a ≡ 17( mod 29) −14 ≤ a

discrete math 
functions pegeonhole principle
How many multiples of 6 are in the set $\{171,172,173,..,286\}$ ?

Assume that a procedure yields a binomial distribution with a trial repeated n=13${\displaystyle n=13}$ times. Use either the binomial probability formula (or technology) to find the probability of k=8${\displaystyle k=8}$ successes given the probability p=0.73${\displaystyle p=0.73}$ of success on a single trial.

(Report answer accurate to 4 decimal places.)

P(X=k)=

Evaluate the following limit ( IE do not use L'Hopital's rule).

lim𝑥→4 sin(𝑥2−4𝑥)  sin(𝑥2−10𝑥+24) .$$\underset{x\to 4}{lim}{\displaystyle \frac{\sin (x^2-4x)}{\sin (x^2-10x+24)}}.$$

Prove by induction that for all integers n >= 1 , 3 ^ (2n - 1) + 1 is divisible by 4.

Can anyone help with paramaterization of conics?
Im struggling to wrap my head around an example. It considers the conic ${\displaystyle x^2+y^2-z^2=0}$ then proceeds:
Take ${\displaystyle A=[1,0,1]}$ and the line P(U) defined by ${\displaystyle x=0}$. Note that this conic and the point and line are defined over any field since the coefficients are 0 or 1. A point ${\displaystyle X\in P\left(U\right)}$ is of the form ${\displaystyle X=[0,1,t]}$ or [0, 0, 1] and the map ${\displaystyle \alpha }$ is

How do I evaluate B(v,v) or B(v,v)(a,b,c) like they have to go from the first line to the second?

A quadratic function has its vertex at the point (−7,2)${\displaystyle (-7,2)}$. The function passes through the point (8,3)${\displaystyle (8,3)}$. When written in vertex form, the function is f(x)=a(x−h)2+k${\displaystyle f\left(x\right)=a{(x-h)}^2+k}$, where:

iL(6s-4)/((s-2)^(2) +16)