To solve this, you can set up an equation. Make the length of the shortest side x, so the 2 sides double the length will equal 2x. Since they all equal the perimeter of 36, do x + 2x + 2x =36. These values all represent the sides(2 longer, one short). Combine like terms to get 5x=36 then divide by 5 to find the value of x. x=7.2in meaning the shorter side is 7.2 inches while the longer sides are both 14.4 inches each since they are double in size.
So first simplify 11/6x into 11x/6. Then -13/10x into -13x/10. So you should now have (-13x/10-11x/4)-3/2. Combine the like terms -13x/10 and -11x/4 to get -81x/20 and then with your left over -3/2= -81x/20-3/2
Answer:
m∠z= 58.7
Step-by-step explanation:
Remember, all triangles sum up to 180 degrees.
So, the equation would be: 31.3+90+m∠z= 180.
Step 1- Add to simplify.
(31.3+90)+m∠z= 180
121.3+m∠z= 180
Step 2- Subtract to both sides.
121.3+m∠z= 180
-121.3 -121.3
m∠z= 58.7
Write tan in terms of sin and cos.
![\displaystyle \lim_{t\to0}\frac{\tan(6t)}{\sin(2t)} = \lim_{t\to0}\frac{\sin(6t)}{\sin(2t)\cos(6t)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B%5Ctan%286t%29%7D%7B%5Csin%282t%29%7D%20%3D%20%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B%5Csin%286t%29%7D%7B%5Csin%282t%29%5Ccos%286t%29%7D)
Recall that
![\displaystyle \lim_{x\to0}\frac{\sin(x)}x = 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%5Cto0%7D%5Cfrac%7B%5Csin%28x%29%7Dx%20%3D%201)
Rewrite and expand the given limand as the product
![\displaystyle \lim_{t\to0}\frac{\sin(6t)}{\sin(2t)\cos(6t)} = \lim_{t\to0} \frac{\sin(6t)}{6t} \times \frac{2t}{\sin(2t)} \times \frac{6t}{2t\cos(6t)} \\\\ = \left(\lim_{t\to0} \frac{\sin(6t)}{6t}\right) \times \left(\lim_{t\to0}\frac{2t}{\sin(2t)}\right) \times \left(\lim_{t\to0}\frac{3}{\cos(6t)}\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B%5Csin%286t%29%7D%7B%5Csin%282t%29%5Ccos%286t%29%7D%20%3D%20%5Clim_%7Bt%5Cto0%7D%20%5Cfrac%7B%5Csin%286t%29%7D%7B6t%7D%20%5Ctimes%20%5Cfrac%7B2t%7D%7B%5Csin%282t%29%7D%20%5Ctimes%20%5Cfrac%7B6t%7D%7B2t%5Ccos%286t%29%7D%20%5C%5C%5C%5C%20%3D%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%20%5Cfrac%7B%5Csin%286t%29%7D%7B6t%7D%5Cright%29%20%5Ctimes%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B2t%7D%7B%5Csin%282t%29%7D%5Cright%29%20%5Ctimes%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B3%7D%7B%5Ccos%286t%29%7D%5Cright%29)
Then using the known limit above, it follows that
![\displaystyle \left(\lim_{t\to0} \frac{\sin(6t)}{6t}\right) \times \left(\lim_{t\to0}\frac{2t}{\sin(2t)}\right) \times \left(\lim_{t\to0}\frac{3}{\cos(6t)}\right) = 1 \times 1 \times \frac3{\cos(0)} = \boxed{3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%20%5Cfrac%7B%5Csin%286t%29%7D%7B6t%7D%5Cright%29%20%5Ctimes%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B2t%7D%7B%5Csin%282t%29%7D%5Cright%29%20%5Ctimes%20%5Cleft%28%5Clim_%7Bt%5Cto0%7D%5Cfrac%7B3%7D%7B%5Ccos%286t%29%7D%5Cright%29%20%3D%201%20%5Ctimes%201%20%5Ctimes%20%5Cfrac3%7B%5Ccos%280%29%7D%20%3D%20%5Cboxed%7B3%7D)
Answer:
![a \: b \: d \: f \\ mathematical \: sentence \: is \: one \: \\ which \: has \: a \: sign \: like = < \: \: \: \: \: \\ > \: \: \: \: \: \leqslant \: \: \: \: \: \geqslant](https://tex.z-dn.net/?f=a%20%5C%3A%20b%20%5C%3A%20d%20%5C%3A%20f%20%5C%5C%20mathematical%20%5C%3A%20sentence%20%5C%3A%20is%20%5C%3A%20one%20%5C%3A%20%20%5C%5C%20which%20%5C%3A%20has%20%5C%3A%20a%20%5C%3A%20sign%20%5C%3A%20like%20%3D%20%20%3C%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%5C%20%20%20%20%3E%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5Cleqslant%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5Cgeqslant%20)
it must always have one of the sign