Answer: 
<u>Step-by-step explanation:</u>
Isolate w by performing the following steps
- Multiply by 6 on both sides to clear the denominator
- Subtract 3 from both sides
- Divide both sides by 2
![y=\dfrac{1}{2}+\dfrac{w}{3}\\\\\\6\bigg[y=\dfrac{1}{2}+\dfrac{w}{3}\bigg]\quad \implies \quad 6y=3+2w\\\\\\6y-3=3-3+2w\quad \implies \quad 6y-3=2w\\\\\\\dfrac{6y-3}{2}=\dfrac{2w}{2}\quad \implies \quad \large\boxed{\dfrac{6y-3}{2}=w}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B1%7D%7B2%7D%2B%5Cdfrac%7Bw%7D%7B3%7D%5C%5C%5C%5C%5C%5C6%5Cbigg%5By%3D%5Cdfrac%7B1%7D%7B2%7D%2B%5Cdfrac%7Bw%7D%7B3%7D%5Cbigg%5D%5Cquad%20%5Cimplies%20%5Cquad%206y%3D3%2B2w%5C%5C%5C%5C%5C%5C6y-3%3D3-3%2B2w%5Cquad%20%5Cimplies%20%5Cquad%206y-3%3D2w%5C%5C%5C%5C%5C%5C%5Cdfrac%7B6y-3%7D%7B2%7D%3D%5Cdfrac%7B2w%7D%7B2%7D%5Cquad%20%5Cimplies%20%5Cquad%20%5Clarge%5Cboxed%7B%5Cdfrac%7B6y-3%7D%7B2%7D%3Dw%7D)
(- 1 + √3)/2
rationalise the denominator by multiplying the numerator/denominator by the conjugate of the denominator.
the conjugate of 1 + √3 is 1 - √3
(1 - √3)/(1 + √3)(1 - √3) = (1 - √3)/( 1² - (√3)²) = (1 - √3)/(1 - 3) = (1 - √3)/(- 2)
multiply numerator/denominator by (- 1)
=(-1 +√3)/2
My numbers aren't exactly the same due to rounding but you can still see the answer.
Answer:
-2
Step-by-step explanation:
Answer:
i) The value of x is 3.
ii) TE = 20cm
RN = 20cm
Step-by-step explanation:
According to the properties of rectangles,
The diagonals of rectangles are equal and bisect each other at 90°.
As per this,
OR = OT



TE = 2OT
TE = 2(3x + 1)
= 6x + 2
= 6(3) + 2
= 18 + 2
= 20
RN = 2OR
RN = 2(2x + 4)
= 4x + 8
= 4(3) + 8
= 12 + 8
= 20