value: 5

match the items.

a. 1 and -\frac{1}{2}
b. 8 and -10
c. -20 and 13
d. 8 and 3
e. -3 and -14

1. 3n^2 - 33n + 72 = 0
2. x^2 + 7x - 260 = 0
3. m^2 + 17m + 42 = 0
4. 8a^2 - 4a = 4
5. m^2 + 2m = 80

Question

value: 5

match the items.

a. 1 and -\frac{1}{2}
b. 8 and -10
c. -20 and 13
d. 8 and 3
e. -3 and -14

1. 3n^2 - 33n + 72 = 0
2. x^2 + 7x - 260 = 0
3. m^2 + 17m + 42 = 0
4. 8a^2 - 4a = 4
5. m^2 + 2m = 80

Accepted Answer

{ "quality": "clear", "question_count": 5, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Quadratic Equations", "Factoring Quadratic Trinomials" ], "new_concepts": [], "current_concepts": [ "Quadratic Equations", "Factoring Quadratic Trinomials" ] } ## Solve Equation 1 Using the *Quadratic Equations* and *Factoring Quadratic Trinomials* knowledge points $$ \begin{aligned} &3n^2 - 33n + 72 = 0 \ &3(n^2 - 11n + 24) = 0 \ &3(n - 8)(n - 3) = 0 \ &n = 8 \quad \text{or} \quad n = 3 \end{aligned} $$ This matches option **d**. ## Solve Equation 2 Using the *Quadratic Equations* and *Factoring Quadratic Trinomials* knowledge points $$ \begin{aligned} &x^2 + 7x - 260 = 0 \ &(x + 20)(x - 13) = 0 \ &x = -20 \quad \text{or} \quad x = 13 \end{aligned} $$ This matches option **c**. ## Solve Equation 3 Using the *Quadratic Equations* and *Factoring Quadratic Trinomials* knowledge points $$ \begin{aligned} &m^2 + 17m + 42 = 0 \ &(m + 3)(m + 14) = 0 \ &m = -3 \quad \text{or} \quad m = -14 \end{aligned} $$ This matches option **e**. ## Solve Equation 4 Using the *Quadratic Equations* and *Factoring Quadratic Trinomials* knowledge points $$ \begin{aligned} &8a^2 - 4a - 4 = 0 \ &4(2a^2 - a - 1) = 0 \ &4(2a + 1)(a - 1) = 0 \ &a = -\frac{1}{2} \quad \text{or} \quad a = 1 \end{aligned} $$ This matches option **a**. ## Solve Equation 5 Using the *Quadratic Equations* and *Factoring Quadratic Trinomials* knowledge points $$ \begin{aligned} &m^2 + 2m - 80 = 0 \ &(m + 10)(m - 8) = 0 \ &m = -10 \quad \text{or} \quad m = 8 \end{aligned} $$ This matches option **b**. | No. | Problem | Answer | |---|---|---| | 1 | $3n^2 - 33n + 72 = 0$ | d. 8 and 3 | | 2 | $x^2 + 7x - 260 = 0$ | c. -20 and 13 | | 3 | $m^2 + 17m + 42 = 0$ | e. -3 and -14 | | 4 | $8a^2 - 4a = 4$ | a. 1 and -$\frac{1}{2}$ | | 5 | $m^2 + 2m = 80$ | b. 8 and -10 | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Solve Equation 1

Solve Equation 2

Solve Equation 3

Solve Equation 4

Solve Equation 5

Answer:

No.	Problem	Answer
2	\(x^2 + 7x - 260 = 0\)	c. -20 and 13
3	\(m^2 + 17m + 42 = 0\)	e. -3 and -14
4	\(8a^2 - 4a = 4\)	a. 1 and -\(\frac{1}{2}\)
5	\(m^2 + 2m = 80\)	b. 8 and -10