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Dima020 [189]
3 years ago
14

Given the following functions:

Mathematics
1 answer:
andrew-mc [135]3 years ago
5 0

Answer:

x^2 - 6x + 9.

Step-by-step explanation:

f(x) = x^2 and g(x) = x - 3.

To find f(g(x))  we replace the x in f(x) by g(x).

f(g(x)) = (x - 3)^2

= x^2 - 6x + 9.

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The box office manager said about 5,000 people attended the show. Write a number that could be the actual attendance if he corre
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Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a law
NARA [144]

Answer:

Slope of this line is given by:

<em>Aaron’s rate for mowing lawns is 0.5 acres per hour</em>

Step-by-step explanation:

It is given that time is tracked by Aaron related to x coordinate.

and the area of land mowed in acres is related to y coordinate.

Two of his points are given as:

(3, 1.5) and (5,2.5)

We know that the coordinates are represented in the form of (x,y)

i.e. first coordinate represents x coordinate and

second coordinate represents y coordinate.

So, it can be observed that:

x_1=3, y_1=1.5\\x_2=5, y_2=2.5

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Change in y coordinate = y_2-y_1=2.5-1.5 = 1

i.e. total land mowed taken is 1 acre.

In other words, <em>it takes 2 hours for Aaron to mow 1 acre of land.</em>

So, "option 1)  It takes Aaron about 1 hour to mow 2 acres." is incorrect.

<u>Rate of mowing</u> lawn is the <em>land mowed by Aaron in 1 hour</em>.

Land mowed in 2 hours = 1 acre

Land mowed in 1 hours = \frac{1}{2} acre i.e. 0.5 acre

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m = \dfrac{y_2-y_1}{x_2-x_1}

Here y_2 - y_1 = 1

x_2 - x_1 = 2

As per formula:

m = \dfrac{1}{2} = 0.5

So, option 2) Aaron’s rate for mowing lawns is 0.5 acres per hour.

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