12 times 3.14 = 37.68 CM
C=D x 3.14
![\huge \boxed{\mathfrak{Question} \downarrow}](https://tex.z-dn.net/?f=%20%5Chuge%20%5Cboxed%7B%5Cmathfrak%7BQuestion%7D%20%5Cdownarrow%7D)
Solve the following using Substitution method
2x – 5y = -13
3x + 4y = 15
![\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cboxed%7B%5Cmathfrak%7BAnswer%20%5C%3A%20with%20%5C%3A%20Explanation%7D%20%5Cdownarrow%7D)
![\left. \begin{array} { l } { 2 x - 5 y = - 13 } \\ { 3 x + 4 y = 15 } \end{array} \right.](https://tex.z-dn.net/?f=%5Cleft.%20%5Cbegin%7Barray%7D%20%20%7B%20l%20%20%7D%20%20%7B%202%20x%20-%205%20y%20%3D%20-%2013%20%7D%20%5C%5C%20%7B%203%20x%20%2B%204%20y%20%3D%2015%20%7D%20%5Cend%7Barray%7D%20%5Cright.)
- To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
![2x-5y=-13, \: 3x+4y=15](https://tex.z-dn.net/?f=2x-5y%3D-13%2C%20%5C%3A%203x%2B4y%3D15%20)
- Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign. I'm choosing the 1st equation for now.
![2x-5y=-13](https://tex.z-dn.net/?f=2x-5y%3D-13%20)
- Add 5y to both sides of the equation.
![2x=5y-13](https://tex.z-dn.net/?f=2x%3D5y-13%20)
![x=\frac{1}{2}\left(5y-13\right) \\](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B2%7D%5Cleft%285y-13%5Cright%29%20%20%5C%5C%20)
- Multiply
times 5y - 13.
![x=\frac{5}{2}y-\frac{13}{2} \\](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B5%7D%7B2%7Dy-%5Cfrac%7B13%7D%7B2%7D%20%20%5C%5C%20)
- Substitute
for x in the other equation, 3x + 4y = 15.
![3\left(\frac{5}{2}y-\frac{13}{2}\right)+4y=15 \\](https://tex.z-dn.net/?f=3%5Cleft%28%5Cfrac%7B5%7D%7B2%7Dy-%5Cfrac%7B13%7D%7B2%7D%5Cright%29%2B4y%3D15%20%20%5C%5C%20)
- Multiply 3 times
.
![\frac{15}{2}y-\frac{39}{2}+4y=15 \\](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B2%7Dy-%5Cfrac%7B39%7D%7B2%7D%2B4y%3D15%20%20%5C%5C%20)
- Add
to 4y.
![\frac{23}{2}y-\frac{39}{2}=15 \\](https://tex.z-dn.net/?f=%5Cfrac%7B23%7D%7B2%7Dy-%5Cfrac%7B39%7D%7B2%7D%3D15%20%20%5C%5C%20)
- Add
to both sides of the equation.
![\frac{23}{2}y=\frac{69}{2} \\](https://tex.z-dn.net/?f=%5Cfrac%7B23%7D%7B2%7Dy%3D%5Cfrac%7B69%7D%7B2%7D%20%20%5C%5C%20)
- Divide both sides of the equation by 23/2, which is the same as multiplying both sides by the reciprocal of the fraction.
![\large \underline{ \underline{ \sf \: y=3 }}](https://tex.z-dn.net/?f=%5Clarge%20%5Cunderline%7B%20%5Cunderline%7B%20%5Csf%20%5C%3A%20y%3D3%20%7D%7D)
- Substitute 3 for y in
. Because the resulting equation contains only one variable, you can solve for x directly.
![x=\frac{5}{2}\times 3-\frac{13}{2} \\](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B5%7D%7B2%7D%5Ctimes%203-%5Cfrac%7B13%7D%7B2%7D%20%20%5C%5C%20)
![x=\frac{15-13}{2} \\](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B15-13%7D%7B2%7D%20%20%5C%5C%20)
- Add
to
by finding a common denominator and adding the numerators. Then reduce the fraction to its lowest terms if possible.
![\large\underline{ \underline{ \sf \: x=1 }}](https://tex.z-dn.net/?f=%20%5Clarge%5Cunderline%7B%20%5Cunderline%7B%20%5Csf%20%5C%3A%20x%3D1%20%7D%7D)
- The system is now solved. The value of x & y will be 1 & 3 respectively.
![\huge\boxed{ \boxed{\bf \: x=1, \: y=3 }}](https://tex.z-dn.net/?f=%20%5Chuge%5Cboxed%7B%20%20%5Cboxed%7B%5Cbf%20%5C%3A%20x%3D1%2C%20%5C%3A%20y%3D3%20%7D%7D)
<h3>
Answer: 96</h3>
===================================================
Work Shown:
![4\sqrt{576}\\\\4\sqrt{2*2*2*2*2*2*3*3}\\\\4\sqrt{(2*2)*(2*2)*(2*2)*(3*3)}\\\\4\sqrt{(2)^2*(2)^2*(2)^2*(3)^2}\\\\4\sqrt{(2*2*2*3)^2}\\\\4\sqrt{24^2}\\\\4*24\\\\96\\\\](https://tex.z-dn.net/?f=4%5Csqrt%7B576%7D%5C%5C%5C%5C4%5Csqrt%7B2%2A2%2A2%2A2%2A2%2A2%2A3%2A3%7D%5C%5C%5C%5C4%5Csqrt%7B%282%2A2%29%2A%282%2A2%29%2A%282%2A2%29%2A%283%2A3%29%7D%5C%5C%5C%5C4%5Csqrt%7B%282%29%5E2%2A%282%29%5E2%2A%282%29%5E2%2A%283%29%5E2%7D%5C%5C%5C%5C4%5Csqrt%7B%282%2A2%2A2%2A3%29%5E2%7D%5C%5C%5C%5C4%5Csqrt%7B24%5E2%7D%5C%5C%5C%5C4%2A24%5C%5C%5C%5C96%5C%5C%5C%5C)
\left[x _{2}\right] = \left[ \frac{-1+i \,\sqrt{3}+2\,by+\left( -2\,i \right) \,\sqrt{3}\,by}{2^{\frac{2}{3}}\,\sqrt[3]{\left( 432\,by+\sqrt{\left( -6912+41472\,by+103680\,by^{2}+55296\,by^{3}\right) }\right) }}+\frac{\frac{ - \sqrt[3]{\left( 432\,by+\sqrt{\left( -6912+41472\,by+103680\,by^{2}+55296\,by^{3}\right) }\right) }}{24}+\left( \frac{-1}{24}\,i \right) \,\sqrt{3}\,\sqrt[3]{\left( 432\,by+\sqrt{\left( -6912+41472\,by+103680\,by^{2}+55296\,by^{3}\right) }\right) }}{\sqrt[3]{2}}\right][x2]=⎣⎢⎢⎢⎢⎡2323√(432by+√(−6912+41472by+103680by2+55296by3))−1+i√3+2by+(−2i)√3by+3√224−3√(432by+√(−6912+41472by+103680by2+55296by3))+(24−1i)√33√(432by+√(−6912+41472by+103680by2+55296by3))⎦⎥⎥⎥⎥⎤
totally answer.
Answer:
-17-17,-17,-17,-14,-14,-14,-14,6,6,6,6
Step-by-step explanation:
hope it helped.