Solve the system of equations 2x-y=1; x+2y=8 graphically and find the coordinates of the points where corresponding lines intersect y-axis.
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Convert decimals to fractions
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$\dfrac { 1 } { 3 }$
Convert the repeating decimal number to a fraction
$\color{#FF6800}{ 0. \dot{ 3 } }$
$ $ Set the repeating decimal number to x $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 3 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 3 } }$
$ $ Multiply both sides by an appropriate power of 10 to make two expressions with the same part of the prime number $ $
$\begin{cases} \color{#FF6800}{ 10 } \color{#FF6800}{ x } = \color{#FF6800}{ 3. \dot{ 3 } } \\ \color{#FF6800}{ 1 } \color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 3 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 10 } \color{#FF6800}{ x } = \color{#FF6800}{ 3. \dot{ 3 } } \\ \color{#FF6800}{ 1 } \color{#FF6800}{ x } = \color{#FF6800}{ 0. \dot{ 3 } } \end{cases}$
$ $ Since the prime number part of the right side of the two expressions is the same, only the integer part remains $ $
$\color{#FF6800}{ 9 } \color{#FF6800}{ x } = \color{#FF6800}{ 3 }$
$\color{#FF6800}{ 9 } \color{#FF6800}{ x } = \color{#FF6800}{ 3 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 3 } } }$
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$2.$ Consider the proper subsets of $\left(1,2,3,4\right)$ How many of these proper subsets are superset of the set $\left(3\right)$ ? $\left($ (a) $\right)$ $5$ $\left($ (b) $0\right)$ $6$ $\left($ (c) $7$ $\left($ (d) $\right)$ $8$
10th-13th grade
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