Algebra Word Problem Solutions

What is the inverse of the given relation? $y=3x+12$

Explain the difference between a stratified sample and a cluster sample. (Select all that apply.)
1) In a stratified sample, the clusters to be included are selected at random and then all members of each selected cluster are included.
2) In a cluster sample, the clusters to be included are selected at random and then all members of each selected cluster are included.
3) In a cluster sample, random samples from each strata are included.In a stratified sample, random samples from each strata are included.
4) In a cluster sample, the only samples possible are those including every kth item from the random starting position.In a stratified sample, the only samples possible are those including every kth item from the random starting position.
5) In a cluster sample, every sample of size n has an equal chance of being included.In a stratified sample, every sample of size n has an equal chance of being included.

What is the equation of the following graph in vertex form?
the graph shows a positive parabola with the vertex at, (-1,0) and passes through (0,1) and (-2,1)
$$\begin{gathered} y=(x-1{)}^2 \\ y=(x-1{)}^2+1 \\ y=(x+1{)}^2-1 \\ y=(x+1{)}^2 \end{gathered}$$

Name six different forms of energy?

Which product is equivalent to $25x^2-<!--\; -\; -->16$

Can you name the sets of numbers that $1.68$ belongs to.

Do free electrons travel to region of higher potential or lower potential?

What does $\frac{3}{4}$ of an hour mean?

Why does water expands on freezing?

Which is the largest $3$-digit number?

A stone is flung 20 meters per second in a vertical upward motion. How high will it climb before starting to descend? $(g=9.8m/s^2)$

What is the distance between Sun and earth?

What is electrostatic repulsion?

How much do you need to multiply by $4$ to get $36$

Solve the equation.
$5x+6=2(2x–3)$

Find out if the graph is symmetric about the $x$-axis, the $y$-axis, or the origin. $r=2cos5\mathrm{\theta <!--\; \theta \; -->}$

Why n and what does it mean?
Maybe a bit too early to ask, but I give it a shot. I'm trying to study mathematics again during my free time. Now I tried to figure out what exactly is meant with the multiple. Well this formula makes it quite easy to understand for me, but it's not totally clear yet:
$a=n\times <!--\; \times \; -->b$
So if I understand the formula correctly, for $15=3\cdot <!--\; \cdot \; -->5$ 15 is a multiple of 5, and for $15=3\cdot <!--\; \cdot \; -->5$ 15 is a multiple of 3, so 3 and 5 can both be a multiple of 15. But what I don't understand, why n? Why not just $a=b\times <!--\; \times \; -->c$? I cannot really find an answer for this either, in my study book they just start with formulas like:
$a^n\times <!--\; \times \; -->a^m=a^{n+m}$
without any further explanation why to use n or m. Hopefully somebody has an explanation for me

Find a simpler form of the expression of -3(-4y + 3) + 7y
A. 19y – 9
B. 10y
C. -19y + 3
D. -19y – 9

Convert $0.6$ into a fraction

Why this function is undefined at x=0 and x=5
According to my understanding, the domain of $\sqrt{x}$ is $x\ge <!--\; \ge \; -->0$. If this is correct, shouldn't the domain of the function
$\frac{1}{(x^2-<!--\; -\; -->5x{)}^{1/4}}$
be $x\le <!--\; \le \; -->0$or $x\ge <!--\; \ge \; -->5$instead of x<0 or x>5? What am I getting wrong? (the answer is x<0 or x>5).