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Reil [10]
3 years ago
15

Rachel hikes at a steady rate from a ranger station to a campground that is 20 mi away. After 2 h, she is 13 mi from the campgro

und. After 4 h, she is 6 mi from the campground. A graph shows her distance from the campground Y, in miles, after x hours. What is the slope of the graph and what does it represent?
Mathematics
1 answer:
Angelina_Jolie [31]3 years ago
8 0

Answer:

-3.5

The distance Rachel covers per hour is 3.5 miles

Step-by-step explanation:

After 2 hours, she is 13 miles from the campground.

After 4 hours, she is 6 miles from the campground.

Let x be the number of hours, y be the number of miles from the campground, then we have two points (2,13) and (4,6).

The equation of the line passing through the points (x_1,y_1) and (x_2,y_2) is

y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)

Substitute:

x_1=2\\ \\y_1=13\\ \\x_2=4\\ \\y_2=6

Hence,

y-13=\dfrac{6-13}{4-2}(x-2)\\ \\y-13=-3.5(x-2)\\ \\y=-3.5x+7+13\\ \\y=-3.5x+20

The slope of the line is -3.5 and it represents that  the distance Rachel covers per hour is 3.5 miles.

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Answer/Step-by-step explanation:

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When composing functions we do the same thing but instead of plugging in numbers we are

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Examples

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f(x) = 3x + 4 (6)

g(x) = x

2 +

1

x

(7)

When composing functions we always read from right to left. So, first, we will plug x

into g (which is already done) and then g into f. What this means, is that wherever we

see an x in f we will plug in g. That is, g acts as our new variable and we have f(g(x)).

g(x) = x

2 +

1

x

(8)

f(x) = 3x + 4 (9)

f( ) = 3( ) + 4 (10)

f(g(x)) = 3(g(x)) + 4 (11)

f(x

2 +

1

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) = 3(x

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1

x

) + 4 (12)

f(x

2 +

1

x

) = 3x

2 +

3

x

+ 4 (13)

Thus, (f ◦ g)(x) = f(g(x)) = 3x

2 +

3

x + 4.

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f( ) = 2( ) (24)

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f(4x

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f(4x

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2 + 8x (27)

(28)

Thus (f ◦ g ◦ h)(x) = f(g(h(x))) = 8x

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Answer:

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6, -9 = 15

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