Answer:
a) 
b) 
Step-by-step explanation:
Use logarithm properties:
Then
a) 
b) 
Answer:
<span>=3<span>√6</span>−3<span>√5</span></span>
Explanation:
<span>3<span><span>√5</span>+<span>√6</span></span></span>
We rationalise the denominator by multiplying the expression by the conjugate of the denominator. <span><span>√5</span>−<span>√6</span></span>
<span><span>3⋅<span>(<span>√5</span>−<span>√6</span>)</span></span><span><span>(<span>√5</span>+<span>√6</span>)</span>⋅<span>(<span>√5</span>−<span>√6</span>)</span></span></span>
<span>=<span><span>3⋅<span>(<span>√5</span>)</span>+3⋅<span>(−<span>√6</span>)</span></span><span><span>(<span>√5</span>+<span>√6</span>)</span>⋅<span>(<span>√5</span>−<span>√6</span>)</span></span></span></span>
<span>=<span><span>3<span>√5</span>−3<span>√6</span></span><span><span>(<span>√5</span>+<span>√6</span>)</span>⋅<span>(<span>√5</span>−<span>√6</span>)</span></span></span></span>
<span>Applying identity
<span><span>(a+b)</span><span>(a−b)</span>=<span>a2</span>−<span>b2</span></span> to the denominator.</span>
<span>=<span><span>3<span>√5</span>−3<span>√6</span></span><span><span><span>(<span>√5</span>)</span>2</span>−<span><span>(<span>√6</span>)</span>2</span></span></span></span>
<span>=<span><span>3<span>√5</span>−3<span>√6</span></span><span>5−6</span></span></span>
<span>=<span><span>3<span>√5</span>−3<span>√6</span></span><span>−1</span></span></span>
<span>=−3<span>√5</span>+3<span>√6</span></span>
<span>=3<span>√6</span>−3<span>√<span>5
</span></span></span>
A single angle is generally not considered to be supplementary. Supplementary angles are angles that equal 180° when they are added together. For example, 70° and 110° are supplementary because they equal 180°.
However, I guess the supplementary angle can be the angle that must be added to another to total 180°. For example, 80° is the supplementary angle of 100°.
Answer: the statements and resons, from the given bench, that fill in the blank are shown in italic and bold in this table:
Statement Reason
1. K is the midpoint of segment JL Given
2. segment JK ≅ segment KL <em>Definition of midpoint</em>
3. <em>L is the midpoint of segment KM</em> Given
4. <em>segment KL ≅ segment LM</em> Definition of midpoint
5. segment JK ≅ segment LM Transitive Property of
Congruence
Explanation:
1. First blank: you must indicate the reason of the statement "segment JK ≅ segment KL". Since you it is given that K is the midpoint of segment JL, the statement follows from the very <em>Definition of midpoint</em>.
2. Second blank: you must add a given statement. The other given statement is <em>segment KL ≅ segment LM</em> .
3. Third blank: you must indicate the statement that corresponds to the definition of midpoint. That is <em>segment KL ≅ segment LM</em> .
4. Fourth and fith blanks: you must indicate the statement and reason necessary to conclude with the proof. Since, you have already proved that segment JK ≅ segment KL and segment KL ≅ segment LM it is by the transitive property of congruence that segment JK ≅ segment LM.
The square root of 225 is 15 :)
