11. if $x = 2$ and $y = -2$ what is the value of
\x + 45x - 8y\
(a) -76
(b) 76
(c) -108
(d) 108

12. the length of a football field is 30 yards more than its width. express the length of the football field in terms of its width $w$.
(a) $w - 30$
(b) $w + 30$
(c) $w - 40$
(d) $w + 40$

13. combine the like terms:
\-3(-4y - 2y) + 8y - 8x\
(a) $27y - 9x$
(b) $27y + 9x$
(c) $26y - 8x$
(d) $26y + 8x$

14. the quotient of 7 more than $x$ to $x$.
(a) $\frac{x+7}{x}$
(b) $\frac{x-7}{x}$
(c) $\frac{x-7}{7}$
(d) $\frac{x+7}{7}$

15. if $x = 3$ and $y = 2$, what is the value of the above expression?
\\frac{xy}{x+y^2}\
(a) $\frac{5}{7}$
(b) $\frac{6}{8}$
(c) $\frac{6}{7}$
(d) $\frac{7}{9}$

16. translate: the difference of 120 and $k$ is 49.
(a) $120 - k = 50$
(b) $120 + k = 50$
(c) $120 - k = 49$
(d) $120 + k = 49$

17. what is the value of $x$ according to the equation below?
\9x - 9 = 207\
(a) 22
(b) 23
(c) 24
(d) 25

18. \twenty-three of a number is less than nine equals to four over a number.\ which of the following equations is a mathematical translation of the statement?
(a) $23x - 9 = \frac{4}{x}$
(b) $23x + 9 = \frac{4}{x}$
(c) $23x - 9 = \frac{x}{4}$
(d) $23x + 9 = \frac{x}{4}$

19. combine the like terms:
\7(3y - 10) + 3 + 2(3y^2 + 6y^2)\
(a) $9y^2 + 20y + 67$
(b) $9y^2 - 20y + 67$
(c) $18y^2 + 21y - 67$
(d) $18y^2 - 21y - 67$

20. translate: fourteen of a number is one fifth.
(a) $14 + x + 5$
(b) $14x + 5$
(c) $14x = \frac{1}{5}$
(d) $14x = 5$

Question

11. if $x = 2$ and $y = -2$ what is the value of
\x + 45x - 8y\
(a) -76
(b) 76
(c) -108
(d) 108

12. the length of a football field is 30 yards more than its width. express the length of the football field in terms of its width $w$.
(a) $w - 30$
(b) $w + 30$
(c) $w - 40$
(d) $w + 40$

13. combine the like terms:
\-3(-4y - 2y) + 8y - 8x\
(a) $27y - 9x$
(b) $27y + 9x$
(c) $26y - 8x$
(d) $26y + 8x$

14. the quotient of 7 more than $x$ to $x$.
(a) $\frac{x+7}{x}$
(b) $\frac{x-7}{x}$
(c) $\frac{x-7}{7}$
(d) $\frac{x+7}{7}$

15. if $x = 3$ and $y = 2$, what is the value of the above expression?
\\frac{xy}{x+y^2}\
(a) $\frac{5}{7}$
(b) $\frac{6}{8}$
(c) $\frac{6}{7}$
(d) $\frac{7}{9}$

16. translate: the difference of 120 and $k$ is 49.
(a) $120 - k = 50$
(b) $120 + k = 50$
(c) $120 - k = 49$
(d) $120 + k = 49$

17. what is the value of $x$ according to the equation below?
\9x - 9 = 207\
(a) 22
(b) 23
(c) 24
(d) 25

18. \twenty-three of a number is less than nine equals to four over a number.\ which of the following equations is a mathematical translation of the statement?
(a) $23x - 9 = \frac{4}{x}$
(b) $23x + 9 = \frac{4}{x}$
(c) $23x - 9 = \frac{x}{4}$
(d) $23x + 9 = \frac{x}{4}$

19. combine the like terms:
\7(3y - 10) + 3 + 2(3y^2 + 6y^2)\
(a) $9y^2 + 20y + 67$
(b) $9y^2 - 20y + 67$
(c) $18y^2 + 21y - 67$
(d) $18y^2 - 21y - 67$

20. translate: fourteen of a number is one fifth.
(a) $14 + x + 5$
(b) $14x + 5$
(c) $14x = \frac{1}{5}$
(d) $14x = 5$

