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KonstantinChe [14]
3 years ago
6

Two different buses start their routes at the same corner at 9 A.M. Buses from one route stop at the library every 9 minutes. Bu

ses from the other route stop at the library every 12 minutes. In what number of minutes will both buses end up at the library?
Mathematics
1 answer:
Cloud [144]3 years ago
8 0

Answer: In 36 minutes both buses will end up at the library.

Step-by-step explanation:

Given: Buses from one route stop at the library every 9 minutes.

Buses from the other route stop at the library every 12 minutes.

The number of minutes in which both buses will end up at the library= LCM(9,12)

Now , 9= 3 x 3

12= 2 x 2 x 3

LCM(9,12) = 2 x 2 x 3 x 3 = 36

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Please assist with the geometry questions part 1​
kolezko [41]

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Answer:

  1.  sin(x) = a/c; cos(x) = b/c; tan(x) = a/b

  2, 3 see below

Step-by-step explanation:

1. The mnemonic SOH CAH TOA reminds you of the relationships between trig functions and sides of a right triangle:

  Sin = Opposite/Hypotenuse   ⇒   sin(x) = a/c

  Cos = Adjacent/Hypotenuse   ⇒   cos(x) = b/c

  Tan = Opposite/Adjacent   ⇒   tan(x) = a/b

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2. The attachment shows the two special right triangles. The 30-60-90 right triangle has sides in the ratio 1 : √3 : 2. The 45-45-90 isosceles right triangle has sides in the ratio 1 : 1 : √2.

These ratios can be used to write proportions that help you find the length of a missing side.

<em>Example</em>:

Suppose the triangle in problem 1 has x = 30°, and a = 10. Then we could find the length of missing side 'c' using a proportion involving the short side and the long side (hypotenuse).

  2/1 = c/10   ⇒   c = 20

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3. In a right triangle, the acute angles are complementary. The side adjacent to one acute angle is the side opposite the other. So the sine of one of the angles is the cosine of the other, and vice versa. This means the sine of an angle is the cosine of its complement, and vice versa.

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<em>Comment on question 3</em>

The wording of this question is a little strange. Sine and cosine are not complementary. Rather, the angles for which those functions have the same value are complementary.

6 0
3 years ago
tela bought a backpack for 34.99 and 3 notebooks for 1.89 each. What is the total price ,including a 8% sales tax?
Andreyy89
34.99+1.89+8=44.88 Hope this helps 
5 0
4 years ago
1. Are the ratios, 8/12 and 10/25 proportional? Please explain. I will give brainliest for the best explanation.
Marina86 [1]

Answer:

1. No

2. 1,050 bushels of corn

Step-by-step explanation:

1. A number is proportional if it has a constant ratio to another quantity.

8/12 and 10/25 do not.

2. An acre will produce \frac{750}{10} bushels of corn.

750 divided by 10 is 75. <u>This is 75 bushels per acre.</u>

Then you would multiply 75 and 14.

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4 0
3 years ago
Dan invests £11000 into a savings account. The bank gives 3.9% compound interest for the first 3 years and 4.5% thereafter. How
rodikova [14]
The initial amount of the money is £11,000 and the interest is 3.9% per year for first 3 years and then 4.5% after that. If Dan invests it for 7 years, that means the interest would be 3 years of 3.9% and 4 years of 4.5%.
The calculation would be:

total money= initial amount * interestrate1 * interest 2
total money= £11000 *(100%+3.9%)^3<span>*(100%+4.5%)^4
</span>total money= £11000 *(103.9%)^3 * (104.5%)^4
total money= £11000 * <span>1.121622319 </span>* 1.1925186
total money= £14,713.11

8 0
3 years ago
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