To evaluate: The simplified form of the expression -\frac{2}{3}-\frac{1}{2}.

Find a formula for the quadratic function whose graph has its vertex at ${\displaystyle (3,2)}$ and its y-intercept at ${\displaystyle y=0}$. The equation should be in vertex form ${\displaystyle k=a{(x-h)}^2}$.
Please label how you get a, h, k, y, x

To find the equation: $(792)(5.19\times {10}^{-5})$

Solve the equation ${\displaystyle 3^{x+2}=27}$

If you have a system fo linear equations, the solution is where the equations intersect
Using row reduction you get a system of linear equations which still satisfies the intersection
Why are free variables used?
The values in which the free variable can be are limited in a range as for if the solution is a line and not a plane
So what is the point in writing the solutions as a set of vector additions using free variables?
If z in this case is a free variable, writing the solution in a vector equation
Where , denotes a new row
Solving for the pivot variables x and y and writing into decomposed vector form
[x,y] = [4,0] - [0,3] + z[1,2]
Z is said to be any real number zeR But looking at the graph, when z = 4, y=11/8 is not on the line of intersection So why do they say that z is a free variable when it isnt?

Calculate all the values of x such that $$9x^2+261x+1836=0$$.

Simplify the given expressions:
${\displaystyle 2x+2(5x-3[1-(4x-y)])+2y}$

Show that an irrational number $\xi =[a_0;a_1,\cdots ]$ has bounded partial quotients $a_k$ if and only if there exists $\delta >0$ such that
$|\xi -\frac{p}{q}|>\frac{\delta }{q^2}$
for all rational $\frac{p}{q}$.