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BaLLatris [955]
3 years ago
6

Determine the values of n

Mathematics
1 answer:
N76 [4]3 years ago
8 0
<h2>Answer:</h2><h3>b. n is odd</h3><h2>Step-by-step explanation:</h2>

In this problem, we assume that n is a whole number. The definition of inverse functions tells us that a function f has an inverse function if and only if the function is one-to-one, that is, if there is no any horizontal line intersecting the graph of f at more than one point. This only happens if n is odd. This is called the Horizontal Line Test for Inverse Functions. So let's take two examples:

FIRST:

n=2 \\ \\ f(x)=x^2

Since n is even, an horizontal line will pass through two points as indicated in the first figure below.

SECOND:

n=3 \\ \\ f(x)=x^3

Since n is odd, an horizontal line will pass through just one point as indicated in the second figure below.

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Read 2 more answers
Susan has 4 times as many quarters as dimes and 16 less dimes than nickels. If she has $13.45 in coins. How many of each coin do
Maslowich

Using a system of equations, it is found that Susan had 44 quarters, 11 dimes and 27 nickels.

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

We are going to use:

  • x as the number of quarters.
  • y as the number of dimes.
  • z as the number of nickels.

A <em>quarter </em>is worth $0.25. A <em>dime </em>is worth $0.1, and a <em>nickel </em>is worth $0.05. Total of $13.45, then:

0.25x + 0.1y + 0.05z = 13.45

4 times as many <u>quarters as dimes</u>, thus:

x = 4y \rightarrow y = 0.25x

16 less <u>dimes than nickels</u>, thus:

z = y + 16 = 0.25x + 16

Replacing in the first equation, we find x:

0.25x + 0.1y + 0.05z = 13.45

0.25x + 0.1(0.25x) + 0.05(0.25x + 16) = 13.45

0.2875x = 12.65

x = \frac{12.65}{0.2875}

x = 44

Now, with x, we find y and z:

y = 0.25x = 0.25(44) = 11

z = y + 16 = 11 + 16 = 27

Susan had 44 quarters, 11 dimes and 27 nickels.

A similar problem is given at brainly.com/question/24342899

4 0
2 years ago
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