Mathematics 1

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Answer explanation

To solve the equation 3x + 5 = 14, subtract 5 from both sides to get 3x = 9. Then, divide both sides by 3 to find x = 3. Thus, the correct answer is x = 3.

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Answer explanation

To solve the inequality 2x - 3 > 5, add 3 to both sides to get 2x > 8. Then, divide by 2 to find x > 4. The only choice that satisfies this is x = 5.

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Answer explanation

To simplify \( \frac{15}{45} \), divide both the numerator and denominator by their greatest common divisor, which is 15. This gives \( \frac{15 \div 15}{45 \div 15} = \frac{1}{3} \). Thus, the correct answer is \( \frac{1}{3} \).

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What is 25% of 200?

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50

Answer explanation

To find 25% of 200, multiply 200 by 0.25. This gives 200 * 0.25 = 50. Therefore, the correct answer is 50.

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Ratio of boys to girls is 3:4. How many girls if there are 21 boys?

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28

Answer explanation

The ratio of boys to girls is 3:4. If there are 21 boys, we can set up the proportion: 3/4 = 21/x. Cross-multiplying gives 3x = 84, so x = 28. Therefore, there are 28 girls.

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Answer explanation

To find the L.C.M of 3x^2 and 5x^3, take the highest coefficient (15) and the highest power of x (x^3). Thus, the L.C.M is 15x^3, which is the correct choice.

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Answer explanation

To find the H.C.F of 6x^3y^2 and 9x^2y^3, we take the lowest powers of each variable and the greatest common factor of the coefficients. The H.C.F is 3 (from 6 and 9), x^2 (from x^3 and x^2), and y^2 (from y^2 and y^3), giving 3x^2y^2.

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Answer explanation

The y-intercept occurs where x = 0. Substituting x = 0 in the equation y = 2x + 3 gives y = 3. Thus, the coordinates of the intersection with the y-axis are (0, 3), which is the correct answer.

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What is the sum of the interior angles of a hexagon?

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720 degrees

Answer explanation

The sum of the interior angles of a hexagon can be calculated using the formula (n-2) * 180, where n is the number of sides. For a hexagon (n=6), the calculation is (6-2) * 180 = 720 degrees.

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If one exterior angle of a regular polygon is 30 degrees, how many sides does the polygon have?

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12

Answer explanation

The sum of exterior angles of a polygon is 360 degrees. If one exterior angle is 30 degrees, the number of sides is 360 / 30 = 12. Therefore, the polygon has 12 sides.