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Solve the following word problem and calculations: Jack's scores in five successive rounds were 25, -5, -10, 15 and 10. Calculate (10-6)3 and sqrt(24+1) + sqrt(10-1).

Mathematics

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Part 2.4· 3 steps

Solve this word sum and show your calculations.

Jack's scores in five successive rounds were 25,−5,−10,1525, -5, -10, 15 and 10.

  1. Sum all the scores to find the total.

    Total=25+(−5)+(−10)+15+10\text{Total} = 25 + (-5) + (-10) + 15 + 10
  2. Group positive and negative numbers.

    Total=(25+15+10)+(−5−10)\text{Total} = (25 + 15 + 10) + (-5 - 10)
  3. Perform the additions and subtractions.

    Total=50+(−15)\text{Total} = 50 + (-15) Total=50−15\text{Total} = 50 - 15 Total=35\text{Total} = 35

    Jack's total at the end was 35.

    35\boxed{35}

Part 3

Part 3.164

Calculate

(10−6)3(10 - 6)^3
  1. Perform the operation inside the parentheses.

    10−6=410 - 6 = 4
  2. Cube the result.

    43=4×4×44^3 = 4 \times 4 \times 4 43=16×44^3 = 16 \times 4 43=644^3 = 64 64\boxed{64}

Part 3.28

Calculate

24+1+10−1\sqrt{24+1} + \sqrt{10-1}
  1. Perform the operations inside each square root.

    24+1=25\sqrt{24+1} = \sqrt{25} 10−1=9\sqrt{10-1} = \sqrt{9}
  2. Calculate the square root of each number.

    25=5\sqrt{25} = 5 9=3\sqrt{9} = 3
  3. Add the results.

    5+3=85 + 3 = 8 8\boxed{8}
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