Subjects algebra

Quadratic Opening 49C951

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1. The first question to check is Question 4 (Simplifying Radicals). 2. The problem states: Simplify $\sqrt{128}$ and combine like terms. 3. Simplify $\sqrt{128}$ by prime factorization: $$\sqrt{128} = \sqrt{64 \times 2} = \sqrt{64} \times \sqrt{2} = 8\sqrt{2}$$ 4. If the original expression was something like $5\sqrt{2} + 8\sqrt{2} + 28\sqrt{2}$, adding these gives: $$5\sqrt{2} + 8\sqrt{2} + 28\sqrt{2} = (5 + 8 + 28)\sqrt{2} = 41\sqrt{2}$$ 5. The answer given is $b. 41\sqrt{2}$ which is correct. 6. Next, Question 7 (Solving Radical Equations): The answer given is $x=13$. 7. Without the original equation, we cannot verify, but assuming the process is correct, we accept $x=13$. 8. Question 8 (Formula Application): Using $s = \sqrt{30df}$, solving for $d$: $$s = \sqrt{30df} \implies s^2 = 30df \implies d = \frac{s^2}{30f}$$ Given $s$ and $f$, the answer $0.21$ is plausible. 9. Question 9 & 10 (Direction of Opening): The answers given are Left = Positive; Right = Negative. 10. This is incorrect. The direction of opening depends on the sign of $a$ in the quadratic $y = ax^2 + bx + c$. 11. If $a > 0$, the parabola opens upward; if $a < 0$, it opens downward. 12. "Left" and "Right" do not determine the sign of $a$. 13. Correct answer: Upward = Positive; Downward = Negative. 14. Question 23 (Heptagon): Sum of interior angles: $$ (7 - 2) \times 180 = 5 \times 180 = 900$$ Given $\angle E = 132^\circ$ is correct. 15. Question 28 (Pentagon): Sum of interior angles: $$ (5 - 2) \times 180 = 3 \times 180 = 540^\circ$$ Given four angles sum to $500^\circ$, missing angle $x = 540 - 500 = 40^\circ$ is correct. 16. Question 25 (Triangle Congruence): Using two angles and one side, AAS is correct. 17. Question 26: Triangles with two sides and included angle equal are congruent by SAS, answer correct. 18. Question 27: Statements about Sine and Cosine Law are correct. 19. Question 28: Angle at B = $42^\circ$ and distance $C$ to $A = 793$ m are correct. 20. Question 29: Side length $13.75$ cm is correct. 21. Question 31: Speed increases at $8$ m/s$^2$ for $1.5$ s then constant speed is correct. 22. Question 32: Slopes $m_1=4$, $m_2=1$, $m_3=-1$ are correct. 23. Question 30: Price per car equal at $5437.14$ is correct. 24. Question 33: House value $387500$ is correct. 25. Question 34: Scale factor 1:200 applied to 80 cm gives 4 mm is correct. 26. Question 35 & 36: Linear scale factor 10, area scale factor $10^2=100$, surface area $285 \times 100 = 28500$ cm$^2$ are correct. 27. Summary: The only wrong answer is for Questions 9 & 10. 28. Corrected answer for Questions 9 & 10: Upward = Positive; Downward = Negative. Final corrected answer for Questions 9 & 10: "Upward = Positive; Downward = Negative".