Answer:
Step-by-step explanation:
They are closed under addition, subtraction and multiplication.
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>
Based on the data recorded by Isabella, it can be concluded the cube is rather fair.
<h3>How many times did Isabella get each number?</h3>
Based on the data, here are the results:
- Getting a 1: 6 times
- Getting a 2: 5 times
- Getting a 3: 7 times
- Getting a 4: 5 times
- Getting a 5: 6 times
- Getting a 6: 7 times
This implies, in total Isabella got the same number between five and seven times. For example, the number 2 was obtained 5 times, but the number 3 was obtained 7 times.
<h3>What can be concluded based on the results?</h3>
Even though Isabella did not get the same number of times each number, the dice is rather fair because by rolling the dice thirty six times you will obtain the same number at least five times.
Moreover, there is not a big difference in the number of times you obtain each number.
Learn more about dice in: brainly.com/question/23637540
#SPJ1
Answer:
29
Step-by-step explanation:
180-151=29
