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2 years ago

For positive acute angles A and B, it is known that cos A = 4/5 and tan B =5/12 Find the value of cos(A + B) in simplest form.

Mathematics

1 answer:

lys-0071 [83]2 years ago

5 0

Answer:

33/16

Step-by-step explanation:

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2 years ago

Find all numbers such that three times the number is greater than eight less than the number.

klio [65]

Answer:

ALL SUCH NUMBERS WHICH ARE GREATER THAN -4 satisfy the given condition.

Step-by-step explanation:

Here, assume such number = m

Now, given :

3 times the number = 3 x ( m) = 3 m

8 less than the given number = m - 8

Now, according to the question:

3 times the number > 8 less than the given number

or, 3 m > m - 8

or, 3m - m > m - 8 + m

or, 2 m > - 8

or, m > - 4

Hence, all SUCH NUMBERS WHICH ARE GREATER THAN -4 satisfy the given condition.

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3 years ago

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Step-by-step explanation:

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2 years ago

What is the common denominator of (5/x^2-4) - (2/x+2) in the complex fraction (2/x-2) - (3/x^2-4)/(5/x^2-4) - (2/x+2)

PIT_PIT [208]

9514 1404 393

Answer:

common denominator: (x² -4)
simplified complex fraction: (2x +1)/(9 -2x)

Step-by-step explanation:

It is helpful to remember the factoring of the difference of squares:

a² -b² = (a -b)(a +b)

Your denominator of (x² -4) factors as (x -2)(x +2). You will note that one of these factors is the same as the denominator in the other fraction.

It looks like you want to simplify ...

$\dfrac{\left(\dfrac{2}{x-2}-\dfrac{3}{x^2-4}\right)}{\left(\dfrac{5}{x^2-4}-\dfrac{2}{x+2}\right)}=\dfrac{\left(\dfrac{2(x+2)}{(x-2)(x+2)}-\dfrac{3}{(x-2)(x+2)}\right)}{\left(\dfrac{5}{(x-2)(x+2)}-\dfrac{2(x-2)}{(x-2)(x+2)}\right)}\\\\=\dfrac{2(x+2)-3}{5-2(x-2)}=\boxed{\dfrac{2x+1}{9-2x}}$

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2 years ago