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The formula for the diameter (d) of a circle in terms of its radius (r) is d = 2r.

Mathematics

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Answer

B

Step-by-step solution

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Here are the solutions to the questions:

1. Find the diameter of a circle whose radius is 3.4m.

  1. The formula for the diameter (dd) of a circle in terms of its radius (rr) is d=2rd = 2r.

  2. Substitute the given radius r=3.4r = 3.4m into the formula.

    d=2×3.4 md = 2 \times 3.4\, \text{m}
  3. Calculate the diameter.

    d=6.8 md = 6.8\, \text{m}

    The correct option is B.
    The final answer is B. 6.8m\boxed{\text{B. 6.8m}}.

    2. In the balance below, the mass of one shape is given in kilogram. Find □\square if ◯=15\bigcirc = 15.

  4. From the balance, two circles balance three squares.

    Let M◯M_{\bigcirc} be the mass of one circle and M□M_{\square} be the mass of one square.

    2M◯=3M□2 M_{\bigcirc} = 3 M_{\square}
  5. Substitute the given mass of one circle, M◯=15M_{\bigcirc} = 15 kg.

    2×15 kg=3M□2 \times 15\, \text{kg} = 3 M_{\square} 30 kg=3M□30\, \text{kg} = 3 M_{\square}
  6. Solve for M□M_{\square}.

    M□=30 kg3M_{\square} = \frac{30\, \text{kg}}{3} M□=10 kgM_{\square} = 10\, \text{kg}

    The correct option is C.
    The final answer is C. 10kg\boxed{\text{C. 10kg}}.

    3. In the figure below MK and RS are straight lines. Find the value of angle marked n.

  7. The angles 127∘127^\circ and the angle adjacent to it on the straight line MK (or RS) are supplementary, meaning they add up to 180∘180^\circ.

    Let the angle adjacent to 127∘127^\circ be xx.

    127∘+x=180∘127^\circ + x = 180^\circ
  8. Solve for xx.

    x=180∘−127∘x = 180^\circ - 127^\circ x=53∘x = 53^\circ
  9. Angle nn and angle xx are vertically opposite angles.

    Vertically opposite angles are equal.

    n=xn = x n=53∘n = 53^\circ

    The correct option is B.
    The final answer is B. 53°\boxed{\text{B. 53°}}.

    4. A line that divides a circle into two segments is called...
    A chord is a line segment whose endpoints lie on the circle, dividing the circle into two segments. A diameter is a special type of chord that passes through the center.
    The correct option is B.
    The final answer is B. Chord\boxed{\text{B. Chord}}.

    5. Which of the following construction of angles represents 45°?
    A 45∘45^\circ angle is half of a 90∘90^\circ angle. To construct a 45∘45^\circ angle, one typically constructs a 90∘90^\circ angle first and then bisects it. Option A shows the construction of a 90∘90^\circ angle being bisected, which results in a 45∘45^\circ angle.
    The correct option is A.
    The final answer is A\boxed{\text{A}}.

    6. Simplify: 23×32×52^3 \times 3^2 \times 5.

  10. Calculate the powers.

    23=2×2×2=82^3 = 2 \times 2 \times 2 = 8 32=3×3=93^2 = 3 \times 3 = 9
  11. Substitute the calculated values back into the expression.

    8×9×58 \times 9 \times 5
  12. Perform the multiplication.

    8×9=728 \times 9 = 72 72×5=36072 \times 5 = 360

    The correct option is B.
    The final answer is B. 360\boxed{\text{B. 360}}.

    7. Solve for n: 2n+5=3n−72n + 5 = 3n - 7.

  13. Subtract 2n2n from both sides of the equation to gather terms with nn on one side.

    5=3n−2n−75 = 3n - 2n - 7 5=n−75 = n - 7
  14. Add 7 to both sides of the equation to isolate nn.

    5+7=n5 + 7 = n 12=n12 = n

    The correct option is A.
    The final answer is A. 12\boxed{\text{A. 12}}.

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