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3 years ago

7

Find the area of each figure. Round to the nearest hundredth if needed.

1 answer:

Hitman42 [59]3 years ago

6 0

Answer:

<h3>#1</h3>

<u>Trapezoid</u>

A = (b₁ + b₂)h/2
A = (4.8 yd + 29.4 ft)(8 yd)/2 = (14.6 yd)(4 yd) = 58.4 yd²

<h3>#2</h3>

<u>Rectangle</u>

A = ab
A = 2 yd * 3.1 yd = 6.2 yd²

<h3>#3</h3>

<u>Equilateral triangle</u>

A = √3/4a²
A = √3/4(10²) = 25√3

<h3>#4</h3>

<u>Regular octagon</u>

A = aP/2
A = 14.5(12*8)/2 = 696

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In the expansion (ax+by)^7, the coefficients of the first two terms are 128 and -224, respectively. Find the values of a and b

madam [21]

Answer:

a = 2, b = 3.5

Step-by-step explanation:

Expanding $(ax+by)^7$ using Binomial expansion, we have that:

$(ax+by)^7$ =

$(ax)^7(by)^0 + (ax)^6(by)^1 + (ax)^5(by)^2 + (ax)^4(by)^3 + (ax)^3(by)^4 + (ax)^2(by)^5 + (ax)^1(by)^6 + (ax)^0(by)^7$

$= (a)^7(x)^7+ (a)^6(x)^6(b)(y) + (a)^5(x)^5(b)^2(y)^2 + (a)^4(x)^4(b)^3(y)^3 + (a)^3(x)^3(b)^4(y)^4 + (a)^2(x)^2(b)^5(y)^5 + (a)(x)(b)^6(y)^6 + (b)^7(y)^7\\\\\\= (a)^7(x)^7+ (a)^6(b)(x)^6(y) + (a)^5(b)^2(x)^5(y)^2 + (a)^4(b)^3(x)^4(y)^3 + (a)^3(b)^4(x)^3(y)^4 + (a)^2(b)^5(x)^2(y)^5 + (a)(b)^6(x)(y)^6 + (b)^7(y)^7$

We have that the coefficients of the first two terms are 128 and -224.

For the first term:

=> $a^7 = 128$

=> $a = \sqrt[7]{128}\\ \\\\a = 2$

For the second term:

$a^6b = -224$

$b = \frac{-224}{a^6}$

$b = \frac{-224}{2^6} \\\\\\b = \frac{-224}{64} \\\\\\b = 3.5$

Therefore, a = 2, b = 3.5

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Step-by-step explanation:

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The person under has a better answer |

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klio [65]

Answer:

$x=4\sqrt{2}\ units$

Step-by-step explanation:

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Based on the theorem above,

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3 years ago

Factorize the Expression 81w^2 - 36wz + 4z^2

andre [41]

Answer:

( 9w - 2z)^2

Step-by-step explanation:

81w^2 - 36wz + 4z^2

Rewriting as

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We recognize that this is a perfect square binomial

a^2 -2ab + b^2 is a perfect square binomial because it factors to (a - b)^2

let a = 9w b = 2z

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3 years ago