Accepted Answer

{ "quality": "clear", "question_count": 10, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Algebraic Substitution", "Translating Word Problems to Equations", "Combining Like Terms" ], "new_concepts": [], "current_concepts": [ "Algebraic Substitution", "Translating Word Problems to Equations", "Combining Like Terms" ] } ## Evaluate expression for Question 11 Using the *Algebraic Substitution* knowledge point $$ \begin{aligned} &\text{Given: } x = 2,\ y = -2\ &\text{Expression: } x + 45x - 8y\ &\text{Substitute: } 2 + 45(2) - 8(-2)\ &\text{Calculate: } 2 + 90 + 16 = 108 \end{aligned} $$ ## Translate word problem for Question 12 Using the *Translating Word Problems to Equations* knowledge point $$ \begin{aligned} &\text{Let width } = w\ &\text{Length is } 30\text{ yards more than width}\ &\text{Length } = w + 30 \end{aligned} $$ ## Simplify expression for Question 13 Using the *Combining Like Terms* knowledge point $$ \begin{aligned} &\text{Expression: } -3(-4y - 2y) + 8y - 8x\ &\text{Combine inside: } -3(-6y) + 8y - 8x\ &\text{Distribute: } 18y + 8y - 8x\ &\text{Combine like terms: } 26y - 8x \end{aligned} $$ ## Translate quotient for Question 14 Using the *Translating Word Problems to Equations* knowledge point $$ \begin{aligned} &\text{"7 more than } x\text{" } ightarrow x + 7\ &\text{"The quotient of } 7\text{ more than } x\text{ to } x\text{" } ightarrow \frac{x+7}{x} \end{aligned} $$ ## Evaluate expression for Question 15 Using the *Algebraic Substitution* knowledge point $$ \begin{aligned} &\text{Given: } x = 3,\ y = 2\ &\text{Expression: } \frac{xy}{x+y^2}\ &\text{Substitute: } \frac{3 \cdot 2}{3 + 2^2} = \frac{6}{3 + 4} = \frac{6}{7} \end{aligned} $$ ## Translate difference for Question 16 Using the *Translating Word Problems to Equations* knowledge point $$ \begin{aligned} &\text{"The difference of } 120\text{ and } k\text{" } ightarrow 120 - k\ &\text{"is } 49\text{" } ightarrow = 49\ &\text{Equation: } 120 - k = 49 \end{aligned} $$ ## Solve equation for Question 17 We solve the linear equation step-by-step: 1. Add $9$ to both sides: $$ 9x = 207 + 9 \implies 9x = 216 $$ 2. Divide both sides by $9$: $$ x = \frac{216}{9} = 24 $$ ## Translate statement for Question 18 Using the *Translating Word Problems to Equations* knowledge point $$ \begin{aligned} &\text{"Twenty-three of a number" } ightarrow 23x\ &\text{"is less than nine" } ightarrow - 9\ &\text{"equals to four over a number" } ightarrow = \frac{4}{x}\ &\text{Equation: } 23x - 9 = \frac{4}{x} \end{aligned} $$ ## Simplify expression for Question 19 Using the *Combining Like Terms* knowledge point $$ \begin{aligned} &\text{Expression: } 7(3y - 10) + 3 + 2(3y^2 + 6y^2)\ &\text{Combine inside: } 7(3y - 10) + 3 + 2(9y^2)\ &\text{Distribute: } 21y - 70 + 3 + 18y^2\ &\text{Combine constants: } 18y^2 + 21y - 67 \end{aligned} $$ ## Translate statement for Question 20 Using the *Translating Word Problems to Equations* knowledge point $$ \begin{aligned} &\text{"Fourteen of a number" } ightarrow 14x\ &\text{"is" } ightarrow =\ &\text{"one fifth" } ightarrow \frac{1}{5}\ &\text{Equation: } 14x = \frac{1}{5} \end{aligned} $$ ## Question 11 (A) -76

(B) 76

(C) -108

(D) 108 ## Question 12 (A) w - 30

(B) w + 30

(C) w - 40

(D) w + 40 ## Question 13 (A) 27y - 9x

(B) 27y + 9x

(C) 26y - 8x

(D) 26y + 8x ## Question 14 (A) $\frac{x+7}{x}$

(B) $\frac{x-7}{x}$

(C) $\frac{x-7}{7}$

(D) $\frac{x+7}{7}$ ## Question 15 (A) $\frac{5}{7}$

(B) $\frac{6}{8}$

(C) $\frac{6}{7}$

(D) $\frac{7}{9}$ ## Question 16 (A) 120 - k = 50

(B) 120 + k = 50

(C) 120 - k = 49

(D) 120 + k = 49 ## Question 17 (A) 22

(B) 23

(C) 24

(D) 25 ## Question 18 (A) 23x - 9 = $\frac{4}{x}$

(B) 23x + 9 = $\frac{4}{x}$

(C) 23x - 9 = $\frac{x}{4}$

(D) 23x + 9 = $\frac{x}{4}$ ## Question 19 (A) 9y^2 + 20y + 67

(B) 9y^2 - 20y + 67

(C) 18y^2 + 21y - 67

(D) 18y^2 - 21y - 67 ## Question 20 (A) 14 + x + 5

(B) 14x + 5

(C) 14x = $\frac{1}{5}$

(D) 14x = 5

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Translating Word Problems to Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Evaluate expression for Question 11

Translate word problem for Question 12

Simplify expression for Question 13

Translate quotient for Question 14

Evaluate expression for Question 15

Translate difference for Question 16

Solve equation for Question 17

Translate statement for Question 18

Simplify expression for Question 19

Translate statement for Question 20

Answer:

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20