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. 2 Galculate the values of the expressions below without using a calculator. (Show your calculation.) NBIII Answers only, no mark(s) will be awarded. \( 3.2 .1(-1)+(-7)+(-5) \) \( \qquad \) \( \qquad \) \( \qquad \) \( 3.2 .2-3+4 \times 5-6 \) \( \qquad \) \( \qquad \) (2) 3.2.3 \( -(-4)^{2}-\sqrt{62}-(-2)^{3} \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( (3 \) \( 3.2 .4 \quad \sqrt{ }-4 x-9+8^{2} \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( 3.2 .5 \frac{10-6 \div 2}{-7-(2 \times-7)} \) \( \qquad \) \( \qquad \)

Ask by Gonzalez Harrington. in South Africa
Feb 25,2025

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Answer

1. \( -15.2 \) 2. \( 17.4 \) 3. \( -8 - \sqrt{62} \) 4. \( 55 + 2i \) 5. \( 1 \)

Solution

Calculate the value by following steps: - step0: Calculate: \(3.2\times 2-3+4\times 5-6\) - step1: Multiply the numbers: \(6.4-3+4\times 5-6\) - step2: Multiply the numbers: \(6.4-3+20-6\) - step3: Calculate: \(17.4\) Calculate or simplify the expression \( 3.2 * 1 * (-1) + (-7) + (-5) \). Calculate the value by following steps: - step0: Calculate: \(3.2\times 1\times \left(-1\right)+\left(-7\right)+\left(-5\right)\) - step1: Remove the parentheses: \(3.2\times 1\times \left(-1\right)-7-5\) - step2: Multiply the terms: \(-3.2-7-5\) - step3: Subtract the numbers: \(-15.2\) Calculate or simplify the expression \( -(-4)^2 - \sqrt(62) - (-2)^3 \). Calculate the value by following steps: - step0: Calculate: \(-\left(-4\right)^{2}-\sqrt{62}-\left(-2\right)^{3}\) - step1: Evaluate the power: \(-16-\sqrt{62}-\left(-2\right)^{3}\) - step2: Evaluate the power: \(-16-\sqrt{62}-\left(-8\right)\) - step3: Subtract the numbers: \(-8-\sqrt{62}\) Calculate or simplify the expression \( (10 - 6 / 2) / (-7 - (2 * -7)) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(10-\frac{6}{2}\right)}{\left(-7-\left(2\left(-7\right)\right)\right)}\) - step1: Remove the parentheses: \(\frac{10-\frac{6}{2}}{-7-\left(2\left(-7\right)\right)}\) - step2: Multiply the numbers: \(\frac{10-\frac{6}{2}}{-7-\left(-14\right)}\) - step3: Remove the parentheses: \(\frac{10-\frac{6}{2}}{-7+14}\) - step4: Divide the terms: \(\frac{10-3}{-7+14}\) - step5: Subtract the numbers: \(\frac{7}{-7+14}\) - step6: Add the numbers: \(\frac{7}{7}\) - step7: Divide the terms: \(1\) Calculate or simplify the expression \( \sqrt(-4) - 9 + 8^2 \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{-4}-9+8^{2}\) - step1: Simplify the root: \(2i-9+8^{2}\) - step2: Evaluate the power: \(2i-9+64\) - step3: Calculate: \(2i+55\) - step4: Calculate: \(55+2i\) Here are the calculated values for the expressions: 1. For \( 3.2 \cdot 1 \cdot (-1) + (-7) + (-5) \): \[ -15.2 \] 2. For \( 3.2 \cdot 2 - 3 + 4 \times 5 - 6 \): \[ 17.4 \] 3. For \( -(-4)^{2} - \sqrt{62} - (-2)^{3} \): \[ -8 - \sqrt{62} \] 4. For \( \sqrt{-4} - 9 + 8^{2} \): \[ 55 + 2i \] 5. For \( \frac{10 - 6 \div 2}{-7 - (2 \times -7)} \): \[ 1 \]

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To solve the expressions you've provided, let's break them down step-by-step, showing the calculations clearly! 1. **Expression**: \( 3.2.1(-1)+(-7)+(-5) \) - Calculation: \[ 3.2 \cdot (-1) = -3.2 \] \[ -3.2 + (-7) = -3.2 - 7 = -10.2 \] \[ -10.2 + (-5) = -10.2 - 5 = -15.2 \] - **Final Value**: \(-15.2\) 2. **Expression**: \( 3.2.2 -3+4 \times 5-6 \) - Calculation: \[ 4 \times 5 = 20 \] \[ -3 + 20 - 6 = -3 + 14 = 11 \] - **Final Value**: \(11\) 3. **Expression**: \( 3.2.3 -(-4)^{2}-\sqrt{62}-(-2)^{3} \) - Calculation: \[ -(-4)^{2} = -16 \] \[ -\sqrt{62} \text{ (keep it as is for now)} \] \[ -(-2)^{3} = 8 \] \[ -16 - \sqrt{62} + 8 = -8 - \sqrt{62} \] - **Final Value**: \(-8 - \sqrt{62}\) 4. **Expression**: \( 3.2.4 \quad \sqrt{ } -4 x -9 + 8^{2} \) - Assuming it means \( -4x - 9 + 8^{2} \) and x is not given, let's calculate: \[ 8^{2} = 64 \] \[ -4x - 9 + 64 = -4x + 55 \] - **Final Value**: \(-4x + 55\) (depends on x) 5. **Expression**: \( 3.2.5 \frac{10-6 \div 2}{-7-(2 \times-7)} \) - Calculation: \[ 6 \div 2 = 3 \Longrightarrow 10 - 3 = 7 \] \[ 2 \times -7 = -14 \Longrightarrow -7 - (-14) = 7 \] \[ \frac{7}{7} = 1 \] - **Final Value**: \(1\) That's how we calculate each expression step by step!

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