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3 years ago

Find the cosine of angle B.

Mathematics

1 answer:

Alexandra [31]3 years ago

4 0

$\boxed { \text {Cosine Rule : } a^2 = b^2 + c^2 - 2bc \cos(A) }$

9² = 12² + 15² - 2 (12) (15) cos (B)

81 = 144 + 225 - 360 cos(B)

81 = 369 - 360 cos (B)

360 cos (B) = 369 - 81

360 cos (B) = 288

cos (B) = 0.8

Answer: Cosine B = 0.8

$\boxed { \text {Cosine Rule : } a^2 = b^2 + c^2 - 2bc \cos(A) }$

12² = 15² + 9² - 2 (15)(9) cos (A)

144 = 225 + 81 - 270 Cos A

144 = 306 - 270 Cos A

270 Cos A = 162

Cos A = 3/5 or 0.6

Answer: Cosine Angle A = 3/5

You might be interested in

OT bisects ∠DOG. Find the measure of ∠DOG if ∠DOT = 4x + 4 and ∠TOG = 5x – 3

g100num [7]

Answer:

$\huge\boxed{64^o}$

Step-by-step explanation:

If OT is bisects ∠DOG, then m∠DOT = m∠TOG. Therefore

$4x+4=5x-3$ |subtract 4 from both sides

$4x+4-4=5x-3-4\\\\4x=5x-7$ |subtract 5x from both sides

$4x-5x=5x-5x-7\\\\-x=-7$ |change the signs

$x=7$

Calculate the measure of ∠DOG

m∠DOG = 2(m∠DOT)

$m\angle DOG=2(4\cdot7+4)=2(28+4)=2(32)=64$

6 0

3 years ago

Solve 5c + 4 = -26

mr_godi [17]

1) 5 c + 4 = - 26
5 c = -26 -4
5 c = -30
c = -30 / 5
c = -6 so correct option is B..

2) 3 x - x +2 = 12
2 x +2 = 12
2x = 12-2
2x = 10
x = 10/2
x= 5 so correct option is D

3 ) 3 ( x + 1 )+ 6 = 33
3x + 3 + 6 = 33
3x + 9 = 33
3x = 33-9
3x = 24
x = 24/3
x = 8 so correct option is B

4) y/-6=9
y=9 x -6
y= - 54 there is no such option i guess question is missing

5)(x + 4) /2 = 7
x +4 = 7 x 2
x + 4 = 14
x = 14-4
x = 10 so correct option is D

6)1/3 ( 2x - 8) = 4
2x/ 3 - 8 /3 = 4
2x - 8 / 3 = 4
2x - 8 = 4 x 3
2x - 8 = 12
2x = 12 + 8
2x = 20
x = 20/2
x = 10 so correct option is C

6 0

4 years ago

The probability that a rental car will be stolen is. 4. if 3500 cars are rented, what is the approximate poisson probability tha

kozerog [31]

Using the Poisson distribution, there is a 0.8335 = 83.35% probability that 2 or fewer will be stolen.

<h3>What is the Poisson distribution?</h3>

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

$P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}$

The parameters are:

x is the number of successes

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

The probability that a rental car will be stolen is 0.0004, hence, for 3500 cars, the mean is:

$\mu = 3500 \times 0.0004 = 1.4$

The probability that 2 or fewer cars will be stolen is:

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

In which:

$P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-1.4}1.4^{0}}{(0)!} = 0.2466$

$P(X = 1) = \frac{e^{-1.4}1.4^{1}}{(1)!} = 0.3452$

$P(X = 2) = \frac{e^{-1.4}1.4^{2}}{(2)!} = 0.2417$

Then:

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2466 + 0.3452 + 0.2417 = 0.8335$

0.8335 = 83.35% probability that 2 or fewer will be stolen.

More can be learned about the Poisson distribution at brainly.com/question/13971530

#SPJ1

4 0

1 year ago

The median is 28; 16,24,x,48

Nookie1986 [14]

x = 32

To find the media, you take the middle number. If there is no discrete middle number, take the sum of the two closest to the middle and divide by 2.

(24 + x)/2 = 28

Multiply by 2 on both sides to get:

24 + x = 56

Subtract 24 from both sides to isolate the variable:

x = 56 - 24
x = 32

3 0

3 years ago

Product of 7.69×5 be greater or less than its estimate of 8×5?

spayn [35]

The product is a bit less than the estimate. In fact, 7.69 is less than 8, and if you start with an equality, i.e.

$7.69 < 8$

you can multiply both sides by a positive number, and the inequality will still hold:

$7.69 \cdot 5 < 8 \cdot 5$

8 0

3 years ago