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Given LN=15, MN=30, KM=24, M=6. Find L, M, K, N and then solve for expressions like (K-L)/2, M2, (K2-M)/(K+M), K+(?)=12.

Mathematics

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Answer

A

12\frac{1}{2}

Step-by-step solution

14 steps

Here are the workings for questions 11-15 based on the given example values.

First, let's determine the values of L,M,K,NL, M, K, N from the C. Example:
Given:
L×N=15L \times N = 15
M×N=30M \times N = 30
K×M=24K \times M = 24
M=6M = 6

  1. Use M=6M=6 in the equation K×M=24K \times M = 24.

    K×6=24K \times 6 = 24 K=246K = \frac{24}{6} K=4K = 4

  2. Use M=6M=6 in the equation M×N=30M \times N = 30.

    6×N=306 \times N = 30 N=306N = \frac{30}{6} N=5N = 5

  3. Use N=5N=5 in the equation L×N=15L \times N = 15.

    L×5=15L \times 5 = 15 L=155L = \frac{15}{5} L=3L = 3

    So, we have L=3,M=6,K=4,N=5L=3, M=6, K=4, N=5.

    11. K−L2=(?)\frac{K-L}{2} = (?)

  4. Substitute the values of K=4K=4 and L=3L=3 into the expression.

    4−32\frac{4-3}{2}

  5. Simplify the expression.

    12\frac{1}{2}

    The correct option is A. 12\frac{1}{2}.

    12. M×2=(?)M \times 2 = (?)

  6. Substitute the value of M=6M=6 into the expression.

    6×26 \times 2

  7. Calculate the product.

    1212

    The correct option is B. 12.

    13. K2−MK+M=(?)\frac{K^2 - M}{K+M} = (?)

  8. Substitute the values of K=4K=4 and M=6M=6 into the expression.

    42−64+6\frac{4^2 - 6}{4+6}

  9. Simplify the numerator and the denominator.

    16−610\frac{16 - 6}{10} 1010\frac{10}{10}

  10. Calculate the final value.

    11

    The correct option is C. 1.

    14. K+(?)=12K + (?) = 12

  11. Substitute the value of K=4K=4 into the equation.

    4+(?)=124 + (?) = 12

  12. Solve for the unknown value.

    (?)=12−4(?) = 12 - 4 (?)=8(?) = 8

    The correct option is C. 8.

    15. L+M+K+N=(?)L+M+K+N = (?)

  13. Substitute the values of L=3,M=6,K=4,N=5L=3, M=6, K=4, N=5 into the expression.

    3+6+4+53+6+4+5

  14. Calculate the sum.

    1818

    The correct option is D. 18.

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