To get your answer:
9 times 5 times two= 90
9 times 7.5 times two= 135
5 times 7.5 times two= 75
then add all of them together and you will get the surface area
90+135+75=300
you should have an answer of 300 feet²
[ - 6 * x^2 * y^8 + 12* x * y^3 - 36 * x * y^2 ] / [6*x*y^2] =
[-6x^2 y^8 ] / [6xy^2] + [12x y^3] / [6xy^2] - [36xy^2] / [6xy^2] =
- xy^6 + 2y - 6
Answer: - xy^6 + 2y - 6
b must be equal to -6 for infinitely many solutions for system of equations
and ![-3 x+\frac{1}{2} y=-3](https://tex.z-dn.net/?f=-3%20x%2B%5Cfrac%7B1%7D%7B2%7D%20y%3D-3)
<u>Solution:
</u>
Need to calculate value of b so that given system of equations have an infinite number of solutions
![\begin{array}{l}{y=6 x+b} \\\\ {-3 x+\frac{1}{2} y=-3}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7By%3D6%20x%2Bb%7D%20%5C%5C%5C%5C%20%7B-3%20x%2B%5Cfrac%7B1%7D%7B2%7D%20y%3D-3%7D%5Cend%7Barray%7D)
Let us bring the equations in same form for sake of simplicity in comparison
![\begin{array}{l}{y=6 x+b} \\\\ {\Rightarrow-6 x+y-b=0 \Rightarrow (1)} \\\\ {\Rightarrow-3 x+\frac{1}{2} y=-3} \\\\ {\Rightarrow -6 x+y=-6} \\\\ {\Rightarrow -6 x+y+6=0 \Rightarrow(2)}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7By%3D6%20x%2Bb%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow-6%20x%2By-b%3D0%20%5CRightarrow%20%281%29%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow-3%20x%2B%5Cfrac%7B1%7D%7B2%7D%20y%3D-3%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow%20-6%20x%2By%3D-6%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow%20-6%20x%2By%2B6%3D0%20%5CRightarrow%282%29%7D%5Cend%7Barray%7D)
Now we have two equations
![\begin{array}{l}{-6 x+y-b=0\Rightarrow(1)} \\\\ {-6 x+y+6=0\Rightarrow(2)}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B-6%20x%2By-b%3D0%5CRightarrow%281%29%7D%20%5C%5C%5C%5C%20%7B-6%20x%2By%2B6%3D0%5CRightarrow%282%29%7D%5Cend%7Barray%7D)
Let us first see what is requirement for system of equations have an infinite number of solutions
If
and
are two equation
then the given system of equation has no infinitely many solutions.
In our case,
![\begin{array}{l}{a_{1}=-6, \mathrm{b}_{1}=1 \text { and } c_{1}=-\mathrm{b}} \\\\ {a_{2}=-6, \mathrm{b}_{2}=1 \text { and } c_{2}=6} \\\\ {\frac{a_{1}}{a_{2}}=\frac{-6}{-6}=1} \\\\ {\frac{b_{1}}{b_{2}}=\frac{1}{1}=1} \\\\ {\frac{c_{1}}{c_{2}}=\frac{-b}{6}}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7Ba_%7B1%7D%3D-6%2C%20%5Cmathrm%7Bb%7D_%7B1%7D%3D1%20%5Ctext%20%7B%20and%20%7D%20c_%7B1%7D%3D-%5Cmathrm%7Bb%7D%7D%20%5C%5C%5C%5C%20%7Ba_%7B2%7D%3D-6%2C%20%5Cmathrm%7Bb%7D_%7B2%7D%3D1%20%5Ctext%20%7B%20and%20%7D%20c_%7B2%7D%3D6%7D%20%5C%5C%5C%5C%20%7B%5Cfrac%7Ba_%7B1%7D%7D%7Ba_%7B2%7D%7D%3D%5Cfrac%7B-6%7D%7B-6%7D%3D1%7D%20%5C%5C%5C%5C%20%7B%5Cfrac%7Bb_%7B1%7D%7D%7Bb_%7B2%7D%7D%3D%5Cfrac%7B1%7D%7B1%7D%3D1%7D%20%5C%5C%5C%5C%20%7B%5Cfrac%7Bc_%7B1%7D%7D%7Bc_%7B2%7D%7D%3D%5Cfrac%7B-b%7D%7B6%7D%7D%5Cend%7Barray%7D)
As for infinitely many solutions ![\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Ba_%7B1%7D%7D%7Ba_%7B2%7D%7D%3D%5Cfrac%7Bb_%7B1%7D%7D%7Bb_%7B2%7D%7D%3D%5Cfrac%7Bc_%7B1%7D%7D%7Bc_%7B2%7D%7D)
![\begin{array}{l}{\Rightarrow 1=1=\frac{-b}{6}} \\\\ {\Rightarrow6=-b} \\\\ {\Rightarrow b=-6}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5CRightarrow%201%3D1%3D%5Cfrac%7B-b%7D%7B6%7D%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow6%3D-b%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow%20b%3D-6%7D%5Cend%7Barray%7D)
Hence b must be equal to -6 for infinitely many solutions for system of equations
and
Hello,
Five sixths of forty two is = 35.
Answer:
33-27
Step-by-step explanation: