Kira is using the figure shown to prove the Pythagorean theorem. She starts by writing the
equation (a + b)2 – 2 = 4( ab) because she knows two equal ways to represent the area
of the shaded region. Which best describes the next steps Kira should take to complete her
proof?

B. Simplify both sides of the equation to get ; then subtract 2ab and add to both sides of the equation

Step-by-step explanation:

Given

Required

Describe the next steps to

First, we open all brackets

At this point, options A and C are incorrect because they didn't present the right result of the expression.

So, we have options B and D to consider

The next step is to subtract 2ab from both sides

Collect like terms

Lastly, to prove the Pythagoras theorem, the equation has to be in form of; meaning the is added to both sides; See below

Add to both sides

At this point, only option B completes Kira's proof

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

the domain of a function is the set of input values, x , for which a function is defined. the domain is shown in the left oval in the picture below. the function provides an output value, f(x) , for each member of the domain.