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AlekseyPX
3 years ago
7

The sum of Cathy's and Tony's ages is 65. Eight years ago, Cathy's age was 2/5 of Tony's age. How old are they now?

Mathematics
1 answer:
Viktor [21]3 years ago
7 0
Let
x------> Cathy's<span> ages
</span>y------> Tony's ages

we know that
x+y=65-----> x=65-y-----> equation 1
y-8=(2/5)*(x-8)-----> equation 2

substitute equation 1 in equation 2
y-8=(2/5)*(65-y-8)---> y-8=22.8-0.4y----> y+0.4y=22.8+8
1.4y=30.8-----> y=22
x=65-y-----> x=65-22----> x=43

the answer is
Cathy's ages is 43 years 
Tony's ages is 22 years

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Questions Below. Would Appreciate Help!
kherson [118]

Answer:

The function that could be the function described is;

f(x) = -10 \cdot cos \left (\dfrac{2 \cdot \pi }{3} \cdot x \right ) + 10

Step-by-step explanation:

The given parameters of the cosine function are;

The period of the cosine function = 3

The maximum value of the cosine function = 20

The minimum value of the cosine function = 0

The general form of the cosine function is presented as follows;

y = A·cos(ω·x - ∅) + k

Where;

\left | A \right | = The amplitude = Constant

The period, T = 2·π/ω

The phase shift, = ∅/ω

k = The vertical translation = Constant

Therefore, by comparison, we have;

T = 3 = 2·π/ω

∴ ω = 2·π/3

The range of value of the cosine of an angle are;

-1 ≤ cos(θ) ≤ 1

Therefore, when A = 10, cos(ω·x - ∅) = 1 (maximum value of cos(θ)) and k = 10, we have;

y = A × cos(ω·x - ∅) + k

y = 10 × 1 + 10 = 20 = The maximum value of the function

Similarly, when A = 10, cos(ω·x - ∅) = -1 (minimum value of cos(θ)) and k = 10, we get;

y = 10 × -1 + 10 = 0 = The minimum value of the function

Given that the function is a reflection of the parent function, we can have;

A = -10, cos(ω·x - ∅) = -1 (minimum value of cos(θ)) and k = 10, to get;

y = -10 × -1 + 10 = 20 = The maximum value of the function

Similarly, for cos(ω·x - ∅) = 1 we get;

y = -10 × 1 + 10 = 0 = The minimum value of the function

Therefore, the likely values of the function are therefore;

A = -10, k = 10

The function is therefore presented as follows;

y = -10 × cos(2·π/3·x) + 10

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Jennie ran the first 6 miles of a marathon
Mars2501 [29]
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The graph of F(x), shown below, has the same shape as the graph of G(x) = x2, but it is shifted up 3 units. What is its equation
Aliun [14]
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 Applying the following transformation we have:
 Vertical displacement
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the equation of F (x) is given by:
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Answer:

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Step-by-step explanation:

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