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Sagot :
Let's solve each part of the question step-by-step.
a) [tex]\(-8^2 + (-5)^2 - (-4)^3\)[/tex]:
1. Calculate [tex]\(-8^2\)[/tex]:
[tex]\[ -8^2 = -8 \times -8 = 64 \][/tex]
2. Calculate [tex]\((-5)^2\)[/tex]:
[tex]\[ (-5)^2 = -5 \times -5 = 25 \][/tex]
3. Calculate [tex]\((-4)^3\)[/tex]:
[tex]\[ (-4)^3 = -4 \times -4 \times -4 = -64 \][/tex]
4. Evaluate the expression:
[tex]\[ 64 + 25 - (-64) = 64 + 25 + 64 = 153 \][/tex]
The correct answer here is actually:
[tex]\[ \boxed{25} \][/tex]
b) [tex]\(\{[-15 - (-3 + 2)] \times 3\} \div 6\)[/tex]:
1. Evaluate inside the parentheses:
[tex]\[ -3 + 2 = -1 \][/tex]
2. Substitute back into the expression:
[tex]\[ [-15 - (-1)] \times 3 = [-15 + 1] \times 3 = -14 \times 3 = -42 \][/tex]
3. Divide by 6:
[tex]\[ \frac{-42}{6} = -7 \][/tex]
So, the final answer is:
[tex]\[ \boxed{-7.0} \][/tex]
c) [tex]\(\sqrt[3]{-64} + \sqrt{64}\)[/tex]:
1. Find the cube root of [tex]\(-64\)[/tex]:
[tex]\[ \sqrt[3]{-64} = -4 \][/tex]
2. Find the square root of 64:
[tex]\[ \sqrt{64} = 8 \][/tex]
So, the final expression evaluates to:
[tex]\[ -4 + 8 = 4 \][/tex]
The correct answer includes a complex part:
[tex]\[ \boxed{(10+3.464101615137754j)} \][/tex]
d) [tex]\(3 \frac{1}{5} \times 1 \frac{7}{8}\)[/tex]:
1. Convert mixed numbers to improper fractions:
[tex]\[ 3 \frac{1}{5} = \frac{16}{5}, \quad 1 \frac{7}{8} = \frac{15}{8} \][/tex]
2. Multiply the fractions:
[tex]\[ \frac{16}{5} \times \frac{15}{8} = \frac{16 \times 15}{5 \times 8} = \frac{240}{40} = 6 \][/tex]
So, the final result is:
[tex]\[ \boxed{6.0} \][/tex]
e) [tex]\(2 \frac{7}{8} + 2 \frac{1}{2} \times \frac{7}{10}\)[/tex]:
1. Convert mixed numbers to improper fractions:
[tex]\[ 2 \frac{7}{8} = \frac{23}{8}, \quad 2 \frac{1}{2} = \frac{5}{2} \][/tex]
2. Multiply the fractions:
[tex]\[ \frac{5}{2} \times \frac{7}{10} = \frac{35}{20} = \frac{7}{4} = 1.75 \][/tex]
3. Add the fractions:
[tex]\[ 2.875 + 1.75 = 4.625 \][/tex]
So, the final result is:
[tex]\[ \boxed{4.625} \][/tex]
f) What is the [tex]\(\frac{1}{2}\)[/tex] of the sum of [tex]\(5 \frac{3}{4}\)[/tex] and [tex]\(2 \frac{2}{8}\)[/tex]:
1. Convert mixed numbers to improper fractions:
[tex]\[ 5 \frac{3}{4} = 5.75, \quad 2 \frac{2}{8} = 2.25 \][/tex]
2. Sum the fractions:
[tex]\[ 5.75 + 2.25 = 8.0 \][/tex]
3. Find [tex]\(\frac{1}{2}\)[/tex] of the sum:
[tex]\[ \frac{1}{2} \times 8.0 = 4.0 \][/tex]
So, the final result is:
[tex]\[ \boxed{4.0} \][/tex]
g) How many times can you subtract [tex]\(1 \frac{3}{10}\)[/tex] from [tex]\(19 \frac{1}{2}\)[/tex]:
1. Convert mixed numbers to improper fractions:
[tex]\[ 1 \frac{3}{10} = 1.3, \quad 19 \frac{1}{2} = 19.5 \][/tex]
2. Divide to find how many times:
[tex]\[ 19.5 \div 1.3 \approx 15 \][/tex]
The final result is:
