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3 years ago

I have a triangle with angles measuring 40, 40, and 100. Is this one a unique triangle, many triangles, or no triangle?

Mathematics

1 answer:

juin [17]3 years ago

5 0

Answer:

Unique triangle.

Step-by-step explanation:

If you were to draw the triangle, you would've been able to see that one angle is open and that the other 2 were closed.

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Find sin 2a and cot 2a:

geniusboy [140]

Answer:

$sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cot(2\alpha ) = \frac{16511}{18720}$

Step-by-step explanation:

$\text{if } cos(\alpha)=\frac{12}{13}\\\text{That must mean we have a triangle with base 12, and hypotenuse 13.}\\\text{Using Pythagoras, we can determine the base of the triangle must be 5.}\\a^2+b^2=c^2 \text{, where c is the hypotenuse and a, b are the two other sides.}\\c^2-b^2=a^2\\\sqrt{c^2-b^2}=a\\\sqrt{13^2-12^2}=\sqrt{169-144}=\sqrt{25}=5\\\text{Therefore, }sin(\alpha) = \frac{5}{12}\\sin(2\alpha)=2sin(\alpha )cos(\alpha)\\\text{(From double angle formulae identities)}\\$

$sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cos(2\alpha )=cos^2(\alpha)-sin^2(\alpha)\\cos(2\alpha )=(\frac{12}{13})^2-(\frac{5}{12})^2=\frac{16511}{24336}\\cot(2\alpha)=\frac{cos(2\alpha)}{sin(2\alpha)}=\frac{\frac{16511}{24336}}{\frac{10}{13}}=\frac{16511}{18720}$

8 0

3 years ago

Adrian jogs 3/4 mile each morning how many days will take to jog 3 miles

lbvjy [14]

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Given Information
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Adrian can run 3/4 mile in 1 morning.

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Find how long he needs to run 1 mile
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3/4 miles = 1 morning

[ Divide by 3/4 on both side ]
3/4 ÷ 3/4 miles = 1 ÷ 3/4

1 miles = 4/3 morning

----------------------------------------------------------------
Find how long he needs to take to run 3 miles
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1 miles = 4/3 morning

[ multiply by 3 through ]
3 miles = 4/3 x 3
3 miles = 4 mornings

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Answer : 4 mornings
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6 0

3 years ago

What is the slope of the line in the graph below? (look at picture)

attashe74 [19]

The answer is 3/4! Explanation: use slope formula

5 0

3 years ago

Marketing company said 259 emails on Monday 431 emails on Tuesday and some emails on Wednesday if the company sent about like 13

atroni [7]

Answer:

610

Step-by-step explanation:

Given:

259 emails on Monday
431 emails on Tuesday
? emails on Wednesday
Total emails = 1300

Add:

259 + 431 = 690

Subtract:

1300 - 690 = 610

So, on Wednesday 610 emails were sent out.

Hope this helped.

6 0

3 years ago

A bag contains blue and yellow marbles. Two marbles are drawn without replacement. The probability of selecting a blue marble an

exis [7]

blue marbles
y = yellow marbles
Sum = b+y
The chance of a blue marble being drawn first is:
b / (b+y) = 0.55
The chance of a blue marble being drawn first then a yellow next is:
b / (b+y) * y / (b+y-1) = 0.37
This can be solve easily by using a theorem of Bayes
0.37/0.55 = .67 or 67%

7 0

3 years ago