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Mila [183]
3 years ago
6

A man drove 5 miles directly east from his home, made a left turn at an intersection, and then traveled 11 miles duc north to hi

s place of work. If a road was made directly from his home to his place of work, what would its distance be?

Mathematics
1 answer:
lubasha [3.4K]3 years ago
5 0
Answer: About 12.083



Explanation:
In order to solve this you would use Pythagorean theorem.

You are given the length of the two legs (5 and 11)

So by plugging in 5 and 11 into A Squared plus B Squared = C Squared, you get that C^2= 146.

By finding the square root of both sides you get square root of 146, which is approximately 12.803

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If tan tetha =8/15,find the value of sin tetha+cos tetha all divided by cos tetha (1-cos tetha)​
Dahasolnce [82]

Answer:  195.5 or 12 7/32

Step-by-step explanation:

There is no letter tetha in the table so I use α instead. However it is not sence to final result.

The expression is:

(sinα+cosα)/(cosα*(1-cosα))

Lets divide the nominator and denominator by cosα

(sinα/cosα+cosα/cosα)/(cosα*(1-cosα)/cosα)= (tanα+1)/(1-cosα)=

=(8/15+1)/(1-cosα)= 23/(15*(1-cosα))    (1)

As known cos²α=1-sin²α   (divide by cos²α both sides of equation)

cos²a/cos²α=1/cos²α-sin²α/cos²α

1=1/cos²α-tg²α

1/cos²α=1+tg²α

cos²α=1/(1+tg²α)

cosα=sqrt(1/(1+tg²α))= +-sqrt(1/(1+64/225))=+-sqrt(225/(225+64))=

=+-sqrt(225/289)=+-15/17   (2)

Substitute in (1) cosα  by (2):

1st use cosα=15/17

1) 23/(15*(1-cosα)) =23/(15*(1-15/17))= 23*17/2=195.5

2-nd use cosα=-15/17

2)23/(15*(1-cosα)) =23/(15*(1+15/17))= 23*17/32=12 7/32

7 0
3 years ago
If angle 1 and angle 2 are supplementary angles, and angle 3 and angle 2 are supplementary angles, what do you know about angle
dusya [7]

Answer:

  angle 1 and angle 3 are congruent

Step-by-step explanation:

Angles supplementary to the same angle are congruent. Here both angles 1 and 3 are supplementary to angle 2, so angles 1 and 3 are congruent.

_____

If you like, you can get there algebraically:

  m∠1 + m∠2 = 180

  m∠3 + m∠2 = 180

Subtract the second equation from the first:

  (m∠1 + m∠2) - (m∠3 + m∠2) = (180) - (180)

  m∠1 -m∠3 = 0 . . . . simplify

  m∠1 = m∠3 . . . . . . add m∠3

When angle measures are the same, the angles are congruent.

  ∠1 ≅ ∠3

4 0
3 years ago
Hello! Can you help you can get more points! Click on the photo for more view etc.
Murrr4er [49]

Answer:

22,950

Step-by-step explanation:

subtract 51,550 and 28,600. 0 - 0 = 0 then 5-0=5 5-6 you can not do so you barrow from the 1. 1 becomes 0 and 5 becomes 15. 15-6=9. 0-8 you can not do so you need to borrow from the 5. 5 becomes 4 and 0 becomes 10. 10-8=2. Finally, 4-2=2. Put is all together and you have 22,950.

4 0
3 years ago
An adult ticket to a museum costs 3$ more than a children’s ticket. When 200 adult tickets and 100 children tickets are sold, th
antiseptic1488 [7]

The cost of children’s ticket is $ 5

<h3><u>Solution:</u></h3>

Let "c" be the cost of one children ticket

Let "a" be the cost of one adult ticket

Given that adult ticket to a museum costs 3$ more than a children’s ticket

<em>Cost of one adult ticket = 3 + cost of one children ticket</em>

a = 3 + c  ------ eqn 1

<em><u>Given that 200 adult tickets and 100 children tickets are sold, the total revenue is $2100</u></em>

200 adult tickets x cost of one adult ticket + 100 children tickets x cost of one children ticket = 2100

200 \times a + 100 \times c = 2100

200a + 100c = 2100 ------ eqn 2

<em><u>Let us solve eqn 1 and eqn 2 to find values of "a" and "c"</u></em>

Substitute eqn 1 in eqn 2

200(3 + c) + 100c = 2100

600 + 200c + 100c = 2100

600 + 300c = 2100

300c = 1500

<h3>c = 5</h3>

Thus the cost of children’s ticket is $ 5

6 0
3 years ago
Hannah has to make 180 gallons of punch for a big party. The punch is made of soda and fruit drink. The cost of the soda is $2.4
vesna_86 [32]

Answer: 90 per each is you want how much money is needed in total that is 47.20 dollars

Step-by-step explanation:

8 0
3 years ago
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