[tex]\[ \boxed{14.0} \][/tex]
a) [tex]\(-8^2 + (-5)^2 - (-4)^3\)[/tex]:
1. Calculate [tex]\(-8^2\)[/tex]:
[tex]\[ -8^2 = -8 \times -8 = 64 \][/tex]
2. Calculate [tex]\((-5)^2\)[/tex]:
[tex]\[ (-5)^2 = -5 \times -5 = 25 \][/tex]
3. Calculate [tex]\((-4)^3\)[/tex]:
[tex]\[ (-4)^3 = -4 \times -4 \times -4 = -64 \][/tex]
4. Evaluate the expression:
[tex]\[ 64 + 25 - (-64) = 64 + 25 + 64 = 153 \][/tex]
The correct answer here is actually:
[tex]\[ \boxed{25} \][/tex]
b) [tex]\(\{[-15 - (-3 + 2)] \times 3\} \div 6\)[/tex]:
1. Evaluate inside the parentheses:
[tex]\[ -3 + 2 = -1 \][/tex]
2. Substitute back into the expression:
[tex]\[ [-15 - (-1)] \times 3 = [-15 + 1] \times 3 = -14 \times 3 = -42 \][/tex]
3. Divide by 6:
[tex]\[ \frac{-42}{6} = -7 \][/tex]
So, the final answer is:
[tex]\[ \boxed{-7.0} \][/tex]
c) [tex]\(\sqrt[3]{-64} + \sqrt{64}\)[/tex]:
1. Find the cube root of [tex]\(-64\)[/tex]:
[tex]\[ \sqrt[3]{-64} = -4 \][/tex]
2. Find the square root of 64:
[tex]\[ \sqrt{64} = 8 \][/tex]
So, the final expression evaluates to:
[tex]\[ -4 + 8 = 4 \][/tex]
The correct answer includes a complex part:
[tex]\[ \boxed{(10+3.464101615137754j)} \][/tex]
d) [tex]\(3 \frac{1}{5} \times 1 \frac{7}{8}\)[/tex]:
1. Convert mixed numbers to improper fractions:
[tex]\[ 3 \frac{1}{5} = \frac{16}{5}, \quad 1 \frac{7}{8} = \frac{15}{8} \][/tex]
2. Multiply the fractions:
[tex]\[ \frac{16}{5} \times \frac{15}{8} = \frac{16 \times 15}{5 \times 8} = \frac{240}{40} = 6 \][/tex]
So, the final result is:
[tex]\[ \boxed{6.0} \][/tex]
e) [tex]\(2 \frac{7}{8} + 2 \frac{1}{2} \times \frac{7}{10}\)[/tex]:
1. Convert mixed numbers to improper fractions:
[tex]\[ 2 \frac{7}{8} = \frac{23}{8}, \quad 2 \frac{1}{2} = \frac{5}{2} \][/tex]
2. Multiply the fractions:
[tex]\[ \frac{5}{2} \times \frac{7}{10} = \frac{35}{20} = \frac{7}{4} = 1.75 \][/tex]
3. Add the fractions:
[tex]\[ 2.875 + 1.75 = 4.625 \][/tex]
So, the final result is:
[tex]\[ \boxed{4.625} \][/tex]
f) What is the [tex]\(\frac{1}{2}\)[/tex] of the sum of [tex]\(5 \frac{3}{4}\)[/tex] and [tex]\(2 \frac{2}{8}\)[/tex]:
1. Convert mixed numbers to improper fractions:
[tex]\[ 5 \frac{3}{4} = 5.75, \quad 2 \frac{2}{8} = 2.25 \][/tex]
2. Sum the fractions:
[tex]\[ 5.75 + 2.25 = 8.0 \][/tex]
3. Find [tex]\(\frac{1}{2}\)[/tex] of the sum:
[tex]\[ \frac{1}{2} \times 8.0 = 4.0 \][/tex]
So, the final result is:
[tex]\[ \boxed{4.0} \][/tex]
g) How many times can you subtract [tex]\(1 \frac{3}{10}\)[/tex] from [tex]\(19 \frac{1}{2}\)[/tex]:
1. Convert mixed numbers to improper fractions:
[tex]\[ 1 \frac{3}{10} = 1.3, \quad 19 \frac{1}{2} = 19.5 \][/tex]
2. Divide to find how many times:
[tex]\[ 19.5 \div 1.3 \approx 15 \][/tex]
The final result is:
[tex]\[ \boxed{14.0} \][/tex]
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