Because PQRS is a parallelogram, you know that
![2x-1=y-1](https://tex.z-dn.net/?f=2x-1%3Dy-1)
and
![3y-11=x+4](https://tex.z-dn.net/?f=3y-11%3Dx%2B4)
. (This is because PT and TR are congruent, and the same goes for ST and TQ.)
Writing the equations in standard form, you have
![\begin{cases}2x-y=0\\x-3y=-15\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D2x-y%3D0%5C%5Cx-3y%3D-15%5Cend%7Bcases%7D)
Solving this system gives
![x=3](https://tex.z-dn.net/?f=x%3D3)
and
![y=6](https://tex.z-dn.net/?f=y%3D6)
. So,
![PT=TR=5](https://tex.z-dn.net/?f=PT%3DTR%3D5)
Answer:
This is a system of equations, meaning there are two equations you will need to use. The first equation would be d + n = 35, where d = dimes and n = nickels. The second equation would be 10d + 5n = 250, since each dime is 10 cents and each nickel is 5 cents totaling at 250 cents. To solve for nickels, solve one equation for dimes and substitute the answer into the d in the other equation. If you need any more help with this one I am happy to help.
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors
Exact Form:
2√10 + 5
Decimal Form:
11.32455532 . . .
Answer: 2√10 + 5
Hope this helps! :)
~Zain
Given:
The number is
.
To find:
The a+bi form of given number.
Solution:
We have,
![\sqrt{-11}](https://tex.z-dn.net/?f=%5Csqrt%7B-11%7D)
It can be written as
![\sqrt{-11}=\sqrt{-1\times 11}](https://tex.z-dn.net/?f=%5Csqrt%7B-11%7D%3D%5Csqrt%7B-1%5Ctimes%2011%7D)
![[\because \sqrt{ab}=\sqrt{a}\sqrt{b}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Csqrt%7Bab%7D%3D%5Csqrt%7Ba%7D%5Csqrt%7Bb%7D%5D)
![[\because \sqrt{-1}=i]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Csqrt%7B-1%7D%3Di%5D)
![\sqrt{-11}=\sqrt{11}i](https://tex.z-dn.net/?f=%5Csqrt%7B-11%7D%3D%5Csqrt%7B11%7Di)
Here, real part is missing. So, it can be taken as 0.
![\sqrt{-11}=0+\sqrt{11}i](https://tex.z-dn.net/?f=%5Csqrt%7B-11%7D%3D0%2B%5Csqrt%7B11%7Di)
So, a = 0 and
.
Therefore, the a+bi form of given number is
.
The answer is .001...................................