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2 years ago

Find the measure of x, then the measure of А (33-9x)" 48/Dc x = degrees I need it now please!!!

Mathematics

1 answer:

erastova [34]2 years ago

8 0

Answer:

x = - 11 ; m∠B = 132°

Step-by-step explanation:

(33 - 9x)° + 48° = 180°

33 - 9x + 48 = 180

81 - 9x = 180

- 9x = 99

x = - 11

m∠B = [33 - 9(- 11)]° = (33 + 99)° = 132°

m∠B = 132°

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Adam must fly home to city A from a business meeting in city B. One flight option flies directly to city A from B, a distance o

g100num [7]

Answer:

The value is $k =109.6 \ miles$

Step-by-step explanation:

The diagram illustrating the question is shown on the first uploaded image

From the question we are told that

The distance from city A to B is AB = 467.3 miles

The bearing from B to C is $\theta_{BC} = N 28.7E$

The bearing from B to A is $\theta_{BA} = N 60.7E$

The bearing from A to B is $\theta_{AB} = S60.7W$

The bearing from A to C is $\theta_{AC} = S79.1W$

Generally from the diagram

$\theta_A = 180 - 60.7 -79.1$

=> $\theta_A = 40.2 ^o$

Also

$\theta_B = 32^o$

and

$\theta_C = 180 - (\theta_A +\theta_B )$

=> $\theta_C = 180 - (40.2 + 32 )$

=> $\theta_C = 107.8 ^o$

Generally according to Sine Rule

$\frac{BC}{sin (\theta_A)} = \frac{CA}{sin (\theta_B)} =\frac{AB}{sin (\theta_C)}$

=> $\frac{BC}{sin (40.2)} = \frac{CA}{sin (32)} =\frac{467.3 }{sin (107.8)}$

$\frac{BC}{sin (40.2)} = \frac{467.3 }{sin (107.8)}$

=> $BC = 316.8 \ miles$

Also

$\frac{CA}{sin (32)} = \frac{467.3 }{sin (107.8)}$

$CA = 260 .1 \ miles$

Generally the additional flyer miles that Adam will receive if he takes the connecting flight rather than the direct flight is mathematically represented as

$k = [CA +BC] - AB$

=> $k = [260 .1 +316.8]- 467.3$

=> $k =109.6 \ miles$

4 0

2 years ago

How many positive integers $n$ from 1 to 5000 satisfy the congruence $n \equiv 5 \pmod{12}$?

irga5000 [103]

The equivalence $n \equiv 5 \pmod{12}$

means that n-5 is a multiple of 12.

that is

n-5=12k, for some integer k

and so

n=12k+5

for k=-1, n=-12+5=-7

for k= 0, n=0+5=5 (the first positive integer n, is for k=0)

we solve 5000=12k+5 to find the last k

12k=5000-5=4995

k=4995/12=416.25

so check k = 415, 416, 417 to be sure we have the right k:

n=12k+5=12*415+5=4985

n=12k+5=12*416+5=4997

n=12k+5=12*417+5=5009

The last k which produces n<5000 is 416

For all k∈{0, 1, 2, 3, ....416}, n is a positive integer from 1 to 5000,

thus there are 417 integers n satisfying the congruence.

Answer: 417

6 0

3 years ago

HELP ASAP!!

Monica [59]

B because it makes sense

3 0

3 years ago

Read 2 more answers

If i get a 22 out of 29 what's the percent out of 100?

Thepotemich [5.8K]

22/29 = 0.76
0.76*100 = 76
You got a 76%

7 0