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3 years ago

(continued)

Mathematics

1 answer:

prisoha [69]3 years ago

6 0

Arrays are used to represent data sets in rows and columns

The librarian could use 3 and 18 as a factor pair

<h3>How to determine the factor pair</h3>

The number of books is given as:

n = 54

Express 54 as a product of two numbers

54 = (1, 54), (2, 27),(3, 18) and (6, 9).

From the options, we have the following factor pair

3 and 18

Hence, the librarian could use 3 and 18 as a factor pair

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e-lub [12.9K]

Answer:

Part 1) The inverse function is $f^{-1}(x) =\frac{2x-3}{4}$

Part 2) 25.75 weeks

Step-by-step explanation:

Let

x ---->the number of weeks in the course

f(x) ---> the number of assignments he has completed

we have

$f(x)=\frac{4x-3}{2}$

Part 1) Find the inverse

Let

y=f(x)

$y=\frac{4x-3}{2}$

Exchange the variables (x for y and y for x)

$x=\frac{4y-3}{2}$

Isolate the variable y

$2x=4y-3\\4y=2x+3\\\\y=\frac{2x+3}{4}$

Let

$f^{-1}(x) =y$

$f^{-1}(x) =\frac{2x+3}{4}$

Part 2) we have

$f^{-1}(x) =\frac{2x+3}{4}$

where

$f^{-1}(x)$ ---->the number of weeks in the course

x ---> the number of assignments he has completed

For x=50

substitute in the inverse function

$f^{-1}(x) =\frac{2(50)+3}{4}=25.75\ weeks$

Note: Juliana don't need to use the inverse function. you can just use the function you have where f(x)=50 assignments and solve for x to get the amount of weeks.

$50=\frac{4x-3}{2}\\\\100=4x-3\\4x=103\\x=25.75\ weeks$