A 10 -foot ladder is leaning on a tree. The bottom of the ladder on the ground at a distance of 6 feet from the base of the tree. The base of the tree and the ground form a right angle as shown. What is the distance, in feet, between the ground and the top of the ladder?

x=8,-8

Step-by-step explanation:

Rewrite the equation as  

x 2 + 6 2 = 10 2 . x2+62=102

Raise  

6

to the power of  

2 .x2+36 =102

Raise  

10

to the power of  

2 .x2+36=100

Move all terms not containing  

x

to the right side of the equation.

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Subtract  

36

from both sides of the equation.

x 2 = 100 − 36  Subtract  36 from 100

x 2 = 64

Take the square root of both sides of the equation to eliminate the exponent on the left side.

x

=

±

√

64

The complete solution is the result of both the positive and negative portions of the solution.

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Simplify the right side of the equation.

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Rewrite  

64

as  

8

2

.

x

=

±

√

8

2

Pull terms out from under the radical, assuming positive real numbers.

x

=

±

8

The complete solution is the result of both the positive and negative portions of the solution.

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First, use the positive value of the  

±

to find the first solution.

x

=

8

Next, use the negative value of the  

±

to find the second solution.

x

=

−

8

The complete solution is the result of both the positive and negative portions of the solution.

x = 8 ,−8

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.

lol 2

step-by-step explanation: