Main home here.

- The hypotenuse of a right triangle measures $(2x+1)$ units, while the legs are $2x$ and $(x-1)$ units. Find the value of $x$.

- Assuming $x> 0$, find the value of $x$ for which $(x,x+1,x+2)$ is a pythagorean triple.

- At any time $t$, the height $h$ of an object thrown up is given by $h=-4.9t^2+14.7t$. Find the initial height of the object.

- At any time $t$, the height $h$ of an object thrown up is given by $h=-5t^2+20t$. At what time does it attain its maximum height?

- At any time $t$ seconds, the height $h$ of an object thrown up is given by $h=-4.9t^2+19.6t+3$ (in meters). Which statement is wrong?

- The profit function for a certain item is given by $P(x)=-5x^2+300x$, where $x$ is the number of items. What is the
__break-even__point?

- The length and width of a rectangle are $(x+3)$ and $(x-2)$. Find $x$ if its area is $50$ sq. units.

- A square measures $(2x-1)\times(2x-1)$. Its area is $49$ sq. units. Find the admissible value of $x$.

- Find the distance between the points of intersection of the quadratics $y=x^2$ and $y=-x^2+6x+8$.

- Find two consecutive positive numbers numbers whose squares add up to $85$.