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Stolb23 [73]
2 years ago
12

A is two years older than b who is twice as old as c. If the total of the ages of a, b and c be 27, then how old is b?.

Mathematics
1 answer:
RoseWind [281]2 years ago
8 0
A is 12 years
b is 10 years
c is 5 years
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Answer:

See explanation

Step-by-step explanation:

Simplify left and right parts separately.

<u>Left part:</u>

\left(1+\dfrac{1}{\tan^2A}\right)\left(1+\dfrac{1}{\cot ^2A}\right)\\ \\=\left(1+\dfrac{1}{\frac{\sin^2A}{\cos^2A}}\right)\left(1+\dfrac{1}{\frac{\cos^2A}{\sin^2A}}\right)\\ \\=\left(1+\dfrac{\cos^2A}{\sin^2A}\right)\left(1+\dfrac{\sin^2A}{\cos^2A}\right)\\ \\=\dfrac{\sin^2A+\cos^2A}{\sin^2A}\cdot \dfrac{\cos^2A+\sin^A}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A}\cdot \dfrac{1}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A\cos^2A}

<u>Right part:</u>

\dfrac{1}{\sin^2A-\sin^4A}\\ \\=\dfrac{1}{\sin^2A(1-\sin^2A)}\\ \\=\dfrac{1}{\sin^2A\cos^2A}

Since simplified left and right parts are the same, then the equality is true.

3 0
3 years ago
a total of $9500 is invested, part at 10% simple interest and part at 9%. if the total annual return from the two investments is
Nutka1998 [239]

a total of $9500 is invested, part at 10% simple interest and part at 9%

if the total annual return from the two investments is $914.00

Amount invested = 9500

Total amount return means total yield = $914

Let x amount  is invested at 10% simple interest

Interest for first part =  10 % times x = 0.10x

Remaining part invested is 9500 -x

Interest for remaining amount = 9% (9500 -x) = 0.09(9500-x)

Total interest yield is 914. Now we frame an equation

0.10x + 0.09(9500-x) = 914

0.10x +855 - 0.09x = 914 (combine like terms)

0.01 x + 855 = 914 (subtract 855)

0.01x = 59 ( divide both sides by 0.01)

So x = 5900

$5900 is invested in 10% simple interest

9500 - 5900 = $3600 is invested in 9% simple interest


3 0
3 years ago
Please help I will give brainliest.
salantis [7]

Answer:

Multiply the numbers then Add on both sides then simplify

Step-by-step explanation:

8 0
2 years ago
What is the slope of the line that passes through (-12, -5) and (0, -8)?
Lady bird [3.3K]

Answer:

-3/12

Step-by-step explanation:

8 0
3 years ago
Please help me, only answer if you know for sure
Galina-37 [17]

Answer:

Step-by-step explanation:

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If number of data's is even, then median = average of n/2th and (n+2)/2th term.

1) 1 , 3 , 5 , 5 , 6

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6 0
3 years ago
Read 2 more answers
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