12. what is the sum of the 2 solutions of the equation $x^2 - 4x - 45 = 0$?
f. $-45$
g. $-5$
h. $0$
j. $4$

13. quadrant i of the standard $(x,y)$ coordinate plane is shown on a large computer screen. a blinking dot is positioned at $(2,3)$. the dot makes exactly 2 moves: first, horizontally in the positive $x$ direction for 4 seconds at a speed of 0.5 coordinate units per second; then, vertically in the positive $y$ direction for 2 seconds at the same speed. at what point is the dot located after these 2 moves?
a. $(2,6)$
b. $(3,5)$
c. $(4,4)$
d. $(5,3)$

Question

12. what is the sum of the 2 solutions of the equation $x^2 - 4x - 45 = 0$?
f. $-45$
g. $-5$
h. $0$
j. $4$

13. quadrant i of the standard $(x,y)$ coordinate plane is shown on a large computer screen. a blinking dot is positioned at $(2,3)$. the dot makes exactly 2 moves: first, horizontally in the positive $x$ direction for 4 seconds at a speed of 0.5 coordinate units per second; then, vertically in the positive $y$ direction for 2 seconds at the same speed. at what point is the dot located after these 2 moves?
a. $(2,6)$
b. $(3,5)$
c. $(4,4)$
d. $(5,3)$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Vietas Formulas", "Coordinate Motion" ], "current_concepts": [ "Quadratic Equations", "Vietas Formulas", "Coordinate Motion", "Distance Rate Time" ] } ## Solve Question 12 using Vieta's formulas $$ \begin{aligned} &x^2 - 4x - 45 = 0\ &\text{Sum of roots } (x_1 + x_2) = -\frac{b}{a} = -\frac{-4}{1} = 4 \end{aligned} $$ ## Calculate horizontal displacement for Question 13 $$ \begin{aligned} &\Delta x = \text{speed} \times \text{time} = 0.5 \times 4 = 2\ &x_{\text{new}} = x_{\text{initial}} + \Delta x = 2 + 2 = 4 \end{aligned} $$ ## Calculate vertical displacement for Question 13 $$ \begin{aligned} &\Delta y = \text{speed} \times \text{time} = 0.5 \times 2 = 1\ &y_{\text{new}} = y_{\text{initial}} + \Delta y = 3 + 1 = 4\ &\text{Final Point} = (4, 4) \end{aligned} $$ ## Question 12 F. $-45$

G. $-5$

H. $0$

J. $4$ ## Question 13 A. $(2,6)$

B. $(3,5)$

C. $(4,4)$

D. $(5,3)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Solve Question 12 using Vieta's formulas

Calculate horizontal displacement for Question 13

Calculate vertical displacement for Question 13

Answer:

Question 12

Question 13