y=x+1 y=3x−7

Suppose that $x$, $y$ and $z$ are three integers (positive,negative or zero) such that we get the following relationships simultaneously
1. $x+y=1-z$
and
2. $x^3+y^3=1-z^2$
Find all such $x$, $y$ and $z$.

Factor ${\displaystyle 2x^2-8x-10}$ completely.

Prove:
${\displaystyle \underset{n\Rightarrow \mathrm{\infty }}{lim}\ln \left(\frac{n+1}{n}\right)=0}$

Determine the set of points at which the function is continuous. ${\displaystyle f(x,y)=\left(\frac{x^2{y}^3}{2x^2+y^2}\right)}$ if (x,y) not equal to (0,0) and 1 if (x,y)=(0,0)

Find the coordinates of the x-intercepts of the graph of the equation. (If an answer does not exist, enter DNE.)
${\displaystyle y=-x^2-4x-11}$
${\displaystyle (x,y)=}$
Find the minimum or maximum value of the quadratic function.
${\displaystyle f\left(x\right)=-4x^2+8x-6}$ --Select— minimum value maximum value
${\displaystyle f\left(x\right)=}$

Using the concept of exponential growth and exponential decay, solve the given problem. Show complete and systematic solutions.
1. An unknown radioactive element decreases 12% of its amount every 5 days. What is exponential function? that describes the amount left after t days? If there are 300g of the substance at present, how much is left after 30 days? (round off the value up to two decimal places)

The folowing table gives the frequency distribution of the sales athletic shoes at a store in an outlet mall cach day during the past 30 days. Calculate the mode a algebraically.
$\begin{array}{cc}Namberofsales& Namberofdays\\ 14-18& 5\\ 19-23& 9\\ 24-28& 6\\ 29-22& 10\end{array}$