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andrew-mc [135]
2 years ago
6

Mrs.Stone is three times older than her younger daughter, Joyce, but only two times older than her older daughter, Alex. How old

is Mrs.Stone now, if 9 years ago Alex was two times okder than Joyce? Mrs.Stone is three times older than her younger daughter, Joyce, but only two times older than her older daughter, Alex. How old is Mrs.Stone now, if 9 years ago Alex was two times okder than Joyce?
Mathematics
1 answer:
olchik [2.2K]2 years ago
5 0

Answer:

54 years

Step-by-step explanation:

Joyce age = x

Alex age = y

3x = 2y - - - (1)

y - 9 = 2(x - 9)

y - 9 = 2x - 18

-9 + 18 = 2x - y

9 = 2x - y

y = 2x - 9 - - (2)

3x = 2y

3x = 2(2x - 9)

3x = 4x - 18

18 = 4x - 3x

18 = x

Hence,

Mrs stone is 3 * 18 = 54 years

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Answer:

(x - 1)²/4² - (y - 2)²/2² = 1 ⇒ The bold labels are the choices

Step-by-step explanation:

* Lets explain how to solve this problem

- The equation of the hyperbola is x² - 4y² - 2x + 16y - 31 = 0

- The standard form of the equation of hyperbola is

  (x - h)²/a² - (y - k)²/b² = 1 where a > b

- So lets collect x in a bracket and make it a completing square and

  also collect y in a bracket and make it a completing square

∵ x² - 4y² - 2x + 16y - 31 = 0

∴ (x² - 2x) + (-4y² + 16y) - 31 = 0

- Take from the second bracket -4 as a common factor

∴ (x² - 2x) + -4(y² - 4y) - 31 = 0

∴ (x² - 2x) - 4(y² - 4y) - 31 = 0

- Lets make (x² - 2x) completing square

∵ √x² = x

∴ The 1st term in the bracket is x

∵ 2x ÷ 2 = x

∴ The product of the 1st term and the 2nd term is x

∵ The 1st term is x

∴ the second term = x ÷ x = 1

∴ The bracket is (x - 1)²

∵  (x - 1)² = (x² - 2x + 1)

∴ To complete the square add 1 to the bracket and subtract 1 out

   the bracket to keep the equation as it

∴ (x² - 2x + 1) - 1

- We will do the same withe bracket of y

- Lets make 4(y² - 4y) completing square

∵ √y² = y

∴ The 1st term in the bracket is x

∵ 4y ÷ 2 = 2y

∴ The product of the 1st term and the 2nd term is 2y

∵ The 1st term is y

∴ the second term = 2y ÷ y = 2

∴ The bracket is 4(y - 2)²

∵ 4(y - 2)² = 4(y² - 4y + 4)

∴ To complete the square add 4 to the bracket and subtract 4 out

   the bracket to keep the equation as it

∴ 4[y² - 4y + 4) - 4]

- Lets put the equation after making the completing square

∴ (x - 1)² - 1 - 4[(y - 2)² - 4] - 31 = 0 ⇒ simplify

∴ (x - 1)² - 1 - 4(y - 2)² + 16 - 31 = 0 ⇒ add the numerical terms

∴ (x - 1)² - 4(y - 2)² - 16 = 0 ⇒ add 14 to both sides

∴ (x - 1)² - 4(y - 2)² = 16 ⇒ divide both sides by 16

∴ (x - 1)²/16 - (y - 2)²/4 = 1

∵ 16 = (4)² and 4 = (2)²

∴ The standard form of the equation of the hyperbola is

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4 0
3 years ago
Solve for x given the equation x-5+7=11
Alexeev081 [22]

Answer:

9

Step-by-step explanation:

x-5+7=11

First think of what +7 = 11 then subtract by 5

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7 0
3 years ago
68 * 27 - 81 + ? = 600
tankabanditka [31]

The missing term is -1155.

Step-by-step explanation:

Given expression is

68 * 27 - 81 + ? = 600

Let the missing term be x

68*27-81+x=600\\1836-81+x=600\\1755+x=600

Subtracting 1755 from both sides

1755-1755+x=600-1755\\x=-1155

Therefore,

The missing term is -1155.

Keywords: multiplication, addition

Learn more about multiplication at:

  • brainly.com/question/10364988
  • brainly.com/question/10435816

#LearnwithBrainly

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3 years ago
What is the slope of a line perpendicular to the line whose equation is
seropon [69]

Answer:

1

Step-by-step explanation:

x+y=-9

y=-x-9

So slope of original line is -1.

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2 years ago
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jek_recluse [69]

Answer:

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Step-by-step explanation:

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