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1 year ago

8. Olivia's brother is twice her age

Mathematics

1 answer:

slava [35]1 year ago

8 0

The ages of Olivia and her brother are 10 years and 11 years respectively

Let x₁, and x₂ be the ages of Olivia and her brother respectively.

Given that Olivia's brother is twice her age minus 9 years.

⇒ x₂ = 2x₁ - 9 → equation 1

Also given that Olivia's brother is as old as half the sum of the ages of Olivia and both of her 12-year-old twin brothers.

⇒ x₂ = 1/2 × (x₁ + 12) → equation 2

Using equation 1 in equation 2, we get

2x₁ - 9 = 1/2 × (x₁ + 12)

⇒ 4x₁ - 18 = x₁ + 12 (multiplying by 2 on both sides)

⇒ 4x₁ - x₁ = 12 + 18

⇒ 3x₁ = 30

⇒ x₁ = 10 (dividing by 3 on both sides)

Using the value of x₁, in equation 1,

⇒ x₂ = 2(10) - 9

⇒ x₂ = 20 - 9

⇒ x₂ = 11

Therefore the ages of Olivia and her brother are 10 years and 11 years respectively.

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Answer:

see explanation

Step-by-step explanation:

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$(1-3x)^{6}$

= 1. $1^{6}$ $(-3x)^{0}$ + 6. $1^{5}$ $(-3x)^{1}$ + 15. $1^{4}$ $(-3x)^{2}$ + 20. $1^{3}$ $(-3x)^{3}$ + 15.1² $(-3x)^{4}$ + 6. $1^{1}$ $(-3x)^{5}$ + 1. $1^{0}$ $(-3x)^{6}$

= 1 - 18x + 135x² - 540x³ + 1215 $x^{4}$ - 1458 $x^{5}$ + 729 $x^{6}$

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Collecting like terms from both expressions

$(1+3x)^{6}$ + $(1-3x)^{6}$

= 2 + 270x² + 2430 $x^{4}$ + 1458 $x^{6}$

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(2)

Using Pascal's triangle with n = 5

1 5 10 10 5 1

Decreasing powers of 1 from $1^{5}$ to $1^{0}$

Increasing powers of 2x from $(2x)^{0}$ to $(2x)^{5}$

$(1+2x)^{5}$

= 1. $1^{5}$ $(2x)^{0}$ + 5. $1^{4}$ $(2x)^{1}$ + 10. $1^{3}$ $(2x)^{2}$ + 10. $1^{2}$ $(2x)^{3}$ + 5. $1^{1}$ $(2x)^{4}$ + 1. $1^{0}$ $(2x)^{5}$

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3 years ago

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Answer:

Not entirely positive of about the answers, but all of the values would equal 15

First Y = 5

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