There exists a trigonometric identity which states that,
sin (A - B) = sin A cos B - cos A sin B
This is very similar to the given expression with A equal to 57° and B equal to 13°. The simplified form of the angle is,
sin (57° - 13°) = sin 44°

5 0

3 years ago

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Please help math

Naddika [18.5K]

$\displaystyle\\
15(2a - 2) = 5(a^2 -1) \\ \\ 
30a - 30 = 5a^2-5\\\\
-5a^2 + 30a -30 + 5 =0\\\\
-5a^2 + 30a -25 =0 ~~~~~\Big| \times (-1) \\\\
5a^2 - 30a +25 = 0~~~~~\Big| : 5 \\\\
a^2 - 6a +5 = 0 \\ \\ 
a_{12}= \frac{-b\pm \sqrt{b^2-4ac}}{2a}= \frac{6\pm \sqrt{36-20}}{2}= \frac{6\pm \sqrt{16}}{2}=\frac{6\pm 4}{2}= \boxed{3\pm 2} \\ \\ 
a_1 = 3+ 2 = \boxed{5}\\\\
a_2 = 3-2 = \boxed{1}$

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3 years ago

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Help please! I have choral practice...

Maslowich

This polygon is composed of a right triangle and a parallelogram.

The area of right angle :
$A_\Delta=\frac{1}{2}\cdot15\cdot8=\frac{1}{2}\cdot120=\boxed{60\ (cm^2)}$

The area of the parallelogram:
$A_P=15\cdot(13-8)=15\cdot5=\boxed{75\ (cm^2)}$

The area of the polygon is equal: $A=A_\Delta+A_P$

Therefore, the answer is:
$\boxed{\boxed{A=60\ cm^2+75\ cm^2=135\ cm^2}}$

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3 years ago

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