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klio [65]
3 years ago
14

Please find the missing side of the triangle and round the answer to the nearest tenth. Thanks.

Mathematics
1 answer:
Ede4ka [16]3 years ago
3 0

Answer:

x = 74.3

Step-by-step explanation:

Using the trigonometric ratio formula, the missing side, x, of the right angled triangle, can be found as follows:

Ѳ = 22°,

adjacent side length = x

Opposite side length = 30

Thus, we would apply the formula:

tan Ѳ = opposite length/adjacent length

tan 22 = \frac{30}{x}

Multiply both sides by x

tan 22*x = \frac{30}{x}*x

tan 22*x = 30

0.4040*x = 30

Divide both sides by 0.4040 to make x the subject of the formula

\frac{0.4040*x}{0.4040} = \frac{30}{0.4040}

x = \frac{30}{0.4040}

x = 74.26

x ≈ 74.3 (to the nearest tenth)

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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

5 0
3 years ago
Choose any method to find the gcf of 40 16 and 24
Juli2301 [7.4K]

The GCF of 40 16 and 24 is 8

<h3>How to determine the GCF of 40 16 and 24?</h3>

The numbers are given as:

40 16 and 24

Start by listing out the factors of the numbers:

This is done as follows:

  • The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40
  • The factors of 16 are: 1, 2, 4, 8, 16
  • The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

Then the greatest common factor in the above list is 8.

Hence, the GCF of 40 16 and 24 is 8

Read more about GCF at:

brainly.com/question/219464

#SPJ1

8 0
2 years ago
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larisa86 [58]
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Answer:

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Step-by-step explanation:

s = (∅/360) * πr²

s = (135/360) * π(4²)

s = (135/360)(16) * π

s = 4π mi²

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HACTEHA [7]

Answer:

The new cost is $ 2.34 and sales tax is .14.  Total cost is $2.48

Step-by-step explanation:

1.80 x 1.3 = 2.34

2.34 x .06 = .14

Add the two together for the total

6 0
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