Give a geometric interpretation of the triangle inequality

1 answer:

6 0

The sides must be long enough to make a triangle. (If the sides are not long enough, they won't meet, so cannot form a triangle.)

_____

If your version of the triangle inequality includes the "or equal to" case, then the segments must be long enough to meet, even though the result may look like a line segment.

You might be interested in

The rate of change in the function y=x+4 is________ the rate of change of the function represented in the table.

Snezhnost [94]

Recall that the slope is the "average rate of change" of any function.

$\bf y=\stackrel{slope}{1}x+4\qquad \qquad 
\begin{array}{ccll}
x&y\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
0&6\\2&8\\4&10\\6&12
\end{array}
\\\\\\
\textit{let's check what is the slope of the tabled function}\\
\textit{by using two points from it}$

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 2}}\quad ,&{{ 8}})\quad 
% (c,d)
&({{ 6}}\quad ,&{{ 12}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{12-8}{6-2}\implies \cfrac{4}{4}\implies 1$

4 0

3 years ago

Read 2 more answers

A company produces screens of different sizes. Based on the table, could there be a relationship between the number of pixels an

alexdok [17]

Answer:

1 in. = 5184 pixels

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Susan drove at an average speed of 30 miles per hour for the first 30 miles of a trip and then at an average speed of 60 miles p