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DanielleElmas [232]
3 years ago
6

Which number make this sentence true 27:45=45:x​

Mathematics
2 answers:
jarptica [38.1K]3 years ago
6 0

Answer:

x = 75

Step-by-step explanation:

Let's consider the following equality.

27:45=45:x​

We can write this proportion in the fractional form.

27/45 = 45/x

We can solve for x using the Cross Product Property of Proportions.

27 × x = 45 × 45

27 × x = 2025

x = 2025/27

x = 75

The unknown number that satisfies the proportion is x = 75.

PSYCHO15rus [73]3 years ago
5 0

Answer:

x = 75

Step-by-step explanation:

We can write this as a proportion

27            45

--------- = --------

45            x

We can use cross products to solve

27 x = 45 *45

Divide each side by 27

27 x/27 = 45*45 /27

x = 75

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\frac{ \sin5A}{\sin A}  -  \frac{ \cos5A}{\cos A}  = 4\cos2A \\  \\ LHS = \frac{ \sin5A}{\sin A}  -  \frac{ \cos5A}{\cos A}   \\  \\  =  \frac{ \sin5A \:\cos A -  \cos5A \:  \sin A}{\sin A \:\cos A }  \\  \\  =  \frac{ \sin(5A -A )}{\sin A \:\cos A}  \\  \\ =  \frac{ \sin 4A}{\sin A \:\cos A}  \\  \\ =  \frac{ 2\sin 2A \: \cos 2A}{\sin A \:\cos A}  \\  \\ =  \frac{ 2 \times 2\sin A \: \cos A \: \cos 2A}{\sin A \:\cos A}  \\  \\ =  \frac{ 4\sin A \: \cos A \: \cos 2A}{\sin A \:\cos A}  \\  \\ =4\cos 2A \\  \\  = RHS \\  \\ thus \\  \\  \frac{ \sin5A}{\sin A}  -  \frac{ \cos5A}{\cos A}  = 4\cos2A \\  \\ hence \: proved

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