / 0.2 = 1.5

That is, P(X) is 1.5 times P(Y), which means that the amount of members of X is greater than the members of Y.

7 0

3 years ago