The picture in the attached figure
we know that
area of the <span>the shaded region=area of rectangle -area of a kite
area of rectangle=(3x+x)*(x+x)----> 4x*2x---> 8x</span>²
area of a kite=(1/2)*[d1*d2]
where d1 and d2 are the diagonals
d1=4x
d2=2x
so
area of a kite=(1/2)*[4x*2x]----> 4x²
area of the the shaded region=8x²-4x²-----> 4x²
the answer is 4x²
<span>The vertical asymptotes of the function cosecant are determined by the points that are not in the domain.</span>
We know the cofunction identity
![tan(90-x)=cotx](https://tex.z-dn.net/?f=tan%2890-x%29%3Dcotx)
.
Thus, the tangent of 90° minus <span>θ also equals
5.</span>
Answer:
a) ![-2x^2+5xy](https://tex.z-dn.net/?f=-2x%5E2%2B5xy)
b) ![-3y^2+5xy](https://tex.z-dn.net/?f=-3y%5E2%2B5xy)
Step-by-step explanation:
<u>Part (a)</u>
Given polynomial :![2x^2+3y^2-5xy+1](https://tex.z-dn.net/?f=2x%5E2%2B3y%5E2-5xy%2B1)
The binomial that should be added to the given polynomial to get a polynomial that does not contain the variable x is:
![-2x^2+5xy](https://tex.z-dn.net/?f=-2x%5E2%2B5xy)
![(2x^2+3y^2-5xy+1)+(-2x^2+5xy)](https://tex.z-dn.net/?f=%282x%5E2%2B3y%5E2-5xy%2B1%29%2B%28-2x%5E2%2B5xy%29)
![=2x^2+3y^2-5xy+1-2x^2+5xy](https://tex.z-dn.net/?f=%3D2x%5E2%2B3y%5E2-5xy%2B1-2x%5E2%2B5xy)
![=2x^2-2x^2+3y^2-5xy+5xy+1](https://tex.z-dn.net/?f=%3D2x%5E2-2x%5E2%2B3y%5E2-5xy%2B5xy%2B1)
![=3y^2+1](https://tex.z-dn.net/?f=%3D3y%5E2%2B1)
<u>Part (b)</u>
Given polynomial :![2x^2+3y^2-5xy+1](https://tex.z-dn.net/?f=2x%5E2%2B3y%5E2-5xy%2B1)
The binomial that should be added to the given polynomial to get a polynomial that does not contain the variable y is:
![-3y^2+5xy](https://tex.z-dn.net/?f=-3y%5E2%2B5xy)
![(2x^2+3y^2-5xy+1)+(-3y^2+5xy)](https://tex.z-dn.net/?f=%282x%5E2%2B3y%5E2-5xy%2B1%29%2B%28-3y%5E2%2B5xy%29)
![=2x^2+3y^2-5xy+1-3y^2+5xy](https://tex.z-dn.net/?f=%3D2x%5E2%2B3y%5E2-5xy%2B1-3y%5E2%2B5xy)
![=2x^2+3y^2-3y^2-5xy+5xy+1](https://tex.z-dn.net/?f=%3D2x%5E2%2B3y%5E2-3y%5E2-5xy%2B5xy%2B1)
![=2x^2+1](https://tex.z-dn.net/?f=%3D2x%5E2%2B1)
$39.40 all together. You would multiply the cost of 2.90 by the amount needed which is 6 and get you an answer of 17.4. Then you would multiply the cost of 4.40 by the amount needed which is 5 and get you the answer of 22. You would then add the sums 17.4 and 22 and get you your answer of $39.40