[size=150]Both [math]\left(x-3\right)\left(x+3\right)[/math] and [math]\left(3-x\right)\left(3+x\right)[/math] contain a sum and a difference and have only 3 and [math]x[/math] in each factor.[/size][br][br]If each expression is rewritten in standard form, will the two expressions be the same? Explain or show your reasoning.
[size=150]Show that the expressions [math]\left(5+1\right)\left(5-1\right)[/math] and [math]5^2-1^2[/math] are equivalent.[/size][br]
[size=150]The expressions [math]\left(30-2\right)\left(30+2\right)[/math] and [math]30^2-2^2[/math] are equivalent and can help us find the product of two numbers. [br][/size][br]Which two numbers are they?[br]
[size=150]Write [math]94\cdot106[/math] as a product of a sum and a difference, and then as a difference of two squares. [/size][br][br]What is the value of [math]94\cdot106[/math]?
[size=150]What are the solutions to the equation [math]\left(x-a\right)\left(x+b\right)=0[/math]?[/size]
[size=150]Select [b]all[/b] the expressions that are equivalent to [math]8-x[/math].[/size]
[size=150]Mai fills a tall cup with hot cocoa, 12 centimeters in height. She waits 5 minutes for it to cool. Then, she starts drinking in sips, at an average rate of 2 centimeters of height every 2 minutes, until the cup is empty.[br][br]The function [math]C[/math] gives the height of hot cocoa in Mai’s cup, in centimeters, as a function of time, in minutes.[/size][br]Sketch a possible graph of [math]C[/math] in the applet below. Be sure to include a label and a scale for each axis.
What quantities do the domain and range represent in this situation?
Describe the domain and range of [math]C[/math].
[size=150]One bacteria population, [math]p[/math], is modeled by the equation [math]p=250,000\cdot\left(\frac{1}{2}\right)^d[/math], where [math]d[/math] is the number of days since it was first measured.[br][br]A second bacteria population, [math]q[/math], is modeled by the equation [math]q=500,000\cdot\left(\frac{1}{3}\right)^d[/math], where [math]d[/math] is the number of days since it was first measured.[br][/size][br]Which statement is true about the two populations?