Master Algebra 1 Word Problems with our Comprehensive Practice

Solve each of the quadratic equations $3x=0.5x^2$ and $0=5x^2-<!--\; -\; -->2x+6$
a. x = -6 or x = 0
b. x = -4 or x = 3
c. x = -2 or x = 1.5
d. x = 0 or x = 6

What is the difference between a formula and a function?

a)Apply the chain rule to u = xyz, where x, y, and z are functions of t, to get a rule for differentiating a product of three functions of one variable.
b)Derive the rule in (a) by using one-variable calculus.

Find the absolute minimum value of $f(x)=5+4x+\frac{16}{x}$ for x>0

Factor the polynomial completely.
$P(X)-<!--\; -\; -->=x^6+16x^3+64$
Find all its zeros. state the multiplicity of each zero. (order your answers from smallest to largest real, followed by complex answers ordered smallest to largest real part,then smallest to largest imaginary part.)
x =-2 with multiplicity 2
$x=1-<!--\; -\; -->i\sqrt{3}$ with multiplicity 2
$x=1+i\sqrt{3}$ with multiplicity 2

Divide $\frac{(x^3+x-<!--\; -\; -->30)}{x-<!--\; -\; -->3}$

which is the closest approximation to ​open paren the square root of 2 plus the square root of 5 close paren squared $(\sqrt{2}+\sqrt{5}{)}^2$

Find the sum of all natural numbers from$1$ to $100.$

What's the greatest common factor of twenty-eight and forty-two?

Which rational functions is graphed below

At 't' minutes past 2pm, the time needed per minute hand of a clock to show 3pm was found to be 3minutes less than $t^2/4$ find 't'.

Sum of a rational and an irrational number is a/an
A)rational number
B)irrational number
C)real number
D)We can't add a rational and an irrational number

Which of the following statements is true for the function
$f(x)=\frac{x^2+x}{2(x^2-<!--\; -\; -->1)}$
a) y=1^2 is a horizontal asymptote and x=2 is a vertical asymptote.
b) y=1^2 is a horizontal asymptote and x=1 is a vertical asymptote.
c) y=3 is a horizontal asymptote and x=-1 is a vertical asymptote.
d) y=3 is a horizontal asymptote and x=2 is a vertical asymptote

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.

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

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

Why does water expands on freezing?

What is the distance between Sun and earth?

What is electrostatic repulsion?

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