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3 years ago

Help please !!! At a local Brownsville play production, 420 tickets were sold. The ticket prices varied on the seating

Mathematics

1 answer:

Radda [10]3 years ago

7 0

Answer:

n = 12$ x = 8$ y = 10$ where n, x, and y are number of tickets

12 n + 8 x + 10 y = 3920 and n + x + y = 420

12n + 8 (x + y) + 2 y = 3920

12 n + 8 (5 n) + 2 y = 3920 since 5 (x + y) = n

52 n + 2 y = 3920 or y = 1960 - 26 n

Also, n + x + y = 420 or n + 5 n = 420 since x + y = 5 n

n = 70 so 70 of the $12 were sold

And since y = 1960 - 26 n we have y = 140 tickets

Now 12 * 70 + 8 x + 140 * 10 = 3920

This gives x = 210 tickets

Check: 210 + 140 + 70 = 420 tickets

Also, 12 * 70 + 210 * 8 + 140 * 10 = 3920

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Island A is 250 miles from island B. A ship captain travels 260 miles from island A and then finds out he is off course and 160

elena-14-01-66 [18.8K]

CHECK THE COMPLETE QUESTION BELOW

Island A is 250 miles from island B. A ship captain travels 260 miles from island A and then finds that he is off course and 160 miles from island B. What bearing should he turn to, so he is heading straight towards island B?

A. 111.65

B. 119.84

C. 21.65

D. 135.53

Answer:

OPTION A IS CORRECT

A. 111.65

Step-by-step explanation:

This question can be explained using a triangle, let us say triangle ABD

and let us say A and B represent the islands and D is the particular point from where the captain is standing at a distance of 160 miles from B island .

We will be making use of cosines rule to calculate our angles, and we know that from cosine rule

D² = a² + b² -2abCosD

Where, a= 160 b = 260 and d = 250 then we can substitute in order to calculate our angles

250²= 60² + 260² - 2(160*260)Cos(D)

62500= 625600+ 67600- 83200CosD

83200CosD= 25600+ 67600 - 625600

83200CosD= 30700

CosD= 30700/83200

CosD= 0.369

D= cos⁻¹ (0.369)

D=68.35

Therefore, the angle inside the triangle is 68.35°

Now we can now find the bearing the captain supposed to turn , if he is heading to island B which will be the external angle of the triangle, but we know that The external angle =180°(supplimentary angles )

Then the angle he would turn will be external angle of the triangle - 68.35°

= (180 - 68.35)

= 111.65°

Therefore, the bearing the captain should turn is 111.65° for him to be heading straight towards island B.

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3 years ago

Please see attachment and SHOW WORK. Thank You. Will mark brainliest!!

Fofino [41]

a. Let c and b represent the numbers of capped and broken bottles, respectively. Here is the system of equations.

... c + b = 15 . . . . 15 bottles have come Erica's way

... 4c -2b = 6 . . . .Erica's net pay for the day is 6 cents

b. By substitution, we can write an expression for b in terms of c:

... b = 15 - c

Then put it into the second equation:

... 4c - 2(15-c) = 6

... 6c - 30 = 6 . . . . eliminate parentheses

... 6c = 36 . . . . . . .add 30

... c = 6 . . . . . . . . . divide by 6

... b = 15 - 6 = 9 . . find the value of b

Erica has capped 6 bottles and broken 9.

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Here's one way to do it by elimination. We can divide the second equation by 2 to put it into standard form:

... 2c - b = 3

Now, adding it to the first equation gives

... (2c -b) + (c +b) = (3) + (15)

... 3c = 18 . . . . . simplify. Notice the b variable has been eliminated

... c = 6 . . . . . . . divide by 3

... 6 + b = 15

... b = 9 . . . . . . substitute into the first equation and solve for b by subtracting 6

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