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:
-41/65
Step-by-step explanation:
Answer:
128
Step-by-step explanation:
N(t) = 4(2)^t
N(t) = 4(2)^5
N(t) = 4(32)
N(t) = 128
1) Taking in account that the function is f(x)= -(2/3) |x+4|-6, I enclose a file with the graph.
That helps you to conclude:
a) The graph of f(x) has a vertex on (-4, -6)
b) When you multiply a function times 2/3 it is vertically compressed which is equivalent to horizontally streched.
c) The graph of f(x) opens downward
d) The domain of f(x) is all the real values (the absolute function accepts any value of x either positive or negative)
Answer: the graph of f(x) is horizontally stretched.
Firstly, seeing that the sequence is based on odd numbers I would say that this is the formula (which will allow you to know whatever term):
nth term = 2n-1
Hope this helps!