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FromTheMoon [43]
3 years ago
12

If f(x) = 2/3x + 9, find f^-1(x)

Mathematics
1 answer:
Degger [83]3 years ago
5 0

Answer:

  • Option D

Step-by-step explanation:

<u>Given function:</u>

  • f(x) = 2/3x + 9

<u>Find its inverse:</u>

  • x = 2/3*f⁻¹(x) + 9
  • 2/3*f⁻¹(x) = x - 9
  • f⁻¹(x)  = 3/2(x - 9)
  • f⁻¹(x) = 3/2x - 27/2

Correct choice is D

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The path of two bumper cars can be represented by the functions x + y = –5 and y = x2 – x – 6. At which locations will the bumpe
Alex Ar [27]

Equaling the equations, it is found that the cars hit each other at: (-1,-4) and (1,-6).

---------------------------------

For the first car, we have that:

x + y = -5

Thus:

y_1 = -5 - x

---------------------------------

For the second car:

y_2 = x^2 - x - 6

---------------------------------

They meet at the the values of x for which:

y_1 = y_2

Thus:

-5 - x = x^2 - x - 6

x^2 - 1 = 0

x^2 = 1

x = \pm \sqrt{1}

x = \pm 1

  • When x = 1, they meet at y = -5 - 1 = -6
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Thus (-1,-4) and (1,-6).

A similar problem is given at brainly.com/question/13308311

3 0
3 years ago
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Represent the geometric series using the explicit formula.
user100 [1]

Answer:  f(n)=12(-3)^{(n-1)}

Step-by-step explanation:

The Explicit formula in function notation for a geometric series is:

f(n)=f(1)r^{(n-1)}

Where f(n) is the nth term of the sequence, f(1) is the first term in the sequence and r is the common ratio.

Given the following geometric serie:

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The common ratio is:

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I am getting stuxk on this question
grandymaker [24]
Answer: Choice B) 3 years

--------------------------------------

Explanation:

The simple interest formula is
i = P*r*t
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i = interest
P = principal
r = interest rate in decimal form
t = time in years

In this case,
i = 840
P = 7000
r = 0.04 (move the decimal point 2 spots to the left go to from 4% to 0.04)
t = unknown; we'll leave it as t

Plug the given values above and solve for, or isolate, t
i = P*r*t 
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