SAT Math: Advanced Math

$x=49$

$y = \sqrt{x} + 9$

The graphs of the given equations intersect at the point $(x,y)$ in the $xy$-plane. What is the value of $y$?

One solution to the equation $x^2 - 2x - 9 = 0$ can be written as $1 + \sqrt{k}$, where $k$ is a constant. What is the value of $k$?

Which expression is equivalent to $(8yz)(y)(7z)$?

$f(x) = 4x^2 + 64x + 262$

The function $g$ is defined by $g(x) = f(x + 5)$. For what value of $x$ does $g(x)$ reach its minimum?

A scientist initially measures $12,000$ bacteria in a growth medium. $4$ hours later, the scientist measures $24,000$ bacteria. Assuming exponential growth, the formula $P = C(2)^{rt}$ gives the number of bacteria in the growth medium, where $r$ and $C$ are constants and $P$ is the number of bacteria $t$ hours after the initial measurement. What is the value of $r$?