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>
Answer:
Step-by-step explanation:
This question is asking you to insert two equations, f(x) and g(x), into the equation g(x) - f(x). This will lead to the equation below.
Now we can solve for the equation.
(-$11) x 12. That would be the equation because there are 12 months, so you would multiply -11 from 12 to get -132 every year for the tennis club membership.
<span>The proportion of clay uses is 3/8 (Three Eighths). That is 3 lbs. of clay to every 8 vases. This is determined by the first given proportion 3 lbs./8 vases and confirmed by the second. To prove that is the case you divide the second ration by the first numerator:
9 divided by 3 = 3 and 24 divided by 3 = 8. So the proportion for 9/24 is still 3/8. This can also be used to increase the number of vases made. For example if 40 vases need to be made:
we divide 40 by the numerator 8 = 5. So we need 5 portions of 3 to make 40 vases. 5 times 3 = 15. So the 15 lbs. of clay is needed for 40 vases.</span>
