He price of the cone before tax was 2.26 dollars. hope this helps!
Answer:
3x-3
Step-by-step explanation:
(6x-5) - (3x-2)
remove parenthesees (Not needed
6x-5 - 3x-2
simplify
3x-5-2
3x-3
12,000
Underline the number in the ten thousands place
look to the right
if number is greater than 5
add 1 to the underlined number
leave the numbers behind the underlined number zero
❍ Let's say, that the numerator of the fraction be <em>x</em> and denominator of the fraction be <em>y</em>.
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![\underline{\sf{Case\;}\it{1}:}](https://tex.z-dn.net/?f=%5Cunderline%7B%5Csf%7BCase%5C%3B%7D%5Cit%7B1%7D%3A%7D)
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- If 2 is added to the numerator of the fraction, it reduces to 1/2.
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Therefore,
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![\begin{gathered}:\implies\sf{\dfrac{x+2}{y}=\dfrac{1}{2}}\\\\\\:\implies\sf{2x+4=y}\\\\\\:\implies\sf{2x=y-4}\qquad\qquad\bigg\lgroup\sf{eq^n\;1}\bigg\rgroup\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%3A%5Cimplies%5Csf%7B%5Cdfrac%7Bx%2B2%7D%7By%7D%3D%5Cdfrac%7B1%7D%7B2%7D%7D%5C%5C%5C%5C%5C%5C%3A%5Cimplies%5Csf%7B2x%2B4%3Dy%7D%5C%5C%5C%5C%5C%5C%3A%5Cimplies%5Csf%7B2x%3Dy-4%7D%5Cqquad%5Cqquad%5Cbigg%5Clgroup%5Csf%7Beq%5En%5C%3B1%7D%5Cbigg%5Crgroup%5Cend%7Bgathered%7D)
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![\underline{\sf{Case\;}\it{2}:}](https://tex.z-dn.net/?f=%5Cunderline%7B%5Csf%7BCase%5C%3B%7D%5Cit%7B2%7D%3A%7D)
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- If 1 is subtracted from the denominator of the fraction, it reduces to 1/3.
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Therefore,
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![\begin{gathered}:\implies\sf{\dfrac{x}{y-1}=\dfrac{1}{3}}\\\\\\:\implies\sf{3x=y-1}\qquad\qquad\bigg\lgroup\sf{eq^n\;2}\bigg\rgroup\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%3A%5Cimplies%5Csf%7B%5Cdfrac%7Bx%7D%7By-1%7D%3D%5Cdfrac%7B1%7D%7B3%7D%7D%5C%5C%5C%5C%5C%5C%3A%5Cimplies%5Csf%7B3x%3Dy-1%7D%5Cqquad%5Cqquad%5Cbigg%5Clgroup%5Csf%7Beq%5En%5C%3B2%7D%5Cbigg%5Crgroup%5Cend%7Bgathered%7D)
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![\qquad\qquad\footnotesize{\underline{\bf{\dag\;}\frak{Subtracting\;eq^n\;2\;from\;eq^n\;1:}}}](https://tex.z-dn.net/?f=%5Cqquad%5Cqquad%5Cfootnotesize%7B%5Cunderline%7B%5Cbf%7B%5Cdag%5C%3B%7D%5Cfrak%7BSubtracting%5C%3Beq%5En%5C%3B2%5C%3Bfrom%5C%3Beq%5En%5C%3B1%3A%7D%7D%7D)
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![\begin{gathered}:\implies\sf{3x-2x=y-1-y-4}\\\\\\:\implies\underline{\boxed{\pink{\frak{\pmb{x=3}}}}}\;\bigstar\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%3A%5Cimplies%5Csf%7B3x-2x%3Dy-1-y-4%7D%5C%5C%5C%5C%5C%5C%3A%5Cimplies%5Cunderline%7B%5Cboxed%7B%5Cpink%7B%5Cfrak%7B%5Cpmb%7Bx%3D3%7D%7D%7D%7D%7D%5C%3B%5Cbigstar%5Cend%7Bgathered%7D)
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![\qquad\qquad\footnotesize{\underline{\bf{\dag\;}\frak{Substituting\;value\;of\;x\;in\;eq^n\;1:}}}](https://tex.z-dn.net/?f=%5Cqquad%5Cqquad%5Cfootnotesize%7B%5Cunderline%7B%5Cbf%7B%5Cdag%5C%3B%7D%5Cfrak%7BSubstituting%5C%3Bvalue%5C%3Bof%5C%3Bx%5C%3Bin%5C%3Beq%5En%5C%3B1%3A%7D%7D%7D)
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![\begin{gathered}:\implies\sf{2x=y-4}\\\\\\:\implies\sf{2(3)=y-4}\\\\\\:\implies\sf{6=y-4}\\\\\\:\implies\sf{6=y-4}\\\\\\:\implies\sf{y=-4-6}\\\\\\:\implies\underline{\boxed{\purple{\frak{\pmb{y=10}}}}}\;\bigstar\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%3A%5Cimplies%5Csf%7B2x%3Dy-4%7D%5C%5C%5C%5C%5C%5C%3A%5Cimplies%5Csf%7B2%283%29%3Dy-4%7D%5C%5C%5C%5C%5C%5C%3A%5Cimplies%5Csf%7B6%3Dy-4%7D%5C%5C%5C%5C%5C%5C%3A%5Cimplies%5Csf%7B6%3Dy-4%7D%5C%5C%5C%5C%5C%5C%3A%5Cimplies%5Csf%7By%3D-4-6%7D%5C%5C%5C%5C%5C%5C%3A%5Cimplies%5Cunderline%7B%5Cboxed%7B%5Cpurple%7B%5Cfrak%7B%5Cpmb%7By%3D10%7D%7D%7D%7D%7D%5C%3B%5Cbigstar%5Cend%7Bgathered%7D)
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Hence,
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- Numerator = x = 3
- Denominator = y = 10
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The answer would be:The determinant of a singular matrix is equal to zero.