# 5.5 Midsegment Theorem Investigation

##### QUESTION:
Any segment connecting midpoints of 2 sides of a triangle is called a MIDSEGMENT of that triangle. Move the triangle's vertices around. What seems to be true about the midsegment of ANY TRIANGLE?
##### GeoGebra for MEANINGFUL REMEDIATION or CONCEPTUAL DISCOVERY for Students Needing More Support. Move the triangle's WHITE VERTICES anywhere you'd like!
[b][color=#0000ff][url=https://docs.google.com/document/d/1HsFCBz3suKP-AhU50diM9G9zdtdswAsaR-m4jCJ8omI/edit?usp=sharing]Triangle Midsegment Action: Link to a Discovery Learning Lesson using the applet above[/url]﻿. [/color][/b]

# Exponential Functions: Graphs

The following applet displays the graph of the exponential function $f\left(x\right)=c\cdot a^{kx}+d$. [br]Interact with the applet below for a few minutes, then answer the questions that follow.
[b][color=#000000]Questions:[/color][/b][br][br][color=#000000]1) How does the parameter [/color][color=#cc0000][b]a[/b][/color] [color=#000000]affect the graph of the exponential function? Explain. [br] What happens if [/color][color=#cc0000][b]a > 1[/b][/color][color=#000000] and [/color][color=#1e84cc][b]k > 0[/b][/color][color=#000000]? What happens if [/color][color=#cc0000][b]a < 1[/b][/color][color=#000000] and [/color][color=#1e84cc][b]k > 0[/b][/color][color=#000000]? [br][br][/color][color=#000000]2) How does the parameter [/color][b][color=#1e84cc]k[/color][/b][color=#000000] affect the graph? Explain. [br] If you need a hint, refer back to [url=https://www.geogebra.org/m/HJvZSUna]this worksheet[/url]. [br][br][/color][color=#000000]3) What does the parameter [/color][color=#980000][b]d[/b][/color][color=#000000] do the graph? Explain. [br][br][/color][color=#000000]4) Suppose [/color][color=#cc0000][b]a < 1[/b][/color][color=#000000]. [br] Given this constraint, is it possible to get the graph of this exponential function to look the way it does[br] when [/color][color=#cc0000][b]a > 1[/b][/color][color=#000000] and [/color][color=#1e84cc][b]k > 0[/b][/color][color=#000000]? Explain. [/color]

# Ellipse eccentricity

 Shows effect on ellipse when eccentricity changes.

# Reimann Sum

Adjust n to increase or decrease number of interval

# Rolling two dice

##### Rolling two dice
Problem: when rolling two fair dice, a sum of 9 occurs more often than a sum of 10. [br]But 9=3+6=4+5  and  10=4+6=5+5, therefore there are 2 ways to get a sum of 9 and 10.