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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$\dfrac { 1354 } { 495 }$
Convert the repeating decimal number to a fraction
$\color{#FF6800}{ 2.7 \dot{ 3 } \dot{ 5 } }$
$ $ Set the repeating decimal number to x $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 2.7 \dot{ 3 } \dot{ 5 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 2.7 \dot{ 3 } \dot{ 5 } }$
$ $ Multiply both sides by an appropriate power of 10 to make two expressions with the same part of the prime number $ $
$\begin{cases} \color{#FF6800}{ 1000 } \color{#FF6800}{ x } = \color{#FF6800}{ 2735. \dot{ 3 } \dot{ 5 } } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ x } = \color{#FF6800}{ 27. \dot{ 3 } \dot{ 5 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 1000 } \color{#FF6800}{ x } = \color{#FF6800}{ 2735. \dot{ 3 } \dot{ 5 } } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ x } = \color{#FF6800}{ 27. \dot{ 3 } \dot{ 5 } } \end{cases}$
$ $ Since the prime number part of the right side of the two expressions is the same, only the integer part remains $ $
$\color{#FF6800}{ 990 } \color{#FF6800}{ x } = \color{#FF6800}{ 2708 }$
$\color{#FF6800}{ 990 } \color{#FF6800}{ x } = \color{#FF6800}{ 2708 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1354 } } { \color{#FF6800}{ 495 } } }$
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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
Other
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(d) Fill in the blanks from the choices given in the bracket $\left(5\right)$ $1$ Down a group, the ionization potential_ _(increases, decreases) $s\right)$ $2$ The basicity of acetic acid is $\left(1,2,4\right)$ $3$ Lower the pH value of a solution the more (acidic, alkaline) it $15.$ $4.$ The volume occupied by one mole of any gas at $STPis\left(22.4m^{3},22.4dm^{3}\right)$ $5$ Aqueous solutions of mineral acids are _electrolytes (strong, weak) $\right)$
10th-13th grade
Chemistry
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