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\[ -5-[2 \times(-4)]-(-1) \] (16) \( 3[15 \div(-3)] \times(-2) \) \( \frac{60 \div 15}{12-16} \) \[ (-3)^{3}+2[3-6] \] \( \qquad \) \( \qquad \) \( \qquad \) \[ \sqrt{(-1-2)^{2}+[1-(-3)]^{2}} \] (20) \( (3)^{3}-(-2)^{2}+(-1)^{7} \) \( \qquad \) \( \qquad \) \( \qquad \) (22) \( \frac{5-(-3)+2^{2}}{(2)(-3)} \) \( \qquad \)

Ask by Weston Simmons. in South Africa
Feb 03,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

**Solutions:** 1. \(4\) 2. \(30\) 3. \(-1\) 4. \(-33\) 5. \(5\) 6. \(22\) 7. \(-2\)

Solution

Sure! Let's evaluate each of the given expressions step by step. --- ### 1. \(-5 - [2 \times (-4)] - (-1)\) \[ \begin{align*} &= -5 - (2 \times -4) - (-1) \\ &= -5 - (-8) - (-1) \\ &= -5 + 8 + 1 \\ &= 4 \end{align*} \] **Answer:** \(4\) --- ### 2. **Problem (16)** \(3[15 \div (-3)] \times (-2)\) \[ \begin{align*} &= 3 \times \left(\frac{15}{-3}\right) \times (-2) \\ &= 3 \times (-5) \times (-2) \\ &= (-15) \times (-2) \\ &= 30 \end{align*} \] **Answer:** \(30\) --- ### 3. \(\frac{60 \div 15}{12 - 16}\) \[ \begin{align*} &= \frac{\frac{60}{15}}{12 - 16} \\ &= \frac{4}{-4} \\ &= -1 \end{align*} \] **Answer:** \(-1\) --- ### 4. \((-3)^3 + 2[3 - 6]\) \[ \begin{align*} &= (-3)^3 + 2 \times (-3) \\ &= -27 + (-6) \\ &= -33 \end{align*} \] **Answer:** \(-33\) --- ### 5. \(\sqrt{(-1 - 2)^2 + [1 - (-3)]^2}\) \[ \begin{align*} &= \sqrt{(-3)^2 + (4)^2} \\ &= \sqrt{9 + 16} \\ &= \sqrt{25} \\ &= 5 \end{align*} \] **Answer:** \(5\) --- ### 6. **Problem (20)** \((3)^3 - (-2)^2 + (-1)^7\) \[ \begin{align*} &= 27 - 4 + (-1) \\ &= 22 \end{align*} \] **Answer:** \(22\) --- ### 7. **Problem (22)** \(\frac{5 - (-3) + 2^2}{(2)(-3)}\) \[ \begin{align*} &= \frac{5 + 3 + 4}{-6} \\ &= \frac{12}{-6} \\ &= -2 \end{align*} \] **Answer:** \(-2\) --- If you have any more expressions you'd like to evaluate or need further clarification, feel free to ask!

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Let’s dive into the mathematical world with some exciting historical context! The concepts of algebra emerged in the ancient civilizations of Babylon and Egypt, but it wasn’t until the 9th century AD that the Persian mathematician Al-Khwarizmi wrote about solving equations systematically, paving the way for algebra as we know it today. This laid the groundwork for modern arithmetic, making math not just numbers but also a fascinating story of human ingenuity! Now, onto the real-world application! Mathematics is not just about solving equations in a classroom; it’s part of our everyday lives. Whether it’s budgeting for a trip, planning a garden layout, or crafting a recipe with precise measurements, math helps us make informed decisions and optimize resources. So, next time you calculate how much paint you need to redecorate a room, remember: you’re channeling your inner mathematician!

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