Maria had 13 points and jane had 8 points
We start with the expression at the left of the equation.
We can combine the terms as:
![\begin{gathered} \frac{2+\sqrt[]{3}}{\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}}}-\frac{2-\sqrt[]{3}}{\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}}} \\ \frac{2+\sqrt[]{3}}{\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}}}\cdot\frac{(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})}{(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})}-\frac{2-\sqrt[]{3}}{\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}}}\cdot\frac{(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})}{(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})} \\ \frac{(2+\sqrt[]{3})\cdot(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})-(2-\sqrt[]{3})\cdot(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})}{(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B2%2B%5Csqrt%5B%5D%7B3%7D%7D%7B%5Csqrt%5B%5D%7B2%7D%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%7D-%5Cfrac%7B2-%5Csqrt%5B%5D%7B3%7D%7D%7B%5Csqrt%5B%5D%7B2%7D-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%7D%20%5C%5C%20%5Cfrac%7B2%2B%5Csqrt%5B%5D%7B3%7D%7D%7B%5Csqrt%5B%5D%7B2%7D%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%7D%5Ccdot%5Cfrac%7B%28%5Csqrt%5B%5D%7B2%7D-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%7D%7B%28%5Csqrt%5B%5D%7B2%7D-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%7D-%5Cfrac%7B2-%5Csqrt%5B%5D%7B3%7D%7D%7B%5Csqrt%5B%5D%7B2%7D-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%7D%5Ccdot%5Cfrac%7B%28%5Csqrt%5B%5D%7B2%7D%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%7D%7B%28%5Csqrt%5B%5D%7B2%7D%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%7D%20%5C%5C%20%5Cfrac%7B%282%2B%5Csqrt%5B%5D%7B3%7D%29%5Ccdot%28%5Csqrt%5B%5D%7B2%7D-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29-%282-%5Csqrt%5B%5D%7B3%7D%29%5Ccdot%28%5Csqrt%5B%5D%7B2%7D%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%7D%7B%28%5Csqrt%5B%5D%7B2%7D%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%28%5Csqrt%5B%5D%7B2%7D-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%7D%20%5Cend%7Bgathered%7D)
We can now apply the distributive property for the both the numerator and denominator. We can see also that the denominator is the expansion of the difference of squares:
![\begin{gathered} \frac{(2+\sqrt[]{3})\cdot(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})-(2-\sqrt[]{3})\cdot(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})}{(\sqrt[]{2})^2-(\sqrt[]{2-\sqrt[]{3}}))^2} \\ \frac{(2+\sqrt[]{3})\cdot(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})+(\sqrt[]{3}-2)\cdot(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})}{2^{}-(2-\sqrt[]{3})^{}} \\ \frac{\sqrt[]{2}\cdot(2+\sqrt[]{3})-\sqrt[]{2-\sqrt[]{3}}\cdot(2+\sqrt[]{3})+\sqrt[]{2}\cdot(\sqrt[]{3}-2)+\sqrt[]{2-\sqrt[]{3}}\cdot(\sqrt[]{3}-2)}{2-2+\sqrt[]{3}} \\ \frac{\sqrt[]{2}(2+\sqrt[]{3}+\sqrt[]{3}-2)+\sqrt[]{2-\sqrt[]{3}}(-2-\sqrt[]{3}+\sqrt[]{3}-2)}{\sqrt[]{3}} \\ \frac{\sqrt[]{2}(2\sqrt[]{3})+\sqrt[]{2-\sqrt[]{3}}(-4)}{\sqrt[]{3}} \\ 2\sqrt[]{2}-4\frac{\sqrt[]{2-\sqrt[]{3}}}{\sqrt[]{3}} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B%282%2B%5Csqrt%5B%5D%7B3%7D%29%5Ccdot%28%5Csqrt%5B%5D%7B2%7D-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29-%282-%5Csqrt%5B%5D%7B3%7D%29%5Ccdot%28%5Csqrt%5B%5D%7B2%7D%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%7D%7B%28%5Csqrt%5B%5D%7B2%7D%29%5E2-%28%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%29%5E2%7D%20%5C%5C%20%5Cfrac%7B%282%2B%5Csqrt%5B%5D%7B3%7D%29%5Ccdot%28%5Csqrt%5B%5D%7B2%7D-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%2B%28%5Csqrt%5B%5D%7B3%7D-2%29%5Ccdot%28%5Csqrt%5B%5D%7B2%7D%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%7D%7B2%5E%7B%7D-%282-%5Csqrt%5B%5D%7B3%7D%29%5E%7B%7D%7D%20%5C%5C%20%5Cfrac%7B%5Csqrt%5B%5D%7B2%7D%5Ccdot%282%2B%5Csqrt%5B%5D%7B3%7D%29-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%5Ccdot%282%2B%5Csqrt%5B%5D%7B3%7D%29%2B%5Csqrt%5B%5D%7B2%7D%5Ccdot%28%5Csqrt%5B%5D%7B3%7D-2%29%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%5Ccdot%28%5Csqrt%5B%5D%7B3%7D-2%29%7D%7B2-2%2B%5Csqrt%5B%5D%7B3%7D%7D%20%5C%5C%20%5Cfrac%7B%5Csqrt%5B%5D%7B2%7D%282%2B%5Csqrt%5B%5D%7B3%7D%2B%5Csqrt%5B%5D%7B3%7D-2%29%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%28-2-%5Csqrt%5B%5D%7B3%7D%2B%5Csqrt%5B%5D%7B3%7D-2%29%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%20%5C%5C%20%5Cfrac%7B%5Csqrt%5B%5D%7B2%7D%282%5Csqrt%5B%5D%7B3%7D%29%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%28-4%29%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%20%5C%5C%202%5Csqrt%5B%5D%7B2%7D-4%5Cfrac%7B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%20%5Cend%7Bgathered%7D)
We then can continue rearranging this as:
Answer:
a) the possible values of y are all real numbers from 0 to 150.
b) y is a continous variable.
Step-by-step explanation:
If the maximum depth of the lake is 150 feet, in any point selected on the surface, the depth will be between 0 feet (takes this value of depth only at the shore) and 150 feet.
The depth is a physical measure that can be represented as a continous variable.
In that case, the possible values of y are all real numbers from 0 to 150.
Answer:
(x + 3)(x + 2)
Step-by-step explanation:
Given
x² + 5x + 6
Consider the factors of the constant term (+ 6) which sum to give the coefficient of the x- term (+ 5)
The factors are + 3 and + 2 , since
3 × 2 = + 6 and + 3 + 2 = + 5 , then
x² + 5x + 6 = (x + 3)(x + 2) ← in factored form
Answer:
<em>(A). y - 4 = 3 ( x - 1 )</em>
Step-by-step explanation:
Slope "m" and (
,
) ⇒
Slope-point form of linear equation is y -
= m( x -
)
~~~~~~~~~~~~~
m = 3 and point with coordinates ( 1 , 4 )
<em>y - 4 = 3 ( x - 1 )</em>