Practice Pakistan questions with answers and explanations.
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The discriminant is b² - 4ac.
Here it is 4² - 4(1)(1) = 16 - 4 = 12.
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A zero discriminant makes the square-root term in the formula zero.
Both solutions therefore coincide.
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Subtract 7 from both sides of the equation.
This gives x = 19 - 7 = 12.
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Divide both sides by the coefficient 3.
Thus, x = 27 ÷ 3 = 9.
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Subtract 5 to get 2x = 12.
Dividing by 2 gives x = 6.
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Move variable terms to one side and constants to the other.
Then 3x = 15, so x = 5.
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Multiply both sides by 4.
Thus, x = 7 × 4 = 28.
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Adding the equations gives 2x = 14, so x = 7.
Substituting into x + y = 10 gives y = 3.
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Substitute x = 2 to obtain 4 + 3y = 13.
Then 3y = 9, so y = 3.
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The expression is a difference of squares: x² - 3².
Thus, it factors as (x - 3)(x + 3).
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For equal distances, average speed is the harmonic mean 2ab/(a + b).
Thus, 2 × 40 × 60 ÷ 100 = 48 km/h.
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The path forms a right triangle with legs 5 and 12.
By Pythagoras, distance is √(25 + 144) = 13 km.
