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makvit [3.9K]
3 years ago
7

In triangle ABC, the measure of ∠B is 90°, BC=16, and AC=20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F

 correspond to vertices A, B, and C, respectively, and each side of triangle DEF is 13 the length of the corresponding side of triangle ABC. What is the value of sinF?
Mathematics
1 answer:
nevsk [136]3 years ago
6 0
The third side of triangle ABC is AB. Using the Pythagorean Theorem, its length is 12. 
12² + 16² = 20² 

∠F is congruent to ∠C and so the sin(∠F) = sin(∠C) 

The sin(∠C) = opposite/hypotenuse 
= |AB| / |AC| 
= 12/20 
= 3/5 
= 0.6 

Answer: 
Yes, it is 0.6
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(1/2 * 5/6) * 6

Step-by-step explanation:

The associative property of multiplication states that the product of three or more numbers remains the same regardless of how the numbers are grouped.

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19) It will cost $12.50 per person to make dinner. Write an
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Answer:

12.50x less than or equal to $200

Step-by-step explanation:

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A farmer had twice as many chickens as ducks on his farm. After he sold 166 chickens and ducks, he had half as many chickens as
mamaluj [8]

Answer:

The farmer have at first <u>202</u> chickens.

Step-by-step explanation:

Given:

A farmer had twice as many chickens as ducks on his farm. After he sold 166 chickens and ducks, he had half as many chickens as ducks left.

Now, to find the chickens farmer have at first.

Let the chickens be x.

And, the ducks be y.

<em>As, the farmer had twice as many chickens as ducks on his farm.</em>

So, x=2y    ......(1)

<em>As, given the farmer after selling 166 chickens and ducks, he had half as many chickens as ducks left.</em>

According to question:

x-166=(y-29)\times \frac{1}{2}

x-166=\frac{y-29}{2}

Substituting the value of x from equation (1) we get:

2y-166=\frac{y-29}{2}

<em>By cross multiplying we get:</em>

4y-332=y-29

<em>Adding both sides 332 we get:</em>

4y=y+303

<em>Subtracting both sides by </em>y<em> we get:</em>

3y=303

<em>Dividing both sides by 3 we get:</em>

y=101.

Now, to get the number of chickens substituting the value of y in equation (1):

x=2y\\\\x=2\times 101\\\\x=202.

Therefore, the farmer have at first 202 chickens.

7 0
3 years ago
The bakers at Healthy Bakery can make 350 bagels in 10 hours. How many bagels can they bake in 23 hours? What was that rate per
cluponka [151]

Answer:

In 23 hours they make 80.5 bagels. The unit rate is 3.5 bagels per hour

Step-by-step explanation:

Divide 10 hours by 10 hours to get 1 hour.

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Multiply the unit rate by 23, and you get 80.5 hours.

8 0
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How would you solve this? Are there any steps to take?
Genrish500 [490]
You just have to find what x is. Pretend there isn't the signs and think of it as = signs. Then whatever u do on one side do it to all of them
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3 years ago
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