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charle [14.2K]
2 years ago
5

Translate to an algebraic statement. "The quotient of twice a number and 7 is 20."

Mathematics
1 answer:
Genrish500 [490]2 years ago
4 0

<u>Answer:</u>

  • Translation: 2x/7 = 20

<u>Step-by-step explanation:</u>

  • <em>When we listen to the word "quotient", it means the solution to a division problem. </em>
  • <em>An unknown number that has been multiplied by 2 is in the numerator because it came before the 7 in the statement. </em>
  • <em>The number "7" is in the denominator because it came after the 2x in the statement. </em>
  • <em>The word "is" represents an equal sign.</em>
  • <em>The solution to the division problem (quotient) is 20. </em>

<u><em>If we put these clues together, we get 2x/7 = 20 as our translated equation.</em></u>

<u>Hence, our algebraic statement is 2x/7 = 20. The key is to listen to the statement. </u>

BrainiacUser1357

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The 1st and the 5th tables represent the same function

Step-by-step explanation:

* Lets explain how to solve the problem

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- To find the two equal function lets find their equations

- The form of the equation of a line whose endpoints are (x1 , y1) and

  (x2 , y2) is \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

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# (x1 , y1) = (4 , 5) and (x2 , y2) = (6 , 4)

∵ x1 = 4 , x2 = 6 and y1 = 5 , y2 = 4

∴ \frac{y-5}{x-4}=\frac{4-5}{6-4}

∴ \frac{y-5}{x-4}=\frac{-1}{2}

- By using cross multiplication

∴ 2(y - 5) = -1(x - 4) ⇒ simplify

∴ 2y - 10 = -x + 4 ⇒ add x and 10 for two sides

∴ x + 2y = 14 ⇒ (2)

# (x1 , y1) = (2 , 8) and (x2 , y2) = (8 , 5)

∵ x1 = 2 , x2 = 8 and y1 = 8 , y2 = 5

∴ \frac{y-8}{x-2}=\frac{5-8}{8-2}

∴ \frac{y-8}{x-2}=\frac{-3}{6}=====\frac{y-8}{x-2}=\frac{-1}{2}

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∴ 2(y - 8) = -1(x - 2) ⇒ simplify

∴ 2y - 16 = -x + 2 ⇒ add x and 16 for two sides

∴ x + 2y = 18 ⇒ (3)

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∵ x1 = 2 , x2 = 6 and y1 = 10 , y2 = 14

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∴ x + 2y = 20 ⇒ (5)

- Equations (1) and (5) are the same

∴ The 1st and the 5th tables represent the same function

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