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Sergeu [11.5K]
3 years ago
5

Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary.

Mathematics
1 answer:
aliina [53]3 years ago
4 0
\bf \textit{Law of Cosines}\\ \quad \\
c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies 
c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)}\\\\
-----------------------------\\\\
b = \sqrt{{{ a}}^2+{{ c}}^2-(2{{ a}}{{ c}})cos(B)}
\\\\\\
b=\sqrt{{{ 11}}^2+{{ 18}}^2-2(11\cdot 18)cos(104^o)}
\\\\\\
b\approx 23.25512998582180400481\implies b\approx 23.26

so, "b" rounded up is 23.26, now, we know a = 11 and c = 18

well, to get the area then, let  us use Heron's formula

\bf \textit{Heron's Area formula}\\\\
A=\sqrt{s(s-a)(s-b)(s-c)}\qquad 
\begin{cases}
a=11\\
c=18\\
b\approx 23.26\\\\
s=\cfrac{a+b+c}{2}
\end{cases}
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Two friends board an airliner just before departure time. There are only 11 seats left, 4 of which are aisle seats. How many way
Vadim26 [7]

Using the Fundamental Counting Theorem, it is found that:

The 2 people can arrange themselves in 40 ways.

<h3>What is the Fundamental Counting Theorem?</h3>

It is a theorem that states that if there are n things, each with n_1, n_2, \cdots, n_n ways to be done, each thing independent of the other, the number of ways they can be done is:

N = n_1 \times n_2 \times \cdots \times n_n

With one people in the aisle and one in the normal seats, the parameters are:

n1 = 4, n2 = 7

With both in the aisle, the parameters is:

n1 = 4, n2 = 3

Hence the number of ways is:

N = 4 x 7 + 4 x 3 = 28 + 12 = 40.

More can be learned about the Fundamental Counting Theorem at brainly.com/question/24314866

#SPJ1

8 0
2 years ago
Kenneth loaned $1,200 to his niece to buy a computer. Two years later, she paid him back the $1,200 along with an interest of $9
insens350 [35]

Answer:

<u>The  annual interest rate was 4%</u>

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Loan to Kenneth's niece to buy a computer = US$ 1,200

Duration of the loan = 2 years

Niece paid back to Kenneth = US$ 1,296

Annual interest rate = x%

2. Let's find the annual interest rate after 2 years, using the following formula:

FV = PV * (1 + x)

PV = Loan to Kenneth's niece to buy a computer = US$ 1,200

FV = Niece paid back to Kenneth = US$ 1,296

rate (r) = x

Replacing with the real values:

1,296 = 1,200 * (1 + x)

1.296/1.200 = (1 + x) (Dividing by 1,200 at both sides)

1.08 = 1 + x

1.08 - 1 = x (Subtracting 1 at both sides)

<u>0.08 = x</u>

This is the interest rate for two years, for finding the annual interest rate we divide it by 2, this way:

<u>0.08 / 2 = 0.04 * 100 = 4%</u>

7 0
3 years ago
What is the value of 6 / x + 2x squared when x = 3
zavuch27 [327]

Answer:

8

Step-by-step explanation:

The equation will become 6/3+2(3)

-->6/3=2

-->Because of Order of Operation we will multiply the 2 and 3 before adding so 2(3) = 6

--> 6+2=8

6 0
3 years ago
Read 2 more answers
N/5 + -6 = 9 <br> What is n ?
Tatiana [17]
Answer: 75

work: n/5 + -6 = 9
n/5 = 9+ 6
n/5 = 15
n = 15 x 5
n= 75
4 0
3 years ago
68 * 27 - 81 + ? = 600
tankabanditka [31]

The missing term is -1155.

Step-by-step explanation:

Given expression is

68 * 27 - 81 + ? = 600

Let the missing term be x

68*27-81+x=600\\1836-81+x=600\\1755+x=600

Subtracting 1755 from both sides

1755-1755+x=600-1755\\x=-1155

Therefore,

The missing term is -1155.

Keywords: multiplication, addition

Learn more about multiplication at:

  • brainly.com/question/10364988
  • brainly.com/question/10435816

#LearnwithBrainly

8 0
3 years ago
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