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3 years ago

What is the length of a line segment with endpoints of 19 and –39

Mathematics

2 answers:

Vlad [161]3 years ago

6 0

19-(-39)
19+39=58
is solution as
the two end points are 19 and -39 we should subtract then we get the distance between

gtnhenbr [62]3 years ago

5 0

Answer: 58 units

Step-by-step explanation: In this problem, the given numbers 19 and -39 represent the coordinates of the endpoints of a segment and we are asked to find the length of the segment.

To find the length of a segment, we take the greater endpoint coordinate minus the lesser endpoint coordinate.

In this case, the greater endpoint coordinate is 19 and the lesser endpoint coordinate is -39.

So, we have 19 - (-39) which can also be thought of as 19 + 39 which equals 58.

Therefore, the length of this segment is 58 units.

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Let's find the slope between your two points.

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3 years ago

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Answer:

$\textsf{$f(1) = \boxed{1}$ , meaning when a $\boxed{1}$ is rolled on the die, the player is awarded}\\\\ \textsf{ $\boxed{1}$ point. This interpretation $\boxed{\sf makes \; sense}$ in the context of the problem.}$

$\textsf{$f(4.5) = \boxed{8}$ , meaning when a $\boxed{4.5}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{8}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}$

$\textsf{$f(10) = \boxed{19}$ , meaning when a $\boxed{10}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{19}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}$

$\textsf{Based on the observations above, it is clear that an appropriate domain for the}\\\\ \textsf{function is $\boxed{ \{1, 2, 3, 4, 5, 6\}}$ .}$

Step-by-step explanation:

<u>Given function</u>:

$f(x)=2x-1$

where:

x is the value rolled on the six-sided die.
The sides of the die are labelled 1 to 6.

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

f(1) means the value of the function when x = 1.

Therefore, substitute x = 1 into the given function to find f(1):

$\begin{aligned}x=1 \implies f(1)&=2(1)-1\\&=2-1\\&=1\end{aligned}$

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

f(4.5) means the value of the function when x = 4.5.

Therefore, substitute x = 4.5 into the given function to find f(4.5):

$\begin{aligned}x=4.5 \implies f(4.5)&=2(4.5)-1\\&=9-1\\&=8\end{aligned}$

As the faces of the six-sided die are labelled 1 to 6, the only values of x that make sense are 1, 2, 3, 4, 5 and 6. Therefore, rolling a "4.5" does not make sense.

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

f(10) means the value of the function when x = 10.

Therefore, substitute x = 10 into the given function to find f(10):

$\begin{aligned}x=10 \implies f(1)&=2(10)-1\\&=20-1\\&=19\end{aligned}$

As the faces of the six-sided die are labelled 1 to 6, the only values of x that make sense are 1, 2, 3, 4, 5 and 6. Therefore, rolling a "10" does not make sense.

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

The domain of a function is the set of all possible x-values.

As the faces of the six-sided die are labelled 1 to 6, the only possible values of x are 1, 2, 3, 4, 5 and 6.

$\textsf{Based on the observations above, it is clear that an appropriate domain for the}\\\\ \textsf{function is $\boxed{ \{1, 2, 3, 4, 5, 6\}}$ .}$

The domain can also be written as:

$\{x \in \mathbb{N} \; | \; 1 \leq x \leq 6 \}$

or $\{x \in \mathbb{Z} \; | \; 1 \leq x \leq 6 \}$

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