Answer:
x = 17
Step-by-step explanation:
corresponding interior angles are supplementary, meaning they have to add up to 180 degrees so
6x + 8 + 4x + 2 = 180° then combine like terms ( 6x and 4x, 8 and 2 )
10x + 10 = 180 subtract 10 from both sides
-10 -10
10x = 170 divide each side by 10
/10 /10
x = 17
Answer: see proof below
<u>Step-by-step explanation:</u>
Use the following Sum to Product Identities:
<u>Proof LHS → RHS</u>
![\text{Sum to Product:}\qquad \dfrac{\cos 10\bigg[2\cos \bigg(\dfrac{15+25}{2}\bigg)\sin \bigg(\dfrac{15-25}{2}\bigg)\bigg]}{\cos 20\bigg[-2\sin \bigg(\dfrac{15+5}{2}\bigg)\sin \bigg(\dfrac{15-5}{2}\bigg)\bigg]}](https://tex.z-dn.net/?f=%5Ctext%7BSum%20to%20Product%3A%7D%5Cqquad%20%5Cdfrac%7B%5Ccos%2010%5Cbigg%5B2%5Ccos%20%5Cbigg%28%5Cdfrac%7B15%2B25%7D%7B2%7D%5Cbigg%29%5Csin%20%5Cbigg%28%5Cdfrac%7B15-25%7D%7B2%7D%5Cbigg%29%5Cbigg%5D%7D%7B%5Ccos%2020%5Cbigg%5B-2%5Csin%20%5Cbigg%28%5Cdfrac%7B15%2B5%7D%7B2%7D%5Cbigg%29%5Csin%20%5Cbigg%28%5Cdfrac%7B15-5%7D%7B2%7D%5Cbigg%29%5Cbigg%5D%7D)
![\text{Simplify:}\qquad \qquad \dfrac{\cos 10[2\cos 20\sin (-5)]}{\cos 20[-2\sin 10\sin 5]}\\\\\\.\qquad \qquad \qquad =\dfrac{-2\cos10 \cos 20 \sin 5}{-2\sin 10 \cos 20 \sin 5}\\\\\\.\qquad \qquad \qquad =\dfrac{\cos 10}{\sin 10}\\\\\\.\qquad \qquad \qquad =\cot 10](https://tex.z-dn.net/?f=%5Ctext%7BSimplify%3A%7D%5Cqquad%20%5Cqquad%20%5Cdfrac%7B%5Ccos%2010%5B2%5Ccos%2020%5Csin%20%28-5%29%5D%7D%7B%5Ccos%2020%5B-2%5Csin%2010%5Csin%205%5D%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D%5Cdfrac%7B-2%5Ccos10%20%5Ccos%2020%20%5Csin%205%7D%7B-2%5Csin%2010%20%5Ccos%2020%20%5Csin%205%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D%5Cdfrac%7B%5Ccos%2010%7D%7B%5Csin%2010%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D%5Ccot%2010)
LHS = RHS: cot 10 = cot 10 
Answer: Rate of change of Area of the triangle = 2.75cm~/min
Step-by-step explanation:
If the present height of the triangle is 22cm and the height increases by 5cm/min. It means the height was 2cm four minutes earlier: 5cm for 1st min + 5cm for 2nd min + 5cm for 3rd min + 5cm for 4th min = 20cm after 4min.
Therefore height equals 22 - 20 = 2cm four minutes earlier.
Using the same four minutes for the base. Since the base shrinks at 1cm/min, for the base to shrink to 10cm it means it was 14cm four minutes earlier.
The Area of a triangle is given by
A = 1/2 × base × height
Therefore Area= 1/2× 10×22 = 110cm~
Since it took four minutes to get to this area, the rate of change of the area will be 110÷4 = 2.75cm~/min
Answer:
Step-by-step explanation:
the 2nd one
