Answer:
20 1/6 ft
Step-by-step explanation:
The perimeter is the sum of the lengths of the sides:
2×(5 1/3 ft) + 2×(4 3/4 ft) = 10 2/3 ft + 8 6/4 ft
= 10 2/3 ft + 9 2/4 ft . . . . change 6/4 ft to 1 1/2 ft
= 10 8/12 ft + 9 6/12 ft = 19 14/12 ft . . . . . use common denominator of 1/12 ft
= 20 2/12 ft . . . . . . change 14/12 ft to 1 2/12 ft; next reduce that fraction
= 20 1/6 ft . . . . perimeter of Caleb's bathroom
The value of sin(2x) is ![\frac{120}{169}](https://tex.z-dn.net/?f=%5Cfrac%7B120%7D%7B169%7D)
Explanation:
Given that ![tan x =\frac{12}{5}](https://tex.z-dn.net/?f=tan%20x%20%3D%5Cfrac%7B12%7D%7B5%7D)
The formula for
is ![\sin (2 x)=2 \sin x \cos x](https://tex.z-dn.net/?f=%5Csin%20%282%20x%29%3D2%20%5Csin%20x%20%5Ccos%20x)
Since, ![\tan x=\frac{o p p}{a d j}](https://tex.z-dn.net/?f=%5Ctan%20x%3D%5Cfrac%7Bo%20p%20p%7D%7Ba%20d%20j%7D)
Also, it is given that ![tan x =\frac{12}{5}](https://tex.z-dn.net/?f=tan%20x%20%3D%5Cfrac%7B12%7D%7B5%7D)
Thus,
and ![adj=5](https://tex.z-dn.net/?f=adj%3D5)
To find the hypotenuse, let us use the pythagoras theorem,
![\begin{aligned}h y p &=\sqrt{12^{2}+5^{2}} \\&=\sqrt{144+25} \\&=\sqrt{169} \\&=13\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dh%20y%20p%20%26%3D%5Csqrt%7B12%5E%7B2%7D%2B5%5E%7B2%7D%7D%20%5C%5C%26%3D%5Csqrt%7B144%2B25%7D%20%5C%5C%26%3D%5Csqrt%7B169%7D%20%5C%5C%26%3D13%5Cend%7Baligned%7D)
Now, we can find the value of sin x and cos x.
![\sin x=\frac{\text { opp }}{h y p}=\frac{12}{13}](https://tex.z-dn.net/?f=%5Csin%20x%3D%5Cfrac%7B%5Ctext%20%7B%20opp%20%7D%7D%7Bh%20y%20p%7D%3D%5Cfrac%7B12%7D%7B13%7D)
![\cos x=\frac{a d j}{h y p}=\frac{5}{13}](https://tex.z-dn.net/?f=%5Ccos%20x%3D%5Cfrac%7Ba%20d%20j%7D%7Bh%20y%20p%7D%3D%5Cfrac%7B5%7D%7B13%7D)
Now, substituting these values in the formula for sin 2x, we get,
![\begin{aligned}\sin (2 x) &=2 \sin x \cos x \\&=2\left(\frac{12}{13}\right)\left(\frac{5}{13}\right) \\&=\frac{120}{169}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Csin%20%282%20x%29%20%26%3D2%20%5Csin%20x%20%5Ccos%20x%20%5C%5C%26%3D2%5Cleft%28%5Cfrac%7B12%7D%7B13%7D%5Cright%29%5Cleft%28%5Cfrac%7B5%7D%7B13%7D%5Cright%29%20%5C%5C%26%3D%5Cfrac%7B120%7D%7B169%7D%5Cend%7Baligned%7D)
Thus, the value of sin(2x) is ![\frac{120}{169}](https://tex.z-dn.net/?f=%5Cfrac%7B120%7D%7B169%7D)
Answer:
v= 360
Step-by-step explanation:
v= ( l w h) / 3
v= ( 12 * 6 * 15 ) / 3
v = 1080/ 3
v=360
( happy to help) :)
can i get brainliest.
Answer:
10
Step-by-step explanation:
The hypotenuse of a triangle is the side that is opposite to the right angle, meaning that none of its endpoints form the right angle. In this case, the hypotenuse is LN which is 10.