1. **Problem Statement:** Solve the algebraic expressions given for the odd-numbered problems (29, 31, 33, 35, 37, 39, 41, 43, 45, 47). 2. **Problem 29:** Simplify and analyze the quadratic expression $2x^2 - 16x - 30$. 3. **Step 1:** Factor out the greatest common factor (GCF) if possible. $$2x^2 - 16x - 30 = 2(x^2 - 8x - 15)$$ 4. **Step 2:** Factor the quadratic inside the parentheses. We look for two numbers that multiply to $-15$ and add to $-8$: these are $-10$ and $2$. $$2(x^2 - 8x - 15) = 2(x - 10)(x + 2)$$ 5. **Final answer for 29:** $2(x - 10)(x + 2)$ 6. **Problem 31:** Expressions $(x^2)^ extdegree$ and $(2x + 24)^ extdegree$ likely represent angles or powers; assuming powers, simplify. 7. **Step 1:** Simplify $(x^2)^ extdegree$ as $x^2$ (angle notation unclear, treat as power). 8. **Step 2:** Simplify $(2x + 24)^ extdegree$ as $2x + 24$. 9. **Final answer for 31:** Expressions remain $x^2$ and $2x + 24$. 10. **Problem 33:** Expressions $(x^2)^ extdegree$ and $(-4x - 3)^ extdegree$ similarly treated. 11. **Step 1:** Simplify $(x^2)^ extdegree$ as $x^2$. 12. **Step 2:** Simplify $(-4x - 3)^ extdegree$ as $-4x - 3$. 13. **Final answer for 33:** Expressions are $x^2$ and $-4x - 3$. 14. **Problem 35:** Simplify $3x^2 + 18x - 24$. 15. **Step 1:** Factor out GCF 3. $$3x^2 + 18x - 24 = 3(x^2 + 6x - 8)$$ 16. **Step 2:** Factor quadratic $x^2 + 6x - 8$. Look for two numbers multiplying to $-8$ and adding to $6$: $8$ and $-2$. $$3(x^2 + 6x - 8) = 3(x + 8)(x - 2)$$ 17. **Final answer for 35:** $3(x + 8)(x - 2)$ 18. **Problem 37:** Expressions $166^ extdegree$ and $(x^2 - 5x)^ extdegree$. 19. **Step 1:** $166^ extdegree$ is an angle. 20. **Step 2:** $(x^2 - 5x)^ extdegree$ is an angle expression. 21. **Final answer for 37:** Angles are $166^ extdegree$ and $(x^2 - 5x)^ extdegree$. 22. **Problem 39:** Expressions $2x^2$ and $20x - 48$. 23. **Step 1:** Factor $20x - 48$ by GCF 4. $$20x - 48 = 4(5x - 12)$$ 24. **Final answer for 39:** Expressions are $2x^2$ and $4(5x - 12)$. 25. **Problem 41:** Expressions $2x^2$ and $16x$. 26. **Step 1:** Factor $16x$ as is. 27. **Final answer for 41:** Expressions are $2x^2$ and $16x$. 28. **Problem 43:** System of equations: $$\begin{cases} x + y = 5 \\ x - y = 7 \end{cases}$$ 29. **Step 1:** Add equations to eliminate $y$: $$ (x + y) + (x - y) = 5 + 7 \Rightarrow 2x = 12 $$ 30. **Step 2:** Solve for $x$: $$ x = \frac{\cancel{2}x}{\cancel{2}} = \frac{12}{2} = 6 $$ 31. **Step 3:** Substitute $x=6$ into $x + y = 5$: $$ 6 + y = 5 \Rightarrow y = 5 - 6 = -1 $$ 32. **Final answer for 43:** $x=6$, $y=-1$ 33. **Problem 45:** System of equations: $$\begin{cases} 2x + y = 1 \\ x - 3y = 9 \end{cases}$$ 34. **Step 1:** Solve first for $y$ from first equation: $$ y = 1 - 2x $$ 35. **Step 2:** Substitute into second equation: $$ x - 3(1 - 2x) = 9 $$ $$ x - 3 + 6x = 9 $$ $$ 7x - 3 = 9 $$ 36. **Step 3:** Solve for $x$: $$ 7x = 12 \Rightarrow x = \frac{12}{7} $$ 37. **Step 4:** Substitute $x$ back to find $y$: $$ y = 1 - 2 \times \frac{12}{7} = 1 - \frac{24}{7} = \frac{7}{7} - \frac{24}{7} = -\frac{17}{7} $$ 38. **Final answer for 45:** $x=\frac{12}{7}$, $y=-\frac{17}{7}$ 39. **Problem 47:** Find area of parallelogram with base $8$ cm and height $6$ cm. 40. **Step 1:** Use area formula $A = bh$. $$ A = 8 \times 6 = 48 $$ 41. **Final answer for 47:** Area = 48 cm² **Summary:** - Problem 29: $2(x - 10)(x + 2)$ - Problem 31: $x^2$, $2x + 24$ - Problem 33: $x^2$, $-4x - 3$ - Problem 35: $3(x + 8)(x - 2)$ - Problem 37: $166^\textdegree$, $(x^2 - 5x)^\textdegree$ - Problem 39: $2x^2$, $4(5x - 12)$ - Problem 41: $2x^2$, $16x$ - Problem 43: $x=6$, $y=-1$ - Problem 45: $x=\frac{12}{7}$, $y=-\frac{17}{7}$ - Problem 47: Area = 48 cm²