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horrorfan [7]
2 years ago
5

Find the reference angle given: t = −76°

Mathematics
2 answers:
fiasKO [112]2 years ago
6 0
This angle t= -76º lies on the IV quadrant, so the reference angle is the acute positive angle fron this angle to x-axis, so in this case the reference angle is 76º. (if better if you can draw it).
Because, the formula for this quadrant is: Ref angle= 360º - given angle (but given angle has to be positive so for -76º turned positive is 284º) now you can apply the formula Ref angle= 360º - 284º= 76º
Morgarella [4.7K]2 years ago
3 0

Answer:  The required reference angle for the angle t is 284°.

Step-by-step explanation:  We are given to find the reference angle for the following angle t :

t = -76°.

We know that

any two reference angles differ by a measurement of 360°.

So, if s represents one of the reference angles for t, then we get

    s = t + 360°

⇒  s = -76° + 360°

⇒  s = 284°.

Thus, the required reference angle for the angle t is 284°.

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So the circumference of this circle is 3.14*25=78.5 (in)

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3 years ago
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The ratio of the number of dogs the number of cats is 4:5. There are 270 animals on the rescue Farm. The number of dogs is 4/5.
mafiozo [28]

Answer:

<em>Here is the complete question:</em>

The ratio of the number of dogs to the number of cats is 4:5. There are 270 animals on the rescue farm. for each of the following statements, explain whether statements is true or false and why:

a. The number of dogs is 4/5 the number of cats.

b. 4/5 of the pets at the farm are dogs.

c. There are exactly 30 more cats than dogs.

d. There are exactly 30 dogs at the farm.

e. 5/9 of the pets at the farm are cats.

a,c and e are true statements.

Step-by-step explanation:

Let the number of dogs be "d' and number of cats be "c".

According to the question:

⇒ c+d=270   ...equation (i)

Arranging the ratio:

⇒ \frac{4}{5} = \frac{d}{c}

⇒ 4c=5d

⇒ c=(\frac{5}{4})d    ...equation (ii)

Plugging (ii) in equation (i).

⇒ c+d=270

⇒ \frac{5}{4} d+d=270

⇒ \frac{5d+4d}{4} =270

⇒ 9d=270\times 4

⇒ d=\frac{270\times 4}{9}

⇒ d=120

Number of dogs "d" = 120

Number of cats "c" = (270-120) = 150

Lets check each statement:

a.

The number of dogs is 4/5 the number of cats.

⇒ \frac{4}{5} \times 150

⇒ \frac{4\times 150}{5}

⇒ 120

Statement is true.

b.

4/5 of the pets at the farm are dogs.

⇒ \frac{4}{5} \times 270

⇒ 216

Number of dogs = 120

So the above statement is false.

c.

There are exactly 30 more cats than dogs.

⇒ c-d =30

⇒ 150-120=30

Statement is true.

d.

There are exactly 30 dogs at the farm.

False, as there are 120 dogs

e.

5/9 of the pets at the farm are cats.

⇒ \frac{5}{9} \times 270

⇒ 150

Statement is true.

So,

Statement  a,c and e are true as we could observe in the explanation.

8 0
2 years ago